Microstructural and Rheological Properties of
Concentrated Tomato Suspensions during Processing
Elena Bayod
Division of Food Engineering
Department of Food Technology, Engineering and Nutrition
Lund University
Sweden
Doctoral thesis
2008
Microstructural and Rheological Properties of
Concentrated Tomato Suspensions during Processing
Elena Bayod
2008
Doctoral thesis
Division of Food Engineering
Department of Food Technology, Engineering and Nutrition
Lund University
Akademisk avhandling för avläggande av teknologie doktorsexamen vid tekniska fakulteten,
Lunds universitet. Försvaras på engelska fredagen den 7 mars 2008, kl. 09:15 i hörsal B,
Kemicentrum, Getingevägen, 60, Lund. Fakultetsopponent: Dr. Peter Fischer, Institute of Food
Science and Nutrition, ETH, Zürich, Switzerland.
Academic thesis which, by due permission of the Faculty of Engineering at Lund University, will
be publicly defended on Friday, 7th March 2008, at 09:15 in lecture hall B, Centre for Chemistry
and Chemical Engineering, Getingevägen, 60, Lund, for the degree of Doctor of Philosophy in
Engineering. Faculty opponent: Dr. Peter Fischer, Institute of Food Science and Nutrition, ETH,
Zurich, Switzerland.
Microstructural and Rheological Properties of Concentrated Tomato Suspensions during Processing
A doctoral thesis at a university in Sweden is produced either as a monograph or as a collection
of papers. In the latter case, the introductory part constitutes the formal thesis, which
summarizes the accompanying papers. These have either already been published or are
manuscripts at various stages (in press, submitted or in ms).
© 2008, Elena Bayod
Doctoral thesis
Division of Food Engineering
Department of Food Technology, Engineering and Nutrition
Lund University
P.O. Box 124
SE-221 00 Lund
Sweden
Cover: micrographs of tomato suspensions at different stages of processing
ISBN 978-91-976695-4-2
Printed in Sweden by Media-Tryck, Lund University
Lund, 2008
ii
Microstructural and Rheological Properties of Concentrated Tomato Suspensions during Processing
Abstract
Food processing comprises operations such as dilution (changing the concentration),
homogenisation (changing the particle size), and subsequent pumping (shearing), among
others. It is thus of great interest to gain a better understanding of the mechanisms
governing the creation and disruption of structures during these engineering operations,
and the way in which they are related to the textural and rheological properties of the
material.
The influence of processing on the microstructure and the rheological properties of
tomato paste suspensions has been studied. The microstructure was characterised using
light microscopy and particle size distribution analysis. The way in which particles of
varying size are packed in a specified volume at different concentrations was estimated in
terms of the compressive volume fraction. The rheological properties were studied using
small-amplitude oscillatory tests, giving the elastic (G′) and viscous (G′′) moduli, as well
as steady shear measurements, giving the viscosity (η). In the latter case both a rotational
and a tube viscometer were used.
The results indicate that tomato suspensions consist of a collection of whole cells and
cell wall material forming a network (G′>G′′). During the process of homogenisation,
the particles are broken down, resulting in a smoother and more evenly distributed
network of finer particles. The effectiveness of homogenisation in decreasing particle size
seemed to be governed by the inherent susceptibility of the particles to breakage (i.e. the
type of paste), the viscosity of the suspending medium, and the concentration of
particles. Higher viscosities and concentrations were found to prevent breakage to some
extent.
The presence of larger amounts of fine particles in the homogenised suspensions had a
considerable effect on the rheological properties. The yield stress was found to increase,
and time-dependent effects became more apparent. At low deformations (γ ≤ 20), the
system consisting of finer particles exhibited rheopectic behaviour (increasing viscosity
with time), which was suggested to be caused partly by the rotation of the particles
iii
induced by the flow, and partly by the remaining elastic behaviour at stresses close to the
yield stress. At larger deformations (γ ≤ 1000), the non-homogenised system exhibited
steady-state viscosity, while in the homogenised system it continued to decrease. The
unstable behaviour observed in homogenised systems at large deformations gave an
indication of particle rearrangement under flow conditions. Micrographs of homogenised
suspensions subjected to shearing showed the formation of flocs consisting of densely
packed particles that could easily orient in the shearing direction. At high concentrations,
the changes in the microstructure caused by homogenisation and shearing were better
reflected by the compressive volume fraction than by the elastic modulus.
Tube viscometer measurements showed the presence of wall slip in highly concentrated
tomato suspensions, which tended to disappear at lower concentrations. The wall slip,
which could be as high as 70% of the flow rate, was estimated using both the classical
Mooney approach and an inverse numerical method, and the performance of these two
methods was compared. The performance of the methods was complicated by the
relatively poor reproducibility of the data. Steady shear rheological measurements
obtained using a rotational rheometer with different geometries (concentric cylinders,
vane, vane-vane) and tube viscometer measurements agreed when no slip was present,
and the vane and vane-vane geometries were found to be free of wall slip effects.
Finally, the applicability of the Cox-Merz rule (superposition of oscillatory and steady
shear data) seemed to be limited to systems that do not form a network (G′<G′′), and
did not apply to structured systems having a yield value and G′>G′′. However, the
dynamic and steady shear data obtained for tomato suspensions coincided when using a
shifting factor of about 0.1 on the frequency , which was fairly constant for a large range
of tomato paste concentrations (from 100 to 30%, all with G′>G′′).
iv
Microstructural and Rheological Properties of Concentrated Tomato Suspensions during Processing
Populärvetenskaplig sammanfattning
Världens produktion av tomat har ökat kraftigt under de senaste årtiondena och 2004
översteg den 100 miljoner ton. Tomat brukar konsumeras huvudsakligen som färsk
grönsak och/eller som processad tomatprodukt. Tomatpasta är den huvudprodukt, som
används
vid
tillverkning
av
tomatketchup
och
tomatsås.
I
Sverige,
är
ketchupkonsumtionen omkring 2 kg per person och år, och försäljningen uppgår till mer
än 330 MSEK. Tomatketchup består av tomatpasta, vatten, socker, vinäger, salt, kryddor,
och ibland också lök och vitlök som smaktillsats. Även andra tillsatser, såsom
förtjocknings- och stabiliseringsmedel, kan användas för att påverka konsistensen. Smak
och textur/konsistens är för konsumenter de viktigaste parametrarna för att bedöma
kvaliteten hos ketchup. Man vill ha en produkt som smakar gott, men konsistensen måste
vara sådan så att man får rätt munkänsla. Det är också viktigt att undvika
ketchupeffekten, dvs. först kommer inget och sen kommer allt på en gång. Andra
kvalitetsaspekter avseende konsistensen är att tomatketchupen skall ligga kvar på korven
när man äter den. En kvalitetsdefekt hos ketchup, som kan uppfattas negativt av
konsumenten, är serumseparation, som uppkommer som ett tunt vätskeskikt ovanför
ketchupen vid flaskhalsen. Det är därför viktigt att förstå hur tillverkningsprocessen
påverkar konsistensen hos ketchup för att förbättra kvaliteten och minska olika
kvalitetsdefekter. Syftet med denna studie var att lära sig mer om hur tomatfibrerna
uppträder under olika processer, som används för att tillverka såser eller ketchup, och att
studera de mikrostrukturer som kan uppkomma under denna processning. Exempel på
sådana processer är homogenisering och pumpning.
Tomatprodukter kan beskrivas som ett disperst system, där den fasta fasen utgöres av
tomatceller och delar av tomatcellen i form av fibrer och dessa är uppslammade i vatten
med socker och andra lösliga ämnen. Vid processning av detta system förändras
produktens struktur och mekaniska egenskaper, vilket ger upphov till olika textur och
konsistens. Ett sätt att förutsäga dessa olika konsistenser är att mäta produkternas
mikrostruktur och reologiska egenskaper. Reologin är den vetenskap som behandlar flytoch deformationsegenskaper. I föreliggande arbete har effekten av processning
v
(homogenisering och pumpning) undersökts med avseende på olika utspädda
tomatpastors mikrostruktur och reologi. Homogenisering ger mindre partikelstorlek och
förbättrar viskositeten (konsistensen), medan produkterna är efter denna behandling mer
känsliga för fiberaggregering vid efterföljande pumpning. Denna mikrostrukturella
förändring kan ge oönskad lägre viskositet och serumseparation.
Pumpning är en viktig och oundviklig del vid tillverkning av exempelvis tomatketchup,
och för att beräkna pumpens prestationsförmåga krävs bland annat att man känner till
tomatketchupens viskositet. Att överdimensionera pumpen i processen är både
ekonomiskt och energetiskt dyrt, men att underdimensionera pumpen kan orsaka
allvarliga problem för livsmedelsindustrin om livsmedlet ifråga inte kan pumpas vidare.
Därför är det intressant att mäta viskositeten noggrant. Olika problem kan förekomma
vid mätning av viskositet hos produkter med högt fiberinnehåll, som tomatpasta.
Exempelvis, uppträder vid väggen av mätinstrumentet ett väldigt tunt skikt av vätska på
grund av partikelrörelse bort från väggen. Detta fenomen kallas slip. Det gör att man
mäter en lägre viskositet än det i verkligheten är och dimensionerar därför pumpen fel
utifrån den för låga viskositeten. Att kontrollera och korrigera för denna slip så att
viskositetsmätningarna blir korrekta har också varit en del av detta arbete.
Denna studie är ett samarbete med Orkla Foods AS, Tetra Pak AB, Lyckeby-Culinar AB,
Reologica AB, Salico, AB, Mariannes Farm AB, Kiviks Musteri AB.
vi
List of Papers
This thesis is based on the following papers, which will be referred to in the text by their Roman
numerals. The papers are appended at the end of the thesis.
Paper I.
Bayod E., Willers, E. P., Tornberg E. (2007)
Rheological and structural characterization of tomato paste and its influence on
the quality of ketchup
LWT - Food Science and Technology, In Press, DOI: 10.1016/j.lwt.2007.08.011
Paper II.
Bayod E., Månsson P., Innings F., Bergenståhl B., Tornberg E. (2007)
Low shear rheology of tomato products. Effect of particle size and time
Food Biophysics, 2 (4), 146-157
Paper III.
Bayod E., Tornberg E. (2008)
Microstructure of highly concentrated tomato suspensions during
homogenisation and after subsequent shearing
Submitted for publication, 2007
Paper IV.
Bayod E., Jansson P., Innings F., Dejmek P., Bolmstedt U., Tornberg E. (2008)
Rheological behaviour of concentrated fibre suspensions in tube and rotational
viscometers, in the presence of wall slip.
Manuscript
vii
Author’s contribution to the papers
Papers I and III. The author designed the experiment based on discussions with the co-authors.
The author performed all the experimental work, evaluated the results and wrote the papers.
Paper II. The author designed the experiment based on discussions with the co-authors (FI, BB,
ET) and performed part of the experimental work together with PM. The author evaluated the
results and wrote the paper.
Paper IV. The author designed the experiment based on discussions with the co-authors (PJ, FI,
UB, ET) and performed part of the experimental work together with PJ. The author wrote the
Matlab code together with PD. The author evaluated the results and wrote the paper.
Related publications
Bayod E., Bergenstahl B., Innings F., Tornberg E. (2008). The susceptibility to create shear
induced flocs in tomato fiber suspensions on homogenisation and shearing. Accepted for presentation
at the 10th International Congress of Engineering and Food, Viña del Mar, Chile, April 20-24, 2008.
Bayod E., Tornberg E. (2008). Insights into the microstructural properties of tomato products.
Accepted for presentation at Food Colloids, Le Mans, France, April 6-9, 2008
Bayod E., Månsson P., Innings F., Bergenståhl B., Tornberg E. (2006). Combined effect of both
stress and time on the viscosity of high concentrate fibre suspensions. Proceedings of the 4th
International Symposium on Food Rheology and Structure, pp. 523-527, Zurich, Switzerland
Bayod, E., Bolmstedt, U., Innings, F., Tornberg, E. (2005). Rheological characterization of fiber
suspensions prepared from vegetable pulps and dried fibers. A comparative study. Proceedings of the
Nordic Rheology Conference, pp. 249-253, Tampere, Finland
viii
Abbreviations and Symbols
Symbols
Greek letters
ap
-
Aspect ratio
α
-
Slip behaviour index
d32
µm
Area-based diameter
β
m/Paα s
Slip coefficient
d43
µm
Volume-based diameter
γ
-
Strain/deformation
Df
-
Fractal number
γ&
1/s
Shear rate
d
-
Euclidian space dimension
η
Pa s
Apparent viscosity
di
m
Inner tube diameter
η*
Pa s
Complex viscosity
do
m
Outer tube diameter
η0
Pa s
Zero-shear viscosity
dP
Pa
Pressure drop
ηs
Pa s
Viscosity of the supernatant
E
J
Energy
θ
º
Angle of rotation
f/c
-
Fine-to-coarse particle ratio
λ
s
Time constant, Carreau
G*
Pa
Complex modulus
µ
Pa s
Newtonian viscosity
G'
Pa
Elastic/storage modulus
N
-
Exponent, Carreau
G''
Pa
Viscous/loss modulus
σ
Pa
Shear stress
h
m
Vane height
σw
Pa
Wall shear stress
k
J/K
Boltzman constant
σy
Pa
Yield stress
K
Pa sn
Consistency coefficient
φ
-
Volume fraction
L
m
Length
φm
-
Maximum packing fraction
M
Nm
Torque
φc
-
Critical concentration fraction
n
-
Flow behaviour index
Ω
rad/s
Angular velocity
Nj, Nk
-
Number of points j, k
ω
Hz
Frequency
Q
m3/s
Flow rate
Qm
m3/s
Measured flow rate
Qs
m3/s
Flow rate due to slip
Qws
m3/s
Flow rate without slip
R
m
Inner tube radius
Re
-
Reynolds number
Ri
m
Bob radius
Ro
m
Cup radius
S1
-
Tikhonov error
S2
-
Tikhonov smoothness
t
s
Time
vs
m/s
Slip velocity
vx
m/s
Velocity along x-axis
vθ
m/s
Velocity in θ
ix
Abbreviations
ah
After homogenisation
bh
Before homogenisation
CB
Cold break
CC
Concentric cylinder
EDM
Euclidean distance map
H
Homogenisation
HB
Hot break
LVE
Linear viscoelastic region
PSD
Particle size distribution
SH
Shearing
TS
%
Total solids
V
Vane geometry
VV
Vane geometry in vane cup
WIS
%
Water-insoluble solids
x
Contents
1.
INTRODUCTION......................................................................................................................... 1
2.
SCOPE ........................................................................................................................................... 3
3.
THE MICROSTRUCTURE OF FOOD SUSPENSIONS ......................................................... 5
3.1
3.1.1
3.2
Quantifying the microstructure......................................................................................... 8
Image analysis of light micrographs........................................................................................... 9
3.2.2
Particle size distribution ........................................................................................................... 10
3.2.3
Concentration and volume fraction determination ................................................................... 14
Effect of concentration, particle size and shearing......................................................... 16
MECHANICAL SPECTRA OF CONCENTRATED SUSPENSIONS ................................. 23
4.1
Dynamic oscillatory rheology......................................................................................... 23
4.1.1
Strain/stress sweep tests ........................................................................................................... 24
4.1.2
Mechanical spectra in the linear viscoelastic region................................................................. 25
4.2
5.
Morphology and shape of particles ............................................................................................ 7
3.2.1
3.3
4.
Observation of the microstructure.................................................................................... 6
Effect of concentration, particle size and shearing......................................................... 27
FLOW BEHAVIOUR OF CONCENTRATED SUSPENSIONS ........................................... 33
5.1
Suspension rheology ....................................................................................................... 33
5.1.1
Rheological behaviour of tomato products............................................................................... 35
5.1.2
Yield stress ............................................................................................................................... 37
5.1.3
Time dependency ..................................................................................................................... 40
5.2
Measurement systems ..................................................................................................... 45
5.2.1
Rotational rheometers............................................................................................................... 45
5.2.2
Tube viscometers...................................................................................................................... 48
5.3
Quantification of apparent wall slip and determination of flow behaviour in the tube
viscometer ..................................................................................................................................... 51
5.3.1
The classical Mooney method .................................................................................................. 52
5.3.2
A numerical method of quantifying slip and flow behaviour ................................................... 54
5.4
Comparison of dynamic rheology and flow behaviour –The Cox-Merz rule................. 59
6.
CONCLUSIONS ......................................................................................................................... 65
7.
FUTURE OUTLOOK................................................................................................................. 67
ACKNOWLEDGEMENTS ................................................................................................................. 69
REFERENCES ..................................................................................................................................... 71
PAPERS I-IV ........................................................................................................................................ 77
xi
1. Introduction
Tomatoes are an important commercial product, with a total world production in 2004
exceeding 100 million tones (UN Food and Agricultural Organization). Tomatoes can be
consumed fresh, although most of the global production is processed to form tomato
paste. This tomato paste is then used as a main ingredient in other products such as
ketchup, sauces, and juices. The principal quality parameters for consumer acceptance of
tomato products are the appearance, colour and flavour, as well as the consistency and
texture, which in turn depend on the agronomical conditions during the growth of the
tomatoes and the processing conditions during the production of different tomato
products.
Processing fresh tomatoes to provide tomato paste involves a number of stages. First,
the fresh tomatoes are washed, sorted and crushed, usually accompanied by thermal
treatment (called break treatment), followed by peeling, screening and refining. The fluid
is
then
concentrated
by
evaporation,
finally
undergoes
thermal
treatment
(pasteurisation/sterilization) and packaging, often aseptic vacuum-packing. The viscosity
increases throughout the concentration processes, from about 10 mPa s in the initial
tomato juice up to viscosities several orders of magnitude higher in the final tomato
paste. The final product should be as concentrated as possible (usually between 24 and
38% soluble solids), but it should still be pumpable to allow processing. This means that
the accurate determination of the pumping requirements is of great interest. Predictions
of the pressure drop in tomato paste in tube flow based on viscosity values obtained
from rotational rheometers, are frequently found to be incorrect, according to
manufacturers’ experience, but no investigation has so far addressed this problem. It has
been observed in concentrated tomato products that substantial wall slip occurs on tube
flow (Lee et al., 2002) and this may be a reason for the disagreement between tube and
rheometer viscosity data.
The method of producing tomato paste influences the quality of the products to which it
is added as an ingredient, for example, ketchup. The process parameters believed to have
the greatest effects on the rheology of tomato derivatives are the break temperature, and
the screen size (Valencia et al., 2004). Break treatment can be carried out at high
temperatures (> 85°C), i.e. hot break (HB), or at low temperatures (< 70°C), i.e. cold
break (CB). The latter process allows a certain degree of pectin degradation because of
the slow and incomplete inactivation of the enzymes involved, i.e. pectin methyl esterase
and polygalacturonase. This results in products with a lower viscosity, but better
preserves the tomato flavour and colour. The influence of the break temperature on the
rheological properties of tomato products has been studied previously (Fito et al., 1983;
Xu et al., 1986). Moreover, changes in the pectin content and composition during the
processing of HB tomato paste have been described (Hurtado et al, 2002). The difference
in the physical properties of soluble pectin in HB and CB tomato paste has been
attributed to lower average molecular mass and a different chemical structure in the latter
case (Lin et al., 2005). It is believed that a higher pectin content gives rise to higher
viscosity and better textural properties, but Den Ouden (1995) showed that the
contribution of the pectins to the total viscosity was very small, compared with the
contribution of the fibre matrix. The effect of the particle size has also been studied to
some extent (Valencia et al. 2004, Den Ouden, 1995), but the published data are
ambiguous.
Tomato products can be manufactured by diluting tomato paste to the desired content,
mixing with other ingredients (i.e. spices, salt, sugar, vinegar, hydrocolloids), in some
cases homogenisation, and then pasteurization, aseptic cooling and packing.
Homogenisation is performed to obtain a smoother texture, enhance the structure of the
product, to increase its viscosity and to lower the degree of syneresis (Thakur et al., 1995;
Den Ouden, 1995). Generally, tomato products are non-Newtonian, shear thinning fluids
that exhibit yield stress and are strongly dependent on the shear history of the fluid. For
example, tomato juice has been shown to exhibit rheopectic behaviour at low
deformations (De Kee, 1983), i.e. the viscosity increases as a function of time, and
thixotropic behaviour at large deformations, i.e. the viscosity decreases as a function of
time (Tiziani & Vodovotz, 2005). The latter has been suggested to be caused by
structural breakdown of the suspension. This behaviour reflects the complex rheological
nature of tomato products. Tomato products are considered to be concentrated food
suspensions, consisting of whole cells or cell wall material suspended in an aqueous
solution containing sugars, soluble pectins and proteins.
2
2. Scope
Tomato processing constitutes an important industry as large volumes of fresh tomatoes
are processed into tomato ketchup and other products all over the world. As tomato
products are consumed worldwide, understanding the influence of processing on their
quality is of great interest, for both industry and consumers. Because of their economic
impact, tomato products have been subjected to numerous investigations, usually
involving their rheological characterisation. The complex nature of tomato suspensions
can complicate rheological measurements in several ways and thus, the results obtained
depend on the experimental conditions. A better understanding of the difficulties
encountered in rheological measurements might allow us to correct for them and/or to
prevent them, as well as providing more knowledge on tomato suspensions. Moreover,
the influence of the tomato fibres and the microstructure of the suspensions on their
textural and rheological attributes have been little explored so far.
The objectives of this investigation were therefore:
•
To study the different problems encountered in the determination of the
rheological properties of highly concentrated suspensions, such as tomato
products. The determination of the yield stress, and the effect of time
dependency and shear history are reported in Paper II, and the determination of
the wall slip in both tube viscometers and rotational rheometers is described in
Paper IV.
•
To study the effect of processing on the properties of tomato products. The
influence of homogenisation on the particle size distribution (PSD) and particle
shape, and the effect of the PSD on the rheological properties of the
suspensions, regarding the flow behaviour (Paper I), and the time dependency
and yield stress (Paper II) have been investigated. Changes in the microstructure
of the suspensions resulting from processing, i.e. homogenisation and shearing,
have also been investigated (Paper III).
3
3. The Microstructure of Food Suspensions
The processing of foods brings about several changes in their microstructure. The
macroscopic properties of foods, such as rheology and mechanical strength, sensory
attributes, as well as engineering properties, are strongly determined by the
microstructure of the food material (Fig. 1). During the early development of the food
industry, food engineers were mainly concerned with the macroscopic scale, which meant
designing equipment and improving unit operations. Food manufactures were essentially
concerned with producing large quantities of food of more or less acceptable quality.
Nowadays, higher food quality is an increasing consumer demand, together with the
development of new products. Because several sensory attributes, e.g. mouth feel, texture
and even flavour release, are directly related to the microstructure and mechanics of food
materials, understanding the effect of microstructure on the macroscopic properties of
foods is a new challenge facing food researchers.
Transport properties
Rheology
Mechanical strength
Sensory attributes
Macroscopic
structure
Nanostructure
Microstructure
Figure 1. Schematic showing the hierarchy of food structure.
In 1980, Raeuber and Nikolaus noted the importance of food structure and its relation to
textural and rheological properties. They recognised food materials consisting of
elements at different structural levels, from the nanostructure (molecular level), to the
macroscopic level (animal or vegetable tissues). They pointed out the importance of both
the shape and arrangement of the primary elements on the mechanical properties of the
material and, hence only by combining the microstructure with the mechanical behaviour
5
is it possible to obtain a complete picture of a material’s properties. However, the
research in this area has been relatively scarce and, as late as 2005, Aguilera (2005) wrote
a paper entitled “Why Food Microstructure?” in which he highlights the importance of
understanding food microstructure in both food process engineering and food design.
3.1 Observation of the microstructure
Processing can drastically change the mechanical properties, as well as the
microstructure, of food products. An important example is that of whole fruits that are
crushed to produce purees or juices; where both the whole fruit and the juice have
approximately the same chemical composition, but their textural attributes are completely
different. The process of high pressure homogenisation is another example of a process
causing drastic changes in the microstructure, but on the microscopic scale (Fig. 2).
Understanding the macroscopic properties governing food systems with similar
composition, such as tomato suspensions before and after homogenisation, as shown in
Figure 2, thus involves the characterisation and quantification of their microstructure.
A
B
Figure 2. Typical micrograph of A) tomato cells and B) tomato cell fragments after homogenisation. The
scale bar is 150 µm. (Adapted from Paper I.)
Microscopy is the most direct way of examining the microstructure of food materials,
and provides valuable information on the shape and arrangement of the particles in
diluted and semi-diluted systems. However, this type of observation can only be made on
diluted systems, and it is often not suitable for highly concentrated food suspensions,
which are dense, frequently opaque, and contain large particles (10-1000 µm). Diluting
6
highly concentrated suspensions to a concentration suitable for observation in a light
microscope will, however, have a considerable effect on the structure of the suspension
and the arrangement of the particles, so the structure observed will not resemble the
original microstructure. Static light scattering is another technique that fails in systems
subject to strong multiple scattering, such as concentrated food suspensions. Confocal
microscopy is the preferred technique in such cases, but it requires some kind of
fluorescent labelling of the structure under study and, in vegetable material, problems
such as auto-fluorescence are likely to occur. Other techniques used in characterising
food microstructure are summarised and their applicability and limitations discussed
elsewhere (Wyss et al., 2005).
3.1.1
Morphology and shape of particles
The morphology of vegetable cells differs depending on the kind of tissue and its
function in the living vegetable. Different types of cells also show different mechanical
and textural properties. The different types of cells encountered in processed fruit
products, such as tomato paste, are (Fig. 3): parenchyma cells, lignified skin cells, vascular
tissue (e.g. xylem cells) and parts of the seeds. Parenchyma cells constitute the major
fraction of the cells present in tomato paste, and they are characterised by their high
deformability, low mass density and large volume fraction (Table 1). The aggregates of
skin cells, vascular bundles and xylem are harder, high-density materials, and less
deformable (Ilker & Szczesniak, 1990). Products enriched with the latter type of cells
have lower viscosities and lower yield stresses (Den Ouden & Van Vliet, 1997).
Figure 3. Examples of different kinds of cells and cellular structures present in the tomato pastes studied in
this work. From left to right: parenchyma cells, skin cells, vascular tissue and xylem cell. The scale bar is
150 µm .
Parenchyma cells are almost spherical and can be assumed to behave as spherical
particles at rest, although they are highly deformable. Den Ouden and Van Vliet (1997)
7
found that tomato cells can pass through the pores of a sieve significantly smaller than
the size of the cell itself. The aspect ratio, ap, of the parenchyma cells, i.e. the relation
between the length and width of the particles, is normally close to 1. The other types of
cells are found in very small proportions in tomato paste, and have irregular shapes and
variable aspect ratios (Fig. 3).
Table 1. Types of cells present in tomato paste, and the typical mechanical properties. Adapted from Den
Ouden and Van Vliet (1997).
Cell type
Size
Deformability
Density
Properties
Parenchyma cells
<250 µm
Highly
Low mass density
High
deformable
Large volume fraction
viscosity and
yield stress
Aggregates of cells from skin,
seeds and vascular bundles
> 250 µm
Less
High mass density
Low viscosity
deformable
Low volume fraction
and yield
stress
The shape and morphology of the particles in tomato products are drastically changed
after homogenisation (Fig. 2B). The majority of the cells are broken down into smaller
particles, resulting in a system containing large numbers of small particles such as fibre
particles, cell and cell wall fragments, pectins and other polymers. The new arrangement
of the particles in the suspension creates a more continuous and homogeneous system,
giving rise to a different type of network structure.
3.2 Quantifying the microstructure
One of the reasons for the delay in incorporating microstructure into mechanical models
in materials science is the difficulty in quantifying it. The human capacity to quantify
visual features is limited by our own vision, and it is difficult to make objective
assessments. The development of computers and new image analysis techniques has
provided new means of quantifying images. A good description of the available image
processing techniques can be found in the handbook by Russ (2007).
Other ways of “measuring” microstructure by more indirect techniques may be useful in
concentrated suspensions where direct observation is difficult, since the mechanical
8
behaviour of a suspension or gel depends to a great extent on the volume fraction, the
size and shape of the particles, the interparticle forces and the spatial arrangement
between particles (Wyss et al., 2005), all contributing to what is termed the
microstructure.
3.2.1
Image analysis of light micrographs
In the light micrograph images described in Paper III, image processing was necessary
to correct for uneven illumination. This is a common problem in microscopic images,
and can be seen, for example, in Figure 4A, where the right side of the image is much
darker than the left side The differences in illumination were corrected using the rolling
ball technique (radius=40 pixels). Image analysis is commonly performed on binary
images, obtained by thresholding. In order to reduce the noise in the image a mean filter
(radius=1.5 pixels) was first applied, and thresholding was automatically performed at a
fixed grey intensity value of T=137, providing the binary images (Fig. 4B, 5B). Some
simple analysis can be performed on binary images, for example, measurements of the
area occupied by particles (i.e. the sum of the black pixels) and calculation of the fractal
number associated with the image, using a box counting procedure.
A
B
Figure 4. Micrograph showing uneven illumination (A) and binary image after correction (B).
It is also of interest to measure the distance between the particles and/or the size of the
pores in the images. For this purpose, the binary image shown in Figure 5B was
subjected to a series of closing, opening, dilate and erode operations to identify the
particles and separate them from the background (Paper III) (Fig. 5C). Since we are
interested in the voids in this image, it is necessary to invert the processed image (Fig.
9
5D). Combining a so-called Euclidean distance map (EDM, Fig. 5E), in which the
distance between black points is expressed as grey values, and the skeleton of the voids,
which represents the maximum distance between two points, allows us to gain
information about the distance between two particles at several points. The reference
points for the distance measurements correspond to the branching in the skeleton. These
points are obtained by eroding points of the skeleton that have 6 or more background
neighbours. In Figure 5F, the original picture, the skeleton of the voids and the reference
points are combined.
A
B
C
D
E
F
Figure 5. Examples of the results of image processing of the micrographs presented in Paper III. Image
after defect correction (A), threshold image (B), image after binary operations (C), inverse binary image
(D), distance map (E), and combined images original + skeleton (white line) + “reference” points (white
line intersections) (F).
3.2.2
Particle size distribution
The particle size distribution (PSD) of food suspensions has a considerable influence on
the rheological properties. The size distribution of particles can be determined using
different techniques, for example, wet sieving, light microscopy and laser light
diffraction. The last technique has been widely used throughout these studies, and the
10
diffraction data were analysed using the Fraunhofer diffraction method. The Fraunhofer
method can be applied to particle sizes between 1 and 200 µm (Annapragada & Adjei,
1996), and can handle polydisperse systems. It assumes that the particles are spherical,
but it adequately describes the particle size of fibres (i.e. cylinders) with diameters larger
than 8 µm (Powers & Somerford, 1978). The use of the Fraunhofer theory in
determining the PSD of tomato products is rather common (Den Ouden & Van Vliet,
1997; Getchell & Schlimme, 1985).
The size of the particles is usually expressed as the equivalent spherical diameter, and can
be calculated based on the volume or the area occupied by the particles, d43 and d32,
respectively,
d 43 = ∑ ni d i4
∑n d
3
i
(1)
d 32 = ∑ ni d i3
∑n d
2
i
(2)
i
i
i
i
i
i
where ni is the percentage of particles with diameter di. The volume-based diameter is
mainly determined by the large particles present in the suspension. The area-based
diameter also takes smaller particles into account. Small particles are important in
determining the textural properties of the material, because they occupy the space
between the larger particles and contribute to the network structure of the suspension.
Moreover, a qualitative comparison between d32 and microscope images of tomato
suspensions gives considerably better agreement than that using d43 (ocular observations
from results presented in Paper II).
4
2.5
A
B
3.5
2
diff. surf. area (%)
diff. surf. area (%)
3
2.5
2
1.5
1.5
1
1
0.5
0.5
0 −1
10
0
10
1
2
10
10
particle diameter (µm)
10
0 −1
10
3
10
0
1
10
10
particle diameter (µm)
2
Figure 6. Particle size distribution of three tomato pastes (A) and the corresponding processed ketchups
(B), expressed as the percentage surface area (%) as a function of the particle diameter (µm) (Paper I).
11
3
10
Particle size distributions are often expressed as the percentage of particles found in each
size class (as in Figure 6). Foodstuffs often consist of polydispersed particles, with
continuous particle size distributions containing several peaks, i.e. particles of all sizes are
present, but most of them are of one or two specific. In tomato products, the PSD
expressed in terms of the area-based diameter is usually considered to be bi-modal, i.e.
consisting essentially of particles with two sizes (Fig. 6), and better describes the changes
in the suspensions during processing than the volume-based diameter (d43). Papers I, II
and III describe the changes in the size of the particles due to homogenisation. The
percentage of coarse particles (>10 µm) and fine particles (<10 µm), and the average size
of each fraction are summarized in Table 2, for tomato suspensions before
homogenisation, and after homogenisation to the particle size found in commercial
ketchup. Based on the results given in Paper I, it is suggested that different HB pastes
have different susceptibilities to breakage during homogenisation, depending on the
viscosity of the supernatant.
Table 2. Morphological properties of the tomato pastes studied based on their area-based PSDs (Papers IIII). The percentage of fine (< 10 µm) and coarse (> 10 µm) particles present in the suspensions, and the
median diameters of the two fractions, before and after homogenisation to the particle size found in
ketchup are given.
Paper I
Paste typea
Paper II
Paper III
HB
HB
HB
HB
HB
CB
CB
28/30
28/30
28/30
28/30
22/24
36/38
36/38
Before homogenisation
Coarse fraction
%
76
72
69
73
76
63
73
d32
µm
170
196
169
202
157
123
177
Fine fraction
%
24
28
31
27
24
37
27
d32
µm
4.4
2.7
2.7
2.5
3.5
3.1
3.1
After homogenisation
Coarse fraction
%
53
51
54
59
53
41
38
d32
µm
85
78
82
62
64
81
63
Fine fraction
%
47
49
46
41
47
59
62
d32
µm
2.7
2.1
2.1
2.6
2.5
0.6
0.5
a
28/30 are the concentration of soluble solids expressed in ºBrix
The PSD can also be presented by plotting the cumulative percentage of particles as a
function of the particle diameter, as in Figure 7. This way of expressing the particle size
distribution facilitates the mathematical treatment and better reflects the changes caused
12
by small changes in processing, for example, varying the degree of homogenisation
slightly. Suspensions of different concentrations were subjected to different number of
passages through the homogeniser in order to obtain a final particle size similar to that of
commercial ketchup (Paper II). The number of passages varied with the concentration
and the type of tomato paste; HB suspensions needing a much larger number of passages
than CB tomato suspensions in order to reduce the particle size to similar values. The
considerable difference in breakage behaviour between cold break and hot break paste
confirms the earlier suggestion that the viscosity of the suspending medium plays a major
role in determining the susceptibility to breakage of the particles in tomato suspensions.
Cold break suspensions at different concentrations were subjected to a fixed number of
passages through the homogeniser and the resulting particle size was found to be
dependent on the concentration and the number of passages (Paper III). In general,
homogenisation decreased the particle size, while subsequent shearing of the suspensions
resulted in an increase in particle size.
cumulative surf. area [%]
100
80
1000, bh
500, ah
400 ah
300 ah
200 ah
60
40
20
A
0 −1
10
0
10
1
10
10
particle diameter [µm]
2
10
3
Figure 7. Particle size distribution of hot break tomato paste suspensions before homogenisation (bh, solid
line) and after (ah) homogenisation, expressed as the cumulative surface area (%), as a function of the
particle diameter (µm) for different concentrations, given in g/kg (see legend). (Adapted from Paper II).
A great deal of work has been devoted to extracting the maximum packing of particles
( φm ) from the PSD curves. The maximum packing of particles is of great importance in
many fields of engineering, and it is directly related to rheological properties of a material
(Farris, 1968). For example, optimising the PSD so that small particles occupy the spaces
between large particles has the effect of decreasing the viscosity of the suspension by up
13
to a factor of 50, which can significantly reduced the pumping cost (Servais et al., 2002).
It is also a key parameter in powder handling and processing as it determines the total
volume occupied by the powder.
The maximum packing fraction is easily obtained in monodisperse suspensions, binary
suspensions, i.e. particle populations with two discrete sizes, and ternary suspensions
(three discrete particle sizes) (Lee, 1970). In continuous PSDs, the extraction of φm
represents a complex mathematical problem, and the computational requirements make
the solution difficult (Bierwagen & Saunders, 1974). Recently, φm was solved for a
continuous PSD showing power law behaviour (Brouwers, 2006). For more complex
PSDs, such as those found in food suspensions like tomato paste, no mathematical tools
for the determination of the maximum packing of the particles are available today.
3.2.3
Concentration and volume fraction determination
The particle concentration is an important parameter determining the type of suspension,
as well as the microstructure. There are different ways of expressing concentration, for
example, based on the total solids, the water-insoluble solids or the volume fraction, but
only the last one takes into account the microstructure of the suspension. The total solids
and water-insoluble solids are, for example, not affected by processes that clearly change
the microstructure of the suspensions, such as homogenisation. Volume fraction, on the
other hand, is very sensitive to these changes. In this work, the volume fraction was
determined by ultracentrifugation at 110,000 g. This value was used as Den Ouden
(1995) and Rao (1999), claimed that very high centrifugation forces were needed to
separate the solid and liquid phases in tomato paste. The drawback of using the
centrifugation technique to determine the volume fraction is that the resulting value may
be affected by deformation of the particles. Therefore, the volume fraction ( φ )
determined in the present work is indeed a compressive volume fraction and depends on
morphological factors such as the PSD and the particle shape, as well as on the packing
capacity and deformability. In this text, it will simply be referred to as volume fraction.
Suspensions can be classified as being dilute, in the transition region or as concentrated
(Steeneken, 1989). Figure 8 shows illustrations of the arrangement of particles in the
different regimes. In dilute systems, the particles are swollen to their equilibrium size, i.e.
14
they have maximum volume and are free to move in the suspension under Brownian
forces. In the transition region, the particles are in contact with each other, but still have
their maximum volume. In highly concentrated suspensions, the particles are deformed
and fill the space available, and the suspension is thus fully packed. Another definition
was given by Coussot and Ancey (1999), who described concentrated suspensions and
granular pastes from a physical point of view, as “complex systems within which particles
interact strongly, giving rise to viscosities much higher than the viscosity of the
suspending media”. In concentrated systems, the interactions and contact between
particles clearly dominate over the Brownian forces.
Figure 8. Concentration regime in suspensions. From left to right: dilute, transition and concentrated.
(Adapted from Steeneken, 1989.)
In Figure 9, the volume occupied by the particles in tomato paste (100% bh), and in 50%
tomato paste suspensions, before (bh) and after homogenisation (ah), is shown. It can be
seen that homogenisation clearly increases the volume of particles in the suspension, at
the same paste concentration.
100 bh
50 bh
50 ah
Figure 9. The volume fraction of tomato paste suspensions following ultracentrifugation at ~110,000 g for
20 min at 20ºC. The figure shows 100 and 50% paste before homogenisation (bh) and 50% paste after
homogenisation (ah).
15
Different pastes show different behaviour with regard to the volume fraction as a
function of the concentration of the paste. In Figure 10, the hot break (HB 22/24) and
cold break (CB 36/38) suspensions described in Paper II are compared. The expected
decrease in volume fraction due to dilution of the non-homogenised suspensions is
shown as a dashed line, using the volume fraction from 100% paste as a reference. The
behaviour of HB paste almost follows the predicted one, whereas CB suspensions seem
to be more compressed by centrifugation. This shows that the volume fraction includes
information about the ability of the particles to deform and pack at a given centrifugal
force. The process of homogenisation clearly increases the volume fraction in both
pastes. In Paper I, it was suggested that higher value of φ is related to a higher viscosity
of the suspending medium. The case illustrated in Figure 10 is an extreme one, because
the viscosity of the liquid phase in HB suspensions is several times greater than in CB
suspensions (see Section 5.1.1). The higher viscosity of the liquid phase (ηs) may, to some
extent, hinder the deformation of particles caused by centrifugal forces.
Ø
0,7
Ø
0,7
A
0,6
B
0,6
0,5
0,5
ah
0,4
0,4
bh
0,3
0,2
0,2
0,1
0,1
0,0
0
10
20
30
40
50
60
70
80
ah
0,3
90
100
paste content %
0,0
bh
0
10
20
30
40
50
60
70
80
90
100
paste content %
Figure 10. Comparison of the volume fraction obtained in (A) hot break 22/24 and (B) cold break 36/38
tomato paste suspensions at different concentrations, before and after homogenisation (Paper II). The
dashed line shows the predicted behaviour of non-homogenised suspensions.
3.3 Effect of concentration, particle size and shearing
Changes in microstructure due to processing, and vice versa, were studied in Papers IIII, by inducing or creating different types of arrangements in the suspensions studied,
by means of varying the concentration and the particle size, and by shearing the
structures formed. In the study described in Paper I, three HB tomato pastes were
16
studied as raw material in the production of a commercial ketchup. Slight variations in
the composition, particle size distribution and particle susceptibility to breakage are
reflected in the rheological properties of the final ketchups. In the study presented in
Paper II, a more systematic approach was taken. Three different pastes were
homogenised to sizes similar to those found in commercial ketchup, and the effects of
both concentration and particle size on the time-dependent properties of the tomato
suspensions were investigated. Finally, changes in the microstructure due to processing
(homogenisation and shearing) were systematically studied on CB tomato paste
suspensions at different concentrations (Paper III). Table 3 presents an overview of the
studies described in each of the papers. Paper IV is included for completeness.
Table 3. Overview of the experimental studies described in Papers I-IV, including the type of paste used,
range of concentrations studied and the degree of homogenisation applied. The type of rheological
measurements performed in each study is also given.
Factor
Paste type
Concentration
Paper I
Paper II
Paper III
Paper IV
3 HB
2 HB and 1 CB
1 CB
1 HB and 1 CB
1000, 400, 300
1000, 500, 400,
400, 300, 100
1000, 500, 400,
g/kg
Homogenisation
Shearing
300, 200
300
300 g/kg
500-200 g/kg
400-100 g/kg
to ketchup size
to ketchup size
3 degrees
-
During
1 h, magnetic
measurements
stirrer
-
Measurements
Flow curve
+
+
-
+
Creep
-
+
-
-
Dynamic
+
-
+
+
Yield stress
+
+
-
+
Effect of concentration on the particle size
In this study, the concentration of tomato suspensions was expressed in terms of the
volume fraction, φ , instead of the more common forms, Brix degree, water-insoluble
solids or total solids, because these are not related to the microstructure. The effect of
concentration on the microstructure of tomato suspensions can not be studied using
microscopy, because dilution of the samples is required, and their arrangement in the
suspension would thus be disrupted. Therefore, the effects of concentration were
investigated in terms of other parameters, such as the rheological properties (Sections 4.2
17
and 5.1). Moreover, the influence of the concentration on the performance of the
homogeniser, in decreasing the particle size to a set value, was studied. The last point will
be discussed in this section.
In Paper II, the number of passages through the homogeniser required to decrease the
particle size of different tomato pastes to a set value, was determined, taking into account
the concentration of the suspensions and the type of paste (Fig. 11A). In general, fewer
passages were required with decreasing concentration. The effect of a fixed number of
passages on the particle size of the suspension is shown in Figure 11B, for different
concentrations. The decrease in particle size in the more concentrated sample (400 g/kg)
is less pronounced than in the others at a given number of passages. The changes
following homogenisation differ considerably between HB and CB suspensions, the
latter requiring much fewer passages to break down the particles. This may also be
related to the lower viscosity of the suspending medium (ηs), in CB suspensions.
250
15
11
10
150
7
7
2
1
350
A
300
6
250
d43
d43
200
10 1
15
3
100
1
1
B
1
2
3
200
2
2
3
150
3
100
50
50
0
0
500
400
300
400
200
g/kg% paste
300
100
g/kg% paste
Figure 11. Volume-based diameter (d43, µm) as a function of the concentration of the paste (g/kg), for
different numbers of passages through the homogeniser (given above each column). A) Adapted from
Paper II: HB 28/30
, HB 22/24
, and CB 36/38
. B) Adapted from Paper III, CB 36/38.
Finally, it is interesting to note that the behaviour of suspensions during the process of
homogenisation is markedly different from that of emulsions. In emulsions the relevant
parameter in decreasing the size of the particles is the homogenisation pressure
(Tornberg, 1978), while the size of the particles remains approximately constant after
repeated passage at the same pressure. This is not the case in suspensions and Figure 11B
clearly shows the importance of the number of passages in determining the final size of
the particles.
18
Non sheared
Sheared
H0
H1
H2
H3
Figure 12. Effect of homogenisation and subsequent shearing on the microstructure of 10% cold break
tomato paste suspensions before homogenisation (H0) and after 1, 2 and 3 passages (H1-H3) through the
homogeniser (pressure ~90 bar). (Adapted from Paper III.) The scale bar is 250 µm.
19
Effect of homogenisation and subsequent shearing
Homogenisation and subsequent shearing of the suspensions cause substantial changes in
the microstructure of the suspensions, as can be seen in Figure 12, for 10% CB
suspensions (Paper III). The series of images on the left show the successive creation of
an evenly distributed network by passing the suspension through the homogeniser
several times. A decrease in the particle size is evident, which is accompanied by an
increase in the surface area covered by the particles. Subsequent shearing of the
suspensions (right-hand images in Fig. 12) had no visible influence on the surface area at
a low degree of homogenisation, but for the well homogenised suspensions the structure
of the suspensions was considerably different after shearing. In fact, in the most
homogenised and sheared suspensions the individual particles tended to aggregate
forming heterogeneous regions with densely packed flocs, resulting in a completely
different type of network. These observations suggest that the process of
homogenisation creates a smooth network of finer particles that is easily disrupted by
prolonged shearing.
% area
50
2.0
A
Df, fractal number
60
40
30
20
10
0
B
1.6
1.2
0.8
0.4
0.0
H0
H1
H2
H3
H0
Homogenisation degree
H1
H2
H3
Homogenisation degree
Figure 13. A) Percentage area covered by the particles and B) fractal number associated with the 2dimensional images, as a function of the degree of homogenisation in 10% tomato paste suspensions.
Results are shown for non-sheared ( ) and sheared samples ( ).(Adapted from Paper III, CB 36/38.)
The different features revealed in these microscopic images can be quantified using
image analysis, and the area covered by the particles, the fractal number and the size of
the pores or the distance between particles and flocs were determined (the image analysis
procedure is described in Section 3.2.1). The area covered by the particles and the fractal
number (Fig. 13) exhibit similar behaviour upon homogenisation and subsequent
20
shearing. Both variables are found to increase with the degree of homogenisation,
whereas shearing has a negative effect on their values. The structure of the unsheared
well-homogenised suspensions shows a high degree of fractality, and probably consists of
dense areas connected by thin linkages (H3). On shearing, the network is probably
disrupted first at these linkages, followed by the densification of the floc structure and
the growth of the floc size (H3-SH).
The fractality of the network structure is one of the few existing ways to relate
microstructure and rheology, and a number of scaling laws relating them have been
developed for colloidal suspensions and gels (Buscall et al., 1987, Buscall et al., 1988) and
more recently for fat crystals (Narine & Marangoni, 1999). The applicability of such laws
relating microstructure and rheology in tomato suspensions will be discussed in Chapter
4.
The average separation between particles or aggregates, as well as the porosity of the
network, is of importance in understanding the rheological behaviour and the
microstructure of the suspensions. The distance between the particles and/or the
distribution of pores in the network is observed to change on homogenisation followed
by shearing (Fig. 12, Fig. 14). In the non-homogenised samples, the average distance
between the particles (i.e. whole cells) is about 135 µm. During homogenisation, the
microstructure of the network changes, and this change is accompanied by the formation
of smaller pores. At a low degree of homogenisation (H1) only 40% of the pores are
below 45 µm, having an average size of about 80 µm. In the highly homogenised system
(H3), the averaged pore size has decreased to 54 µm and more than 50% of the pores are
now below 45 µm. Successive shearing of this network leads to the formation of
aggregates/flocs, separated by a distance of the order of 100 µm. Note, however, that in
the sheared samples, the distance between particles, i.e. whole cells or aggregates, seems
to be independent of the degree of homogenisation, although the shape, size and
distribution of the particles are drastically different.
21
A
200
150
100
50
0
H0
H1
H2
60
% pores < 45 µm
Pore size µm
250
H3
B
50
40
30
20
10
0
H0
Homogenisation degree
H1
H2
H3
Homogenisation degree
Figure 14. A) Pore size (or distance between particles and/or flocs), and B) percentage of pores with a size
below 45 µm, as a function of the degree of homogenisation in 10% tomato paste suspensions. Results are
shown for non-sheared ( ) and sheared samples ( ).(Adapted from Paper III, CB 36/38.)
Following prolonged shearing, the network of tomato homogenates rearranges, forming
discrete, closely packed flocs, consisting of aggregates of small individual particles. These
flocs are easily oriented in the direction of the flow (in Fig. 12, at about 45º) and have an
aspect ratio of the order of ~10, whereas that of the individual particles is about ~1.5.
Mills et al. (1991) studied the effect of prolonged shearing in model colloid suspensions
and found that the particles tended to form flocs or aggregates, which led to a significant
decrease in yield stress, apparent viscosity and shear modulus. They reported that the size
of the aggregates was independent of the initial volume fraction, and probably
determined by the size of the individual particles.
22
4. Mechanical Spectra of Concentrated Suspensions
The word “rheology” was coined by Bingham in the 1920s and comes from the Greek,
where rheos- means “current or flow” and logos- means “word or science”. Rheology is
thus the study of the deformation and flow of matter in response to a mechanical force.
In this chapter , measurements based on deformation caused by oscillatory shear are
discussed. In the next chapter (Chapter 5) flow behaviour upon the application of steady
shear is discussed.
An overview of the rheological measurements performed and the type of measurement
system used in each of the studies is given in Table 4.
Table 4. Overview of the rheological measurements reported in Papers I-IV. The type of geometries used
in each study is also given.
Paper I
Paper II
Paper III
Paper IV
Concentric cylinder
-
-
-
+
Vane
+
+
+
+
Outer vane
-
-
-
+
Tube viscometer
-
-
-
+
Flow curve
+
+
-
+
Creep
-
+
-
-
Dynamic
+
-
+
+
Yield stress
+
+
-
+
Geometries used
Measurements
4.1 Dynamic oscillatory rheology
A common way of investigating the microstructure of complex fluids is the application
of small-amplitude oscillatory shearing, which does not significantly deform the
microstructure of the fluid being tested. Most food materials are considered to be
23
complex fluids, meaning that they have mechanical properties between those of ordinary
liquids and ordinary solids (Larsson, 1999).
4.1.1
Strain/stress sweep tests
In oscillatory testing, a sample is deformed sinusoidally by the application of smallamplitude, oscillatory deformations in a simple shear field. When the material is tested in
the linear viscoelastic regime, its mechanical properties do not depend on the magnitude
of the strain or stress applied. The linear viscoelastic region can be determined
experimentally for each material, by means of a stress/strain sweep test. This test consists
of increasing the magnitude of the stress or strain, while keeping the frequency of
oscillation constant, usually 1 Hz (Fig. 15). When the material enters the non-linear
region, the material properties become dependent on the level of stress/strain applied. In
food materials, strains are often kept below 1% to avoid non-linear effects (Steffe, 1996).
1000
A
G’, G’’ [Pa]
G’, G’’ [Pa]
10000
8000
6000
4000
750
500
250
2000
0
0.001%
B
0
0.010%
0.100%
1.000%
strain
0.001%
0.010%
0.100%
1.000%
strain
Figure 15. Results of typical strain-sweep measurements performed at a frequency of 1 Hz, for A) tomato
paste and B) ketchup. The elastic modulus G' (♦) and the loss modulus G'' (◊) are expressed in Pa. (From
Paper I).
The non-linear viscoelasticity of foods i.e. the behaviour at large deformation, may be
relevant in many processes, such as swallowing during the sensory evaluation of food,
but in such measurements the microstructure of the material is disrupted. Therefore, only
the linear oscillatory rheology of tomato suspensions at small deformations, which yields
structural information of the “intact” network structure, was studied in this work.
24
In the linear region, the sinusoidally varying stress ( σ ) can be written:
σ (t ) = γ 0 [G' (ω )sin(ωt ) + G' ' (ω )sin(ωt )]
(3)
where ω is the frequency of oscillation, and G ' is the storage or elastic modulus, and
G ' ' is the loss modulus. For solid-like materials G ' >> G ' ' , whereas for liquid-like
materials G′<<G′′. The complex modulus, G * , is defined by G* = G'+iG' ' , and the
complex viscosity is thus defined by η * = G * (ω ) ω .
4.1.2
Mechanical spectra in the linear viscoelastic region
The mechanical spectrum of dilute model solutions is predicted by the general linear
model to scale with the frequency, as G' ∝ ω 2.0 and G' ' ∝ ω1.0 , with the loss modulus
being much higher than the elastic modulus: G ' ' > G ' . The power law is obeyed in the
low-frequency region, ω →0. The mechanical spectrum of a gel is instead expected to be
independent of the frequency ω (Ferry, 1980; Ross-Murphy, 1988, Fig. 16). Recently, it
has been shown experimentally that during the sol-gel transition G' ∝ ω 0.5 (Liu et al.,
2003).
a
b
c
d
Figure 16. Typical mechanical spectra showing elastic modulus and the loss modulus as a function of
frequency, for: A) a solid, B) a weak gel, C) a concentrated suspension and D) a liquid. The elastic modulus
G' is represented by a solid line and the loss modulus G'' is represented by a dashed line. (Adapted from
Ross-Murphy, 1988.)
Real fluids, such as semi-liquid or semi-solid foods, exhibit intermediate mechanical
spectra to those of model solids and liquids. Paper I describes the frequency-dependent
behaviour of tomato pastes and their corresponding ketchups (Fig. 17). Tomato pastes,
for example, are found to behave as weak gels, G ' > G ' ' over all the frequencies studied
25
(0.01-10 Hz). At low frequencies, ω <0.1, the loss modulus is almost independent of the
frequency, whereas G ' increases slightly with ω . At frequencies above this value ( ω >
0.1), G ' and G ' ' scale with the frequency as ω 0.1 and ω 0.2 , respectively. The
corresponding ketchups also show solid-like behaviour, with G' > G ' ' , and in the lowfrequency region, G ' ' shows a minimum, which is also typical of weak gels and highly
concentrated suspensions. At higher frequencies ( ω >0.1), G ' and G ' ' scale as ω 0.1 and
ω 0.3 , respectively.
10000
A
B
G’, G’’ [Pa]
G’, G’’ [Pa]
100000
10000
1000
100
0.01
1000
100
0.1
1
10
0.01
10
Frequency [Hz]
0.1
1
10
Frequency [Hz]
Figure 17. Typical mechanical spectra for A) three tomato pastes and B) the corresponding ketchups. The
elastic modulus (filled symbols) and the loss modulus (open symbols) are shown as a function of the
frequency. Note that the scales in A and B are different. (Adapted from Paper I).
The shape of the G ' (ω ) and G ' ' (ω ) curves shown in Fig. 17 does not seem to vary
between the different types of paste, but varies slightly between pastes and ketchup. This
suggests that processing, i.e. dilution and homogenisation, does not affect the frequency
dependence of tomato suspensions to any great extent. In the study reported in Paper
III it was found that the mechanical spectra of unsheared and sheared tomato
suspensions, at different concentrations, and at several degrees of homogenisation
followed similar trends. However, the magnitude of the elastic and loss moduli varied
with the type of paste, concentration, degree of homogenisation and prolonged shearing.
As an example of non-gelling suspensions, the mechanical spectra of two potato fibre
suspensions, at low and high concentration, are shown in Fig. 18. The low-concentration
sample shows the typical behaviour of a diluted suspension, and behaves as a liquid
26
( G ' ' > G ' ) at all frequencies ( ω = 0.01-10 Hz). It shows stronger frequency dependence
than the tomato suspensions, with G' ∝ ω 0.7 and G' ' ∝ ω 0.7 . Increasing the concentration
of potato fibres to 6.5% leads to more gel-like behaviour at low frequencies, whereas at
about 1 Hz the viscous behaviour of the suspension takes over. The frequency
dependence is now G ' ∝ ω 0.4 and G' ' ∝ ω 0.6 , still much stronger than in tomato
products. These two potato suspensions were used in the pumping experiment reported
in Paper IV.
1000
G’, G’’ [Pa]
G’, G’’ [Pa]
1000
100
10
100
10
A
1
0.01
0.1
1
B
1
0.01
10
Frequency [Hz]
0.1
1
10
Frequency [Hz]
Figure 18. Mechanical spectra for dried potato fibre suspended in 860 mPa s syrup, A) at low concentration
(4.5%), and B) at high concentration (6.5 %). The elastic modulus (filled symbols) and the loss modulus
(open symbols) are given as a function of the frequency . Note that the scales in A and B are different.
(Data for two of the suspensions reported in Paper IV.)
4.2 Effect of concentration, particle size and shearing
The viscoelastic behaviour of suspensions is determined by the particle size distribution
and shape, as well as the volume fraction of particles (Nakajima & Harrell, 2001, Servais
et al., 2002) and the particle-particle interactions (Shah et al., 2003) as well as the spatial
arrangement of the particles; in other words, the viscoelastic properties are dependent on
the microstructure of the suspension.
Some recent experiments show that small changes in the microstructure can have a
drastic effect on the mechanical properties of colloidal suspensions and gels. For
27
example, Channell et al. (2000) induced heterogeneities in the microstructure of
flocculated alumina suspensions and arrived at the conclusion that the yield stress
determined by uniaxial compression was more sensitive to heterogeneities than the elastic
shear modulus. Miller et al. (1996) also found that the suspensions became more
compressible as the particle size is increased.
The fractal description of the microstructure and its relation to rheological properties are
well established for relatively dilute colloid systems (Muthkumar, 1985). In fat crystals,
the fractal description holds for fat concentrations up to a volume fraction of ~0.7
(Narine & Marangoni, 1999), and can be expressed as:
G' = αφ β ,
(4)
where α is a constant that depends on the size of the particles and on the interactions
between them, φ is the volume fraction of particles, and β = 1 (d − D f ) is an exponent
that depends on d , the Euclidean dimension of the network (usually d =3), and D f , the
fractal dimension of the network.
The fractal scaling behaviour should be interpreted with care in highly concentrated gels
(Wyss et al., 2005). Buscall et al. (1987, 1988) found exponents much higher than 3 for
the dependence of the elastic modulus on the concentration, and proposed that the
networks had a highly non-uniform, heterogeneous structure comprising a collection of
interconnected fractal aggregates.
The influence of the microstructure on the rheology of the suspensions is less well
understood for highly concentrated suspensions, probably due to the fact that the
number of techniques available to investigate the microstructure of such suspensions is
rather limited (Wyss et al., 2005), and also because there is no standardised way of
quantifying the microstructure and relating it to the macroscopic properties of the
material, such as the rheological behaviour.
The microstructural changes that tomato suspensions undergo upon homogenisation and
subsequent shearing have been analysed in relation to their mechanical properties, taking
into account the particle size and the concentration of the suspensions, and are described
28
in Paper III. The ratio of the percentage of fine to coarse particles (f/c) is used as a
parameter to represent the PSD of the suspensions investigated. The PSD was found to
vary with the degree of homogenisation and, to a lesser extent, with subsequent shearing.
The particle size of the coarse fraction (> 10 µm) and the compressed volume fraction
were the most relevant parameters in defining the elastic modulus, G′, and an empirical
equation (Eq. 5) was found to accurately describe the whole set of data (R2>99.3%,
p<0.001), as is shown in Fig. 19,
log G ' = 3.75 + log φ 2.47 + 4120 d 32 ,coarse .
(5)
4
10
3
G’ [Pa]
10
2
10
1
10
0
0.1
0.2
0.3
φ [−]
0.4
0.5
0.6
Figure 19. Linear elastic modulus (G′, ω=1Hz) as a function of the volume fraction ( φ ) in suspensions
with predominantly coarse (f/c<1, ●) or fine (1<f/c<3, ○) particles. The values fitted using Equation 5 are
also shown (x). The dotted lines represent the fits to
G' = αφ β . (Adapted from Paper III.)
The elastic modulus was also modelled following the fractal scaling (Eq. 4). The data
plotted in Figure 19 indicate that suspensions with predominantly coarse particles (100
µm, f/c<1) exhibit higher values of G ' than suspensions with predominantly fine
particles (30 µm, f/c>1), at a given volume fraction.
29
The values of α in Equation 4 have values of ~20000 and ~10000, for coarse and fine
fractions, respectively. The fractal number was not substantially different in the coarse
and fine fractions, having a value of D f ~2.58, which is comparable to the averaged
value obtained from the image analysis of the 10% tomato paste suspensions (Fig. 13B).
Note that the images are in 2-D. The averaged D f value for fine and coarse 10%
suspensions can be calculated and converted to 3-D, by assuming that the suspensions
are isotropic. This gives a value of 2.41 for the coarse suspensions (f/c<1) and 2.64 for
the fine suspensions (1<f/c<3), which are in qualitative agreement with the fitted value.
However, it is not possible to confirm the fractal behaviour of the highly concentrated
suspensions, and extrapolating the results from the semi-diluted regime to higher
concentrations is not sufficiently accurate. Moreover, the determination of the volume
fraction involves some compression of the network, and φ is then the volume of the
deformed particles and not necessarily the cumulative volume of the primary fractal
elements. Even with the above mentioned limitations, the power-law scaling holds for a
large range of φ , PSD and particle shapes in tomato suspensions.
10000
0.6
Volume fraction [-]
A
G’ [Pa]
1000
100
B
0.5
0.4
0.3
0.2
0.1
10
0.0
0.0
1.0
2.0
3.0
0.0
4.0
1.0
f/c [-]
2.0
3.0
4.0
f/c [-]
Figure 20. A) Elastic modulus and B) volume fraction determined by centrifugation, as a function of the
ratio of fine-to-coarse particles (f/c) for 10, 30 and 40% tomato paste suspensions (♦, ▲, ●, respectively).
Filled symbols represent samples before shearing and empty symbols samples that were subjected to
prolonged shearing. The lines are a guide to the eye. (Adapted from Paper III.)
The concentration has a strong impact on both the rheological behaviour of the
suspensions and the effectiveness of processing. In semi-diluted regimes, such as 10%,
the particles are probably swollen to equilibrium (Steeneken, 1989) and form a more
30
heterogeneous network consisting of a collection of particles or aggregates/flocs, with
large pores in between (Fig. 13A). The rheological properties (G′) of this type of
suspension depend linearly on f/c, whereas this does not seem to be the case for more
concentrated suspensions, being more independent of f/c (Fig. 20A). The results of the
present work suggest that the 30 and 40% tomato paste suspensions instead form a
continuous particulate network, where the particles fill the available space and are
probably not swollen to equilibrium, but exist as more deformed particles
The volume fraction was found to be more sensitive to changes in the microstructure of
highly concentrated suspensions than the elastic modulus (Fig. 20B). The reason for this
could be that the deformability of the particles comes more into play in more
concentrated suspensions, as pointed out by Steeneken (1989). The deformability of the
particles is a key parameter in explaining why the presence of heterogeneities in the
microstructure could be measured using compressive yield stress (by centrifugation),
while the shear modulus could not differentiate between different types of
microstructures according to Channell et al. (2000). In the present study, large particles,
aggregates or flocs, and large pores or voids in the network caused heterogeneities in the
microstructure of the suspensions. Since the volume fraction was determined by
ultracentrifugation, i.e. uniaxial compression at a given speed (~110,000 g), it could be
affected by the compressive strength of the different networks, i.e. by the heterogeneities
induced by homogenisation and subsequent shearing. However, those changes
introduced by processing may not alter the number of junction points in the network,
especially in the more concentrated suspensions where particles are physically touching
each other and filling the spaces, thus giving similar G ' values in the dynamic shear
measurements.
31
5. Flow Behaviour of Concentrated Suspensions
The flow behaviour of the materials can be described by rheological models. Rheological
models describe the relationship between the shear stress ( σ ) and the shear rate ( γ& ).
Newtonian fluids show a linear relationship between these variables, while nonNewtonian fluids exhibit a non-linear dependence.
σ = η (γ& )γ&
(6)
Tomato products exhibit pronounced non-Newtonian effects, e.g. yield stress, shearthinning behaviour and shear history dependence (Rao, 1999). The rheological properties
of tomato products have been described using the popular power-law equation or, when
the yield stress is taken into account, the Bingham, Herschel-Bulkley and/or Casson
models (Table 5). The applicability of each of these models depends on the range of
shear rates considered.
Table 5. Some typical rheological models used to describe the viscosity of tomato products
Power law
σ = Kγ& n
Bingham
σ = σ y + μγ&
Herschel Bulkley
σ = σ y + Kγ& n
Casson
σ 0.5 = σ y0.5 + K 0.5γ& 0.5
5.1 Suspension rheology
The rheological behaviour of dilute suspensions and colloid dispersions, and some model
concentrated suspensions, is relatively well understood (Coussot & Ancey, 1999). Already
in the early 1900s, Einstein proposed that the viscosity of a dilute suspension of hard
spheres ( φ ≤ 0.03), assuming no interactions, was governed by
η = η s (1+ 2.5φ )
(7)
33
Hydrodynamic effects appear when two spheres are close enough that the flow around
one of them is influenced by the presence of the other. The Krieger-Dougherty equation
appears to described the viscosity of more concentrated suspensions of hard spheres
( φ <0.63), at low shear rates γ& → 0, when hydrodynamic effects dominate and particle
interactions are negligible.
⎛
φ ⎞
η = η s ⎜⎜1 − ⎟⎟
⎝ φm ⎠
−2.5φm
(8)
In highly concentrated suspensions, the interaction between particles dominates over the
hydrodynamic forces, especially at low shear rates, and the material exhibits a yield stress.
If the particles are large, and contact with other particles occurs, frictional and collision
effects may come into play. Coussot and Ancey (1999) proposed a classification of the
different rheological regimes from a physical point of view, considering both the
concentration and the shear rate (Fig. 21). They defined a concentrated suspension as
that in which particle interactions play a major role in the rheological behaviour of the
suspension, giving rise to a viscosity that is several orders of magnitude higher than the
viscosity of the interstitial suspending medium (η s ).
Figure 21. Classification of forces involve in different rheological regimes as a function of the shear rate
and the volume fraction. (Adapted from Coussot & Ancey, 1999.)
34
It is also important to note that several practical difficulties are encountered in
rheological measurements of highly concentrated suspensions and gels, for example poor
reproducibility, sensitivity to shear history and to the preparation of samples, and slip
(Larsson, 1999; Kalyon, 2005). Up to 50% variability has been reported in the rheological
properties of wheat starch at high concentrations (Steeneken, 1989), and between 15 and
30% in the determination of yield stress in model colloidal suspensions (Buscall et al.,
1987). Measurements performed under similar experimental conditions, but in different
geometries, do not always agree (Plucinski et al., 1998), and hence the comparison
and/or prediction of rheological properties from one instrument to another is difficult.
In section 5.2, some considerations regarding measurement systems will be discussed.
5.1.1
Rheological behaviour of tomato products
Den Ouden (1995) reported viscosities of the supernatant of the order of ~20 mPa s for
HB tomato paste and ~4 mPa s for CB tomato paste, and claimed that the contribution
of the suspending medium to the apparent viscosity of tomato paste was very little, and
that the tomato particles and the fibre network accounted for the extremely high
apparent viscosities, especially at low shear rates. In the present work, the viscosity of the
suspending medium was below 7 mPa s for the CB suspensions and below 20 mPa s for
the diluted HB suspensions (Fig. 22).
The behaviour of the viscosity of the supernatant upon dilution is, however, markedly
different in hot and cold break suspensions, and while η s resembles that of a sucrose
solution in CB samples, it increases much more steeply in HB samples. Note that the
viscosity of the supernatant in 100% HB paste is not included in Figure 22 because it
exhibits non-Newtonian behaviour, but for comparison, at γ& =10 s-1, η s ~300 mPa s, for
Brix degrees between 20 and 30. The main difference between hot and cold break
processing is that the former is carried out at high temperatures (> 85°C), while the latter
is only subjected to low temperatures (< 70°C). Low temperatures allow a certain degree
of pectin degradation because of the slow and incomplete inactivation of the enzymes
involved, i.e. pectin methyl esterase and polygalacturonase. Fito et al. (1983) reported that
the content of soluble pectins present in CB pastes was significantly lower than in HB
pastes, and several authors have suggested that the presence of soluble pectins is a key
35
parameter in determining the viscosity of tomato paste (Thakur et al., 1996; Chou &
Viscosity [mPa s]
Kokini, 1987; Hurtado et al., 2002).
25
0.6% pectin
20
15
10
5
sucrose
0
0
10
20
30
40
ºBrix of supernatant
Figure 22. Supernatant viscosity as a function of the Brix degree of the solution, determined at a shear
range of 10 s-1, in the supernatant of three tomato pastes: HB 28-30 (■), HB 22-24 (▲) and CB 36-38 (●),
at different concentrations. Filled and empty symbols show data for suspensions before and after
homogenisation, respectively. For comparison, the viscosity of a sucrose solution and a sucrose solution
with 0.6% pectin added is also shown.
However, the extremely high viscosity that tomato paste exhibits at low shear rates
(η ~106 Pa s, Fig. 23) makes the direct contribution of pectins almost negligible, as
pointed out by Den Ouden (1995). This work suggests that the soluble pectin content or,
in other words, the viscosity of the liquid phase in tomato paste, contributes indirectly to
the viscosity by affecting the microstructure of the suspensions. Observations such as CB
pastes being more compressible, and their constituent particles more easily broken down
by homogenisation, in contrast to HB paste, have been repeatedly made in this work (see
Sections 3.2.3 and 3.3).
The typical flow behaviour of tomato suspensions is shown in Figure 23, as the apparent
shear viscosity as a function of the shear rate. An initial Newtonian plateau is followed by
a shear-thinning region, which seems to change slope at shear rates around 0.1 to 1 s-1. In
Paper I, the Carreau model (Eq. 9) was found to describe the flow behaviour of tomato
36
pastes rather accurately, and the values of the parameters were of similar magnitudes to
those reported by others (Valencia et al., 2003); i.e. the zero-shear viscosity η 0 ~106 Pa s,
the time constant λ ~104 s, and the exponent N~0.4.
η=
η0
(9)
[1 + (λγ& ) ]
2 N
Whether or not the flow behaviour of tomato food systems is better represented by the
zero-shear viscosity or by the presence of a yield stress will be further discussed in the
following section.
6
10
Apparent shear viscosity [Pa s]
5
10
4
10
3
10
2
10
1
10
0
10
−1
10
−6
10
−4
10
−2
10
0
10
2
10
Apparent shear rate ,[1/s]
Figure 23. Typical apparent shear viscosity as a function of the shear rate in tomato paste ( ), ketchup
before homogenisation ( ) and ketchup after homogenisation ( ). (Adapted from Paper I.)
5.1.2
Yield stress
Yield stress is the minimum stress required to achieve flow. When the stress applied to a
material is below a certain value (σ <σy), the material experiences little or no deformation,
and behaves as a Hookean solid. When the stress exceeds a certain value (σ >σy), the
material begins to flow. The yield stress arises from the balance between external and
internal forces (Whittle & Dickinson, 1998; Coussot & Ancey, 1999), i.e. the yield stress
exists while the external forces and internal fluctuations, i.e. Brownian forces, are
insufficient to significantly disrupt the network, Eexternal + kT << Enetwork. In fluids at rest,
37
such as polymers and dilute suspensions (particle size < 10 µm), the Brownian force
dominates (kT), but this effect diminishes with increasing particle number and size, as is
the case in concentrated suspensions.
The presence of a yield stress is a characteristic of concentrated suspensions, and it is
related to the strength of the network structure, which in turn results from attractive
particle-particle interactions (Larsson, 1999; Coussot & Ancey, 1999). The magnitude of
the yield stress is affected by a number of factors, such as the density of the network,
particle concentration, particle size and shape, among others (Dzuy & Boger, 1983).
There has been a long, controversial debate in the literature driven by the articles
published by Barnes and Walters (1985) and Barnes (1999) questioning the concept of
yield stress. The authors claimed that the yield stress does not really exist, but it is a
consequence of the limitations of the measurement system, and when it is possible to
make measurements at very low shear rates, a large but finite viscosity is always found,
i.e. zero-shear viscosity (η 0 ).
The findings of the present work, however, support the idea expressed by Buscall et al.
(1987) among others, that yield stress virtually exists in concentrated systems since they
behave so shear-thinning that a small increase in shear stress, in a critical range, leads to a
decrease in viscosity from a very large value (~106) to a value of the order of 1 Pa s.
In Paper II, data are presented for tomato suspensions subjected to low shear rates. The
first part of the study was dedicated to the identification of the yield stress using creep
measurements. Figure 24A shows the typical response of the transient shear rate as a
function of shearing time. The response is different when different levels of stress are
applied, and three kinds of behaviour have been identified: a) below the yield stress (σ <
σy), b) at low stresses (σ ~ σy) and c) at high stresses (σ >> σy):
a) for σ < σy, the initial response of the system is to exhibit a shear rate below 10-2 s1
followed, at later times, by a marked decrease in the shear rate over several
decades down to ~10-4 s-1, where the measurements become unstable, and the
system basically deforms as a solid.
38
b) for σ ~ σy, the system will begin to flow, at an initial shear rates ranging from 10-2
s-1 to 10-1 s-1. The variation in the shear rate with time is then limited to values
within the same order of magnitude.
c) for σ >> σy, the system begins to flow at shear rates ranging from 10-1 s-1 to 100 s1
, and at long times, a sudden increase in the shear rate over one or more decades,
up to 101 s-1, takes place.
1
Apparent
d γ shear
/d t [1/s] rate [1/s]
A
10
10
10
10
10
η [Paviscosity
s]
Apparent shear
[Pa s]
10
50
89
119
158
211
281
0
−1
−2
−3
−4
0
10
1
2
10
10
t [s]
3
10
6
10
4
10
2
10
0
10 −6
10
4
10
Time [s]
B
−4
10
−2
10
[1/s]
Apparentdγ/dt
shear
rate
0
10
2
10
[1/s]
Figure 24. A) Evolution of the shear rate (s-1) as a function of the shearing time at constant stress (see
legend), and B) apparent shear viscosity as a function of the shear rate, of a HB tomato paste. The dashed
grey lines represent the intervals of shear rates limiting the different rheological responses, see the text.
(Adapted from Paper II.)
The different behaviour described above was observed in HB and CB pastes, at different
concentrations and with different particle sizes. The magnitude of the shearing stress,
however, varied with the parameters mentioned. The behaviour shown in Figure 24A is
interpreted as proof of yielding. Similar behaviour has recently been reported for peanut
butter during creep tests (Citerne et al., 2001).
It is interesting to compare this curve with the more common flow curve, shown in
Figure 24B, where the grey lines represent the intervals of shear rates limiting the
different rheological responses (a, b, c). Considering that the suspensions deform
elastically below the yield value, as stated above, it seems uncertain whether the zeroshear viscosity in the flow curves really exists for this type of suspension. The shear rates
measured in this region may instead be interpreted as a local rearrangement of the
network structure, i.e. elastic deformation, rather than flow (Macosko, 1994).
39
Moreover, the flow curve shows a discontinuity in the shear rate interval between 10-1
and 100 s-1, which corresponds to a sudden increase in shear rates over time in the creep
test. Similar discontinuities in the flow curves of concentrated suspensions and food
dispersions have been attributed to causes such as structural breakage or slip
phenomenon (De Kee et al., 1983; Tiziani & Vodovotz, 2005; Qiu & Rao, 1989).
Tomato suspensions are likely to exhibit slip at the wall, and this may be the case here.
The magnitude of the yield stress increased after homogenisation, for a given water
insoluble solids (Papers I and II, Fig. 25A), and was significantly higher in HB than in
CB pastes (Paper IV), as reported previously by others. In the monodisperse colloidal
suspensions studied by Buscall et al. (1987), the yield stress increased with decreasing
particle size at a given volume fraction of particles (Fig. 25B), as was also observed in the
present work. Upon homogenisation, the nature of the network changes and the bonds
of the network probably increase in number and strength. Buscall et al. (1987) found that
about 40% of the bonds may already be broken prior to yielding.
2
10
B
1
10
Yield stress [Pa]
Dynamic yield stress [Pa]
A
0
10
−1
10
Increasing particle size
bh
ah
−2
10
−1
10
0
10
WIS [%]
1
10
Volume fraction [-]
Figure 25. A) Yield stress as a function of the concentration (WIS) for HB suspensions, before (●) and
after (○) homogenisation. (Adapted from Paper II.) B) Interpretation of the results of Buscall et al. (1987).
5.1.3
Time dependency
In time-independent materials, the rheological response is instantaneous, whereas in
time-dependent materials, the response to the applied mechanical forces is delayed.
Constant shear forces can induce changes in the aggregate structure by altering the
interaction forces between the particles (Macosko, 1994), which gives rise to gradual
40
changes in viscosity. Materials are then classified as thixotropic, if their viscosity
decreases as a function of time at a constant applied shear rate, or as rheopectic, if the
viscosity increases with time, at a constant applied shear rate.
The changes in the microstructure of the suspensions induced by prolonged shearing,
include the breakage of the network into smaller flocs. The subsequent recovery of the
initial structure can take an extremely long time, and might not take place through the
same intermediate states, giving rise to a complex shear history dependence (Macosko,
1994). The forces governing the time-dependent behaviour arise from the balance
between the structural breakdown due to shearing forces, and the build-up due to
attractive forces during collisions and Brownian motion (Barnes, 1997). In flocculated
systems, thixotropy can also result from the orientation of the fibres in the flow
direction. Marti et al. (2005) studied the relation between the time-dependent rheological
behaviour and the well-defined structure of a mixture of spheres and fibres in a
suspension. They found that these particulate suspensions exhibited rheopectic
behaviour at short times and thixotropic behaviour at longer times, the former being very
pronounced only when anisotropic fibres were present in the suspension.
The rheological behaviour of concentrated suspensions, including foodstuffs, is
influenced by the shear history of the sample (De Kee et al., 1983, Cheng, 1986), and
already in 1965, Harper and Sahrigi (1965) found that tomato concentrates exhibited time
dependency. De Kee et al. (1983) studied the behaviour of tomato juice following
prolonged shearing, and found that it exhibited rheopectic behaviour (time-thickening) at
short times, and thixotropic behaviour (time-thinning) at longer times. This behaviour
has also recently been observed by others (Tiziani & Vodovotz, 2005). Detailed reviews
on thixotropy can be found elsewhere (Mewis, 1979; Barnes, 1997).
The second part of the study described in Paper II was concerned with the timedependent rheological properties of tomato suspensions subjected to low and high shear
stresses, taking into account the effect of particle size and concentration.
41
Time dependency at low deformations
At stresses just beyond the yield stress, the transient viscosity is found to increase and
reaches a steady-state value at rather low deformations, γ < 5, in non-homogenised
systems. In homogenised suspensions, the increase in viscosity is more pronounced, and
a peak is observed at high concentrations. The steady-state viscosity is achieved at
relatively larger deformations, i.e. γ > 10 (Fig. 26) for most concentrations.
4
4
10
A
Apparent shear
viscosity [Pa s]
η [Pa.s]
η [Pa.s]
Apparent shear
viscosity [Pa s]
10
3
10
2
10
1
10
0
10
0
B
3
10
2
10
1
10
0
5
10
γ [−] [-]
Deformation
15
10
20
0
5
10
γ [−]
Deformation
[-]
15
20
Figure 26. Transient viscosity as a function of the deformation in HB paste, A) before homogenisation,
and B) after homogenisation, at different concentrations: 50 (long dashed), 40 (dotted), 30 (dash-dotted)
and 20 (solid) % (higher viscosity corresponds to higher concentration). (Adapted from Paper II.)
This initial rheopectic behaviour of the material is characteristic of fibre suspensions and
has been attributed to a combination of causes. According to Marti et al. (2005) these
may be: i) the formation of slip layers leading to very low start-up viscosity readings, ii)
the hindrance of fibre rotation by neighbouring fibres, and iii) the delayed response of
the sheared material due to the elastic properties of the fibre network.
In the present work, it is suggested that the orientation of the fibres in laminar flow can
be described geometrically, following Jeffery orbitals (Jeffery, 1922)
⎛
γ&t
tan θ = a p tan ⎜
⎜a +1 a
p
⎝ p
⎞
⎟ + tan θ 0 .
⎟
⎠
(10)
In the tomato suspensions studied here (Fig. 26), the steady-state viscosity is normally
reached at γ < 5 before homogenisation and at γ > 10 after homogenisation, which
42
would correspond to aspects ratios of the order of 1 to 3 and 10 to 30, respectively.
These aspect ratios are found to be in qualitative agreement with those obtained using
microscopy, reported in Section 3.3 and Paper III, for non-homogenised suspensions
with an aspect ratio of ~1.5 while the flocs formed after homogenisation and subsequent
shearing had a value of ap of ~10.
Time dependency at large deformations (σ >> σy)
Finally, the behaviour of tomato suspensions at large deformations was studied (Fig. 27).
Before homogenisation, the transient viscosity seems to level off at a steady-state value,
whereas that of homogenised suspensions tends to decrease gradually, even at very large
deformations. In the first case, the system seems to become stable, i.e. time-independent.
In the second case, the constant decrease in viscosity at large deformations indicates
particle rearrangement (i.e. instability of the system), which is suggested to be caused by
flocculation. As indicated by microscopy (Section 3.3), when the system is subjected to
shearing, the network is gradually disrupted into apparent aggregates, consisting of
densely packed particles. These results suggest that homogenisation increases the
susceptibility of the structured suspensions to disrupt into smaller aggregates/flocs under
shear.
3
3
300 σ=6
300 σ=8
400 σ=10
400 σ=12
400 σ=15
400 σ=20
500 σ=30
500 σ=45
500 σ=50
A
2
η [Pa.s]
10
10
2
10
1
1
10
10
0
10
300 σ=15
300 σ=30
400 σ=26
400 σ=30
400 σ=65
500 σ=45
500 σ=50
500 σ=65
B
η [Pa.s]
10
0
0
200
400
γ [−]
600
800
10
1000
0
200
400
γ [−]
600
800
1000
Figure 27. Transient viscosity as a function of the deformation in HB paste, A) before homogenisation,
and B) after homogenisation, at different concentrations 500, 400, 300 and 200 g/kg (see legend). The
different stresses used are indicated in the legend in Pa. Adapted from Paper II.
43
Combining the information discussed here, with the microscopic images, suggests that
the presence of fine particles, caused by homogenisation of the tomato suspensions,
plays a major role in determining the time-dependent behaviour of these suspensions
(Fig. 28). Yielding of homogenised suspensions requires higher stresses magnitudes or, in
other words, the strength of the network is enhanced by homogenisation, and more
bonds must be broken before the system overcomes the yield stress and begins to flow.
It is interesting to note that about 40% of the bonds in the structure may be broken just
prior to yield (Buscall et al., 1987). When applying relatively low shear stress (σ ~ σy), a
rheopectic response is seen, which might be related in part to rearrangement of the
particles, and in part to a delay in the response due to the remaining elastic properties of
the network. At these low stresses the system seems to reach an apparent steady-state
viscosity after times of about 30 min. It is however not possible to exclude further
rearrangements of the particles if a longer time frame is considered. Finally, prolonged
and intense shearing gives rise to the formation of flocs of densely packed particles. The
illustrations on the left side of the figure (Fig. 28), before shearing, would correspond to
the images in Figure 12 (non-sheared, H0, H3), whereas the right side of the drawing
Particle size
instead corresponds to the images in Figure 12 (sheared, H0, H3).
Random
distribution
Initial rheopectic
behavior
behaviour
App. steady-state
viscosity
Floc
densification
Deformation and/or Stress
Figure 28. Illustration of the behaviour of concentrated suspensions with predominantly coarse or
predominantly fine particle, upon the application of prolonged shear at small and large deformations.
44
5.2 Measurement systems
There are a large number of instruments and geometries capable of measuring the
rheological properties of fluids, and their different principles, applications and limitations
have been covered in a number of books (e.g. Macosko, 1994; Steffe, 1996). In this work,
a tube viscometer with three diameters, and a rotational rheometer with three geometries:
concentric cylinder, vane and vane-vane were used. Their principles and main governing
equations will be described in the following sections.
5.2.1
Rotational rheometers
The concentric cylinder rheometer was developed at the end of the 19th century by
Couette. Today most instruments have a basic geometry that consists of a static cup, and
an inner rotating cylinder. The equations relating the shear stress to the torque
measurements (Mi), and the shear rate to the angular velocity (Ω) are obtained under the
assumptions of steady, laminar, isothermal flow, and with no end or gravity effects. The
shear stress and the shear rate are defined as follows:
σ rθ =
γ& =
Mi
2πRi2 h
(11)
Ω(RO + Ri ) / 2
RO − Ri
(12)
where Ri and Ro are the radius of the bob and cup, respectively and h is the height of the
bob. Common problems encountered in the use of this geometry are end effects,
disturbance of the flow by the presence of particles, wide gaps with a shear rate gradient
across the gap, and wall slip.
Modifications to the concentric cylinder geometry are useful when studying fluids
containing large particles. These modifications can also prevent slippage at the walls to
some extent. The vane geometry is known to reduce or eliminate these two problems
(Nguyen and Boger, 1992; Barnes, 1999), and simultaneously minimises the amount of
disturbance when it is introduced into a complex fluid. The use of vane geometry in the
yield stress measurements of food suspensions has become increasingly popular (Yoo, et
al., 1995), and recently its use has been extended to the measurement of other rheological
45
properties (Krulis & Rohm, 2004). A detailed review of the use of the vane geometry is
available elsewhere (Barnes & Nguyen, 2001).
Geometries used for all measurements reported in Papers I-IV
A four-blade vane was constructed for measuring the rheological properties of
concentrated tomato suspensions in a smooth cup (Paper I-IV). A vane cup was also
constructed and this was only used in the study described in Paper IV (Fig. 29).
A
B
C
D
Figure 29. Schematic illustrations of: A) a concentric cylinder, B) the vane geometry, C) the previous
geometries inside the smooth cup, and D) the vane geometry in the vane cup.
The stress and shear rate calculations are based on the analysis carried out by Barnes and
Nguyen (2001).
1 ⎛ h 2⎞
⎜ + ⎟
σ = Mσ f = M
2πRi3 ⎜⎝ Ri 3 ⎟⎠
γ& = Ωγ f = Ω
−1
(13)
2 Ro2
.
Ro2 − Ri2
(14)
The conversion factors (σf, γf) from angular velocity (Ω) to shear rate ( γ& ), and from
torque (M) to shear stress (σ), depend on the geometry of the vane. These equations are
derived assuming that the material entrapped between the blades of the vane forms a
virtual inner cylinder. In fact, the vane does not form a “perfect” cylinder and, therefore,
46
the calculated conversion factors have to be slightly corrected. For this correction,
Newtonian syrup with a defined viscosity of 7.1 Pa s at 20°C was measured using both
the conventional concentric cylinder (d =25 mm) and the vane.
The vane cup was employed as it was thought that the slippage at the outer wall could be
avoided. It was constructed such that the radius of the virtual cylinder formed by the
blades in the cup, corresponded to that of the smooth cylinder (Fig. 29). The calibration
procedure followed was the same as in the vane geometry, and the conversion factors
were found to be equal (Table 6).
A tomato paste suspension was measured in the concentric cylinder (CC), the
vane+smooth cup (V) and vane+vane cup (VV), to investigate their performance on
non-Newtonian suspensions. The results were as expected (Fig. 30). The concentric
cylinder gave lower viscosity values probably due to slippage at the wall, while the
viscosity obtained with the vane+smooth cup and vane+vane cup coincided over a large
range of shear rates.
Table 6. Main characteristics of the geometries used in the rheometer.
σf
γf
Ri
Ro
h
Gap
Pa/Nm
1/s
mm
mm
mm
mm
Concentric cylinder
24998
12.25
12.5
13.6
37.5
1.1
Vane / Vane-Vane
24560
4.7
10.5
13.6
45.0
3.1
Type of geometry
10000
CC
V
VV
viscosity [Pa s]
1000
cc25
vane
outer
100
10
1
0.1
0.0001
0.001
0.01
0.1
1
10
100
1000
shear rate [1/s]
Figure 30. Comparison between viscosity measurements performed in a concentric cylinder, with the vane
geometry and smooth cup, and vane geometry in a vane cup on 30% tomato paste suspension.
47
In fact, earlier studies have already suggested that the behaviour of tomato concentrates
at low shear rates may be strongly influenced by secondary effects such as yield
phenomena, time dependency and wall effects, i.e. slippage (Harper and El Sahrigi, 1965).
These effects are related to each other (Windhab, 1988), and they all complicate the
measurement of the rheological properties in common rotational rheometers. The
remaining part of this thesis is devoted to discussing common problems that occur
during the determination of the flow behaviour of concentrated suspensions.
5.2.2
Tube viscometers
Tube or capillary viscometers were developed in mid 19th century to measure the
viscosity of fluids under laminar conditions. Advances in the field of small-bore tubing,
which allowed precise determination of the tube diameter, were key to the development
of this technique (Macosko, 1994). This was important because the viscosity depends on
the tube radius to the power four.
Compared with rotational rheometers, tube viscometers have the advantage of being able
to measure particulate suspensions, i.e. with large particles, in an interval of shear rates
that is relevant for food processing, i.e. 100 < γ& < 1000 s-1. This is sometimes difficult to
achieved in rotational rheometers, as discussed above. Some drawbacks of using tube
viscometers are, however, the fact that they require large floor space and large amounts
of sample.
Tube viscometers employ a pressure-driven flow, which creates a velocity gradient
through the tube, with the maximum velocity at the centre of the pipe. The pressure
drop and volumetric flow rate are measured and converted to shear stress and shear rate,
respectively. The main assumptions in the derivation of rheological data for
incompressible fluids are:
-
fully developed, steady-state, laminar flow in the pipe,
-
velocity only in the length direction (x), and
-
no wall slip, the velocity at the wall is zero, vx(R)=0.
48
The shear stress at the wall (σw) can be derived from a force balance over a cylindrical
fluid element giving Eq. 15,
σw =
RdP
2L
(15)
where R is the radius of the tube and dP is the pressure drop over a distance L. The
volumetric flow rate (Q) can be defined as:
R
R2
0
0
Q = 2π ∫ v x (r )rdr = π ∫ v x (r )dr 2 , or
Q=
(16a)
σw
πR 3
σ 2 f (σ )dσ .
3 ∫
σw 0
(16b)
where vx(r) is the velocity profile over the tube radius. The solution of Equation 16b
depends on the fluid model γ& = f (σ ) considered, and can be performed analytically for
some simple models (Steffe, 1996). In Table 7, some of the analytical solutions are
summarized.
Table 7. Analytical solution of Equation 16b, for some common fluid models.
Fluid model
γ& = f (σ )
Newtonian
σ /μ
Power law
(σ / K )1/ n
HerschelBulkley
⎛σ −σ y
⎜⎜
⎝ K
Analytical solution
Q=
1/ n
⎛ dP ⎞
Q = π⎜
⎟
⎝ 2 LK ⎠
1/ n
⎞
⎟⎟
⎠
πR 4 dP
8 Lμ
Q=
⎛ n ⎞ ( 3 n +1 ) / n
⎜
⎟R
⎝ 3n + 1 ⎠
1+1 n
2+1 n
3
2
2σ w (σ w − σ y )
π ⎛ 2L ⎞ ⎡σ w (σ w − σ y )
⎜ ⎟⎢
K ⎝ dP ⎠ ⎢⎣
1n
1+1 n
−
(1+1 n)(2 +1 n)
2(σ w − σ y )
⎤
⎥
(1+1 n)(2 +1 n)(3 +1 n)⎥⎦
3+1 n
+
Equation 16a reduces to the well-known Weissenberg-Rabinowitsch equation, and the
solution depends on the derivative of the logarithm of the flow rate and the wall shear
stress.
γ& = −
dv x
dr
=
σw
Q
πR 3
⎡
d ln Q ⎤
⎢3 +
⎥
⎣ d ln σ w ⎦
49
(17)
The problem of generating shear rate and shear stress data from capillary data (i.e. from
pressure drop and volumetric flow) is formulated, in Equation 16b, as a Volterra integral
equation of the first kind, and the solution may not be unique and may not depend
continuously on the data. This is known as an ill-posed inverse problem, and its
mathematical treatment can be complicated. Common non-linear methods are difficult to
apply because many local minima may exist and the result is thus very dependent on the
initial conditions.
Tube viscometers are useful for obtaining viscosity data for concentrated suspensions at
high shear rates, which might be difficult to achieve in other kinds of equipment.
However, some problems can be encountered in tube viscometer measurements:
a) entrance effects, b) compression of the material and pressure dependence, c)
deterioration of the material by prolonged shearing, and d) wall slip. Data corrections are
often required and the description of some of these corrections can be found elsewhere
(Steffe, 1996).
Tube viscometer set-up used (Paper IV)
A tube viscometer consisting of three pipes with different diameters, d0 = 20, 25, and 38
mm was constructed. The pressure drop was determined over a straight section of the
pipe with a length of L = 3.42 m. The pressure drop per unit length (dP/L) was checked
to be constant at a given flow rate, by estimating the pressure drop between points 1 and
3 (Fig. 31), which should be equal to the pressure at point 1 dP1−3 = P3 − P1 = P1 , and
hence the entrance pressure losses were assumed to be negligible.
2
1
P
ø 25
P
P
ø 20
P
P
ø 38
P
3
3420 mm
Figure 31. Schematic diagram of the experimental set-up for the determination of rheological properties in
tube flow.
50
The system was first calibrated with several Newtonian syrups with different viscosities,
and was found to perform very accurately (Fig. 32).
Shear stress [Pa]
400
300
200
100
0
0
100
200
300
400
Shear rate [1/s]
Figure 32. Shear stress as a function of the shear rate for 71.8ºBrix syrup at 19.6ºC, with a Newtonian
viscosity of 1 Pa s, measured in tubes of different diameters: 20, 25 and 38 mm ( ,
and , respectively).
The dotted line represents the “real” flow curve, measured in a rotational rheometer using concentric
cylinders.
5.3
Quantification of apparent wall slip and determination of
flow behaviour in the tube viscometer
The flow behaviour of complex suspensions in a tube viscometer may be affected by
apparent wall slip. The apparent slip is caused by the migration of the liquid phase
towards the fluid-wall interface (Martin & Wilson, 2005), because the particles can not
physically occupy the space adjacent to the wall (Kalyon, 2005). This leads to the
formation of a thin layer of less concentrated suspension at the wall, with a thickness of
the same order of magnitude as the particle size (Yilmazer & Kalyon, 1989). The slip
layer has a lower viscosity than the bulk fluid and distorts the velocity profile in the tube
(Fig. 33).
Apparent wall slip has been reported for food products such as tomato paste, apple
sauce, ketchup and mustard (Dervisoglu & Kokini, 1986). Tomato concentrates at
concentrations of 12 ºBrix exhibited slip velocities from 2 to 12 cm/s at shear wall
stresses below 20 Pa, and the flow rate governed by the slip was as high as 80% of the
51
total flow (Lee et al., 2002). The occurrence of slip at the wall results in a lower resistance
to shear, which gives rise to the underestimation of the fluid viscosity. This becomes a
major problem for food engineers when designing industrial equipment based on
rheological data obtained in the presence of slip.
No slip
r=R
σ > σy: bulk shear
σ < σy: plug flow
r=0
vt
Slip
r=R
δ slip layer, high shear
vs
σ > σy: bulk shear
σ < σy: plug flow
r=0
vt
Figure 33. Velocity profiles in a tube viscometer, for a fluid with yield stress, with no slip and under wall
slip conditions.
5.3.1
The classical Mooney method
Mooney (1931) suggested a method for the correction of wall slip based on the
assumption that the slip velocity (vs) is a function only of the wall shear stress,
vs = β (σ w )σ w
(18)
where β is the slip coefficient. The measured flow (Qm) can be divided into two parts,
one due to the slip velocity (Qs), and the other due to the shear rate in the fluid (Qws),
Qm = Qs + Qws = v sπR 2 +
σw
πR 3
σ 2 f (σ )dσ
3 ∫
σw σ
y
By combining Equations 18 and 19, and dividing by 1 σ wπR 3 , he obtained,
52
(19)
σ
Qm
β 1 w 2
=
+
σ f (σ )dσ
σ wπR 3 R σ w4 σ∫y
(20)
Generally, the Mooney graphical correction requires measurements in tubes of at least
three diameters. At a constant wall shear stress, the slope of a plot of Qm σ wπR 3 against
1/R is equal to the slip coefficient β. In practice, it is difficult to obtain data in the tube
viscometer at the same wall shear stress, and the rheological behaviour of the
suspensions must be interpolated and/or extrapolated (Fig. 34A).
0.00025
0.025
A
545
578
611
643
676
709
741
774
807
839
B
0.020
0.00020
Qm
σ wπR 3
0.00015
Qm
0.00010
0.00005
0.015
0.010
0.005
0.00000
400
600
800
1000
0.000
1200
50
σw
60
70
80
90
100
110
120
1/R
Figure 34. Example of the Mooney method for slip correction. A) Tube viscometer data from HB tomato
paste, obtained at different tube diameters 20 mm (●),25 mm (∆) and 38 mm (■). The grey lines represent
the extrapolation made to obtain the Mooney plot shown in B)
Qm σ wπR 3 as a function of 1/R., the
extrapolated wall shear stresses are given in the legend in Pa. (Adapted from Paper IV.)
The dependence of the slip velocity on the wall shear stress was obtained for HB tomato
paste (100%) following the Mooney procedure: v s = 3 ⋅10 −15 σ w4.6 , and the result was of
the same order of magnitude as other published data (Kokini & Dervisoglu, 1990).
However, the Mooney method has been found to fail in some fluids, especially in pastes,
when the Mooney plot does not give linear slopes (Martin & Wilson, 2005), or when the
slope becomes negative. This might arise from the required extrapolation or interpolation
of data, as well as from the inherent poor reproducibility of concentrated suspensions.
This problem was encountered when analysing the CB paste (Paper IV).
53
5.3.2
A numerical method of quantifying slip and flow behaviour
Recently, Yeow et al. (2000) developed a new method to extract rheological data from
tube viscometers in yield stress fluids, using inverse problem solution techniques and
Tikhonov regularization. It has been reported to work on fruit purees with no slip (Yeow
et al., 2001). Later, the method was extended to cope with the presence of wall slip
(Yeow et al., 2003), based on the Mooney analysis, with the advantage that it uses the
whole set of data without any need for extrapolation, and does not require the
assumption of any rheological or slip model. Martin and Wilson (2005) applied this
numerical method to published data for polymers, foams and pastes, and found that the
method worked well on polymers and foams, but not as well on pastes. The same
numerical method was applied in the present work (Paper IV) in order to quantify the
wall slip and to obtain the flow behaviour of dried potato fibres suspended in low- and
high-viscosity syrup, as well as in tomato paste suspensions made from hot and cold
break pastes.
The numerical method used will be referred to as the Mooney-Tikhonov method. The
Mooney equation (Eq. 20) can also be written in the form of apparent shear rate γ&ac as,
σ
c
4v (σ ) 4 w
⎛ 4Q ⎞
γ& = ⎜ m3 ⎟ = s w + 3 ∫ γ& (σ )σ 2 dσ .
R
σ w σy
⎝ πR ⎠
c
a
(21)
The first part is the contribution of the wall slip to the shear rate, and the second part is
that of the shear flow. To apply the Mooney-Tikhonov method, the interval between the
minimum and maximum values of σw in the set of data was divided into Nj uniformly
spaced points, and the unknown slip velocities at these points were represented by a
vector vs=[v1, v2,…vNj]. In the same way, the integration interval (σy to σw) in Equation 21
was divided into Nk uniformly spaced points, and the unknown shear rates at these
points were represented by the vector γ& =[ γ&1 , γ& 2 ,… γ& N k ]. The precision of the solution
was evaluated by the sum of the squares of the deviation between the calculated solution
(superscript c) and the experimental measured data (superscript m),
54
⎡ γ&am,i − γ&ac,i ⎤
S1 = ∑ δ = ∑ ⎢
⎥
m
i =1
⎣⎢ γ&a ,i ⎦⎥
ND
2
2
i
(22)
and to ensure that the shear rate γ& (σ ) and the slip velocity v s (σ ) functions varied
smoothly with the local stress, the sum of the squares of the second derivatives of these
two functions, at the internal discretization points, was minimised,
S2 =
4
Rmin
⎛ d 2 vs
⎜⎜
∑
2
p = 2 ⎝ dσ w
N j −1
N k −1
⎞
⎛ d 2γ& ⎞
⎟⎟ + ∑ ⎜⎜
⎟ .
2 ⎟
⎠ p q =2 ⎝ dσ ⎠ q
(23)
Tikhonov regularization minimises a linear combination of these two quantities,
R = S1 + λ S 2 ,
(24)
where λ is an adjustable numerical factor. For example, a large value of λ favours the
smoothness conditions over the goodness of the fit. The condition that the shear rate is
zero at the yield stress should also be satisfied, and is solved iteratively for γ& (σ y ) = 0 .
Comparison between the classical Mooney method and the Mooney-Tikhonov
method
Paper IV describes a study on the flow behaviour of dried fibre suspensions exhibiting
liquid-like behaviour (G′<G′′), and tomato paste suspensions exhibiting solid-like
behaviour (G′>G′′). The uncorrected tube viscometer data, in the form of wall shear
stress as a function of the apparent Newtonian shear rate, are shown in Figure 35.
It was first determined whether slip occurred by testing if the mean rheological data was
different in different tube diameters, using a t-test. When the t-test was significant,
slippage was assumed to be present (cf. predicted behaviour in Table 8). The solutions
obtained by the application of the classical Mooney method, i.e. graphical procedure,
were then compared with the approximation given by the Mooney-Tikhonov numerical
method. The results are summarised in Table 8.
55
1200
1200
A
B
1000
Wall shear
stress
[Pa]
wall shear
stress
Wall shear
wall shear
stressstress
[Pa]
1000
800
600
400
200
800
600
400
200
0
0
0
100
200
300
400
500
600
0
100
200
300
400
500
600
apparent shear
Apparent Newtonian
shearrate
rate [1/s]
apparent shear
Apparent Newtonian
shearrate
rate [1/s]
Figure 35. Uncorrected tube viscometer data expressed as wall shear stress plotted against apparent
Newtonian shear rate for: A) dried potato fibre at different concentrations: 4.5 (◊), 5.6 (□) and 6.5% (Δ),
suspended in low-viscosity syrup (68 mPa s), and B) HB tomato paste suspensions, at different
concentrations: 100 (◊), 50 (□) 40 (Δ) and 30% (○). The data were obtained with three tube diameters: 20,
25 and 38 mm, corresponding to empty, grey and black symbols, respectively. Three replicate
measurements are shown. (Adapted from Paper IV.)
In the dried potato suspensions, where no slip or almost no slip conditions were
expected, the classical Mooney method tended to give low Qs/Qm values, in most cases,
with the contribution of slip gradually decreasing with increasing shear stress. The
Mooney-Tikhonov procedure gave somewhat higher Qs/Qm ratios for the highly viscous
solution, and negative values of slip velocity for the low viscosity dried fibre suspension.
The behaviour of the Qs/Qm ratio predicted by the numerical method is not gradual, but
usually showed a maximum at low stresses and decreased towards higher stresses (↑↓).
The negative values in the slip velocity give rise to too high calculated shear rate values,
and they tend to appear when no slip was present.
The Mooney method seems not to apply in most of the tomato paste suspensions, as it
results either in non-linear slopes or unrealistic slip flow, Qs/Qm >100%. These problems
could arise from the data extrapolation or from the inherently poor reproducibility of the
data. The error between repeated measurements was found to be acceptable, usually
below 10%, but in some cases it was as high as 17%. Such relatively high error values are
often reported for this type of system, as explained in Section 5.1. There is, however, a
notable exception where the classical Mooney method gave good results, i.e. in HB
tomato paste at 50 and 100% concentration (the latter shown in Fig. 34). The numerical
procedure gave negative slip values at almost all concentrations, except for the pure
56
tomato paste samples and the 50% CB suspension. The Mooney-Tikhonov method
tends to underestimate the slip velocity at high shear rates, resulting in too high
calculated shear rates.
Table 8. Estimation of wall slip using the classical Mooney graphical approach and the numerical MooneyTikhonov method in four series of suspensions: dried potato fibres in high viscous syrup (A) and low
viscous syrup (B) and HB and CB tomato paste at different concentrations. The predicted behaviour was
determined by comparing the mean rheological data between different pipe diameters using a T-test
(p<0.05). The calculated interval for the Qs/Qm ratio is given. (Adapted from Paper IV.)
Predicted behaviour
t-test
Classical Mooney
Mooney-Tikhonov
Qs/Qt (%)
f(σ )b
Qs/Qt (%)
f(σ )c
No slip
1.4 – 14 a
↑
5 – 23
↓
No slip
6.9 –
15 a
→
3 – 43
↑↓
6.3 –
20 a
↓
0 – 15
↑↓
Fibre suspension
A-4.5 %
A-5.6 %
*
A-6.5 %
No slip
B-4.5 %
Slip
8 – 27
↓
vs<0
x
*
B-5.6 %
Slip
0 – 37
↓
vs<0
x
*
B-6.5 %
Slip
1 – 65
↓
1 – 17
↓
HB-30 %
Slip
>100
x
vs<0
x
*
HB-40 %
No slip
>100
x
vs<0
x
*
HB-50 %
Slip
7 – 86
↓
vs<0
x
*
HB-100 %
Slip
27 – 69
↑
3 - 88
↑↓
CB-30 %
Slip
n. l. σ >32 Pa
x
vs<0
x
*
CB-40 %
Slip
n. l. σ >77 Pa
x
vs<0
x
*
CB-50 %
Slip
n. l. σ >130 Pa
x
0 - 23
↓
*
CB-100 %
Slip
>100 x
x
3 - 119
↑↓
*
Tomato paste
a Only
b
two diameters were used
variation of Qs/Qt as a function of σ. ↑ increases, → no variation, ↓ decreases, x no physical meaning
n.l. non linear
* too high calculated shear rates
Since reasonable results were obtained for the 100% HB tomato paste using both the
classical Mooney and the numerical Mooney-Tikhonov methods, the corrected shear rate
values calculated using both methods are compared in Figure 36. Note that the former
method predicts much lower shear rates in the fluid than the measured ones, e.g. at
σw~1100 Pa, the uncorrected shear rate was slightly more than 200 s-1, whereas after slip
57
correction it is only ~50 s-1. The too high shear rates calculated with the MooneyTikhonov method are obvious in the flow curve (Fig. 36), as the shear rates are larger
than the measured ones.
σw
Wall shear stress [Pa]
1200
1000
800
600
400
200
0
0
50
100
150
200
250
300
350
Apparent shear
rate [1/s]
dγ/dt
Figure 36. Uncorrected tube viscometer data expressed as wall shear stress plotted against the apparent
Newtonian shear for different tube diameters (20 ( ), 25 ( ) and 38 mm ( ), and data after correction for
slip using the classical Mooney (dashed line) and the Mooney-Tikhonov methods (heavy line).
Comparison between data obtained in the tube viscometer and rotational
rheometer
A comparison between the tube viscometer data and rheological data (measured in a
rotational rheometer using different geometries) might give some insight into the “real”
flow and slip behaviour of these suspensions. In the rotational rheometer, different
geometries were used to obtain different degrees of slippage on the rheometer walls (Fig.
29). The concentric cylinders had smooth walls and the tomato paste was expected to
exhibit wall slip. The vane was expected to prevent slip on the inner wall of the cylinder,
while slip might occur on the outer wall (i.e. at the cup wall) when high stresses were
applied (see Section 5.1.2). The vane-vane geometry was constructed to prevent slip on
the outer wall.
In Figure 37, the flow curves of 100% HB tomato paste, expressed as shear stress as a
function of the shear rate, are shown for each of the measurement systems used. The
58
flow curves corrected for slip by the classical Mooney and Mooney-Tikhonov methods
are also included. It is interesting to note that the tube viscometer data corrected for slip
by the classical Mooney method correspond well with the rheological data obtained using
the vane and vane-vane geometries. The concentric cylinders with smooth walls gave
similar values at very low shear rates, γ& <2.5 s-1, but the values deviated considerably at
higher shear rates, giving values even lower than those obtained from the uncorrected
data in the tube viscometer, which seems to indicate that the slip in concentric cylinders
is substantially greater than in the tube viscometer.
σ
Wall shear stress [Pa]
10000
1000
100
1
10
100
1000
dγ/dt rate [1/s]
Apparent shear
Figure 37. The flow curves, expressed as shear stress as a function of the shear rate, for 100% HB tomato
paste obtained using different systems: tube viscometer with different diameters (20 ( ), 25 ( ) and 38 mm
( ), uncorrected data), and a rotational rheometer using different geometries: concentric cylinders (-), vane
(x), vane-vane (*). The classical Mooney correction (
) and the Mooney-Tikhonov (
) correction are
included.
5.4
Comparison of dynamic rheology and flow behaviour
–The Cox-Merz rule
In highly concentrated suspensions, dynamic oscillatory measurements are easier to
perform experimentally (Doraiswamy et al., 1991), and show better reproducibility, than
steady shear measurements. Moreover, dynamic experiments on food materials such as
mayonnaise, which often exhibit apparent wall slip in steady shear, have been found to
give true material properties when small strain amplitudes <1% were used, with no
detectable wall slip distorting the results (Plucinski et al., 1998). In 1958, Cox and Merz
59
discovered an astonishingly simple and empirical relationship between the steady shear
viscosity η (γ& ) and the complex viscosity η * (ω ) ,
η * (ω ) = η (γ& = ω ) .
(25)
The Cox-Merz rule holds for simple polymeric fluids, but is not reliable for more
complex and structured fluids such as crystalline polymers, concentrated suspensions or
gels (Larsson, 1999). Bistany and Kokini (1983) reported a lack of validity of this rule for
various types of food materials, such as butter, ketchup, margarine and cream cheese,
where they found that dynamic and steady shear data could only be superposed by using
a shift factor. The same type of shifting was used in data from tomato pastes (Rao &
Cooley, 1992), but no theoretical explanation was given. Recently, Muliawan &
Hatzikiriakos (2007) investigated cheese at different temperatures, and at low
temperatures they observed a shift between dynamic and steady shear data, that tended
to disappear when the cheese melted and lost its structure.
Small-amplitude oscillatory measurements tend to preserve the microstructure of the
material being tested (see Chapter 4), whereas steady shear measurements can induce
changes in the microstructure of the suspensions (see Section 5.1.3), disrupting the
network to some extent. This difference in the conservation of the microstructure might
explain the lack of agreement between the two types of data in complex structured food
materials.
For example, in Figure 35A complex and steady shear viscosities are plotted for a
suspension of dried potato fibres in highly viscous syrup. The Cox-Merz rule seems to
hold for this set of data. In the case of the 30% tomato suspension (Fig. 35B), however,
the complex viscosity is shifted to higher values than those of the steady shear viscosity.
The potato suspension exhibits liquid-like behaviour at all frequencies (G′<G′′) and
exhibits no yield stress. The tomato suspensions, on the other hand, exhibit solid-like
behaviour over the range of frequencies studied (G′>G′′), and had a yield stress. Hence,
the lack of a network structure in the dried fibre suspensions seems to be a key factor in
the validity of the Cox-Merz rule.
60
Apparent shear viscosity [Pa s]
Apparent shear viscosity [Pa s]
100
10
1
0.1
A
0.01
1
10
100
1000
100
10
1
0.1
B
0.01
Apparent shear rate [1/s]
1
10
100
1000
Apparent shear rate [1/s]
Figure 38. Complex viscosity ( ) and steady shear viscosity obtained in a tube viscometer with d=20 ( ),
25 (■) and 38 mm (▲), and a rotational rheometer with concentric cylinders (-), vane (x) and vane-vane
geometries (*), for: A) 5.6% dried potato fibres suspended in a syrup with viscosity 860 mPa s, and B) a
30% HB tomato suspension. (Adapted from Paper IV.)
Some theoretical work has also been devoted to extending the validity of the Cox-Merz
rule to concentrated suspensions with negligible yield stress (Gleissle & Hochstein, 2003)
and other materials with yield stress (Doraiswamy et al., 1991). The former researchers
modified the Cox-Merz rule to give:
η * (ω )
B (c v )
=
η ( B ⋅ γ& = ω )
B (c v )
= η (γ& = ω ) cv =0
(26)
where B is a shifting factor used to superpose the steady shear (η) and the complex
viscosity (η*) curves at a given concentration (cv) to the η or η* curves of the suspending
medium (cv=0). The equation works for situations where the particle-particle interaction
is negligible, i.e. the yield stress σy<<σ, and hydrodynamic effects dominate, i.e. relatively
high shear rates. However, it might be difficult to apply this procedure to real food
systems, such as tomato paste, because the suspending medium is not well defined and is
difficult to reproduce in a lab, since it includes a range of soluble materials such as sugars,
pectins and proteins, among others. In addition, series of tomato paste concentrations
made by dilution in water change the viscosity (Fig. 22) and probably the nature of the
suspending medium.
Doraswamy et al. (1991) developed a model that takes into account the elastic and
viscous behaviour typical of concentrated suspensions, which led to a modified Cox61
Merz rule (Eq. 27), which basically consists of the application of a shift factor to give an
“effective shear rate”. The equation was, however, only tested at γ& < 10 s-1,
η * (γ mω ) = η (γ& = γ mω )
(27)
where γ m is the amplitude of oscillating strain.
Comparison between dynamic and steady shear data
The shift factors used to superpose the complex and the steady shear viscosities, in hot
and cold break tomato pastes in the concentration interval between 30 and 100% were
calculated (Paper IV). The magnitude of the shift factors as a function of the yield stress
of the suspensions is given in Figure 39. The reference steady shear viscosity was that
measured with the vane-vane geometry, which seems to be free of wall effects (as
indicate in Section 5.3.2). The yield stress provides a measure of the structure of the
material. Interestingly, the shift factor is found to be about 0.1 for all the suspensions
studied, regardless of the concentration or the yield stress of the suspension. These
values are somewhat higher than those found in tomato pastes by Rao and Cooley
(1992).
Shift
factor
ξ [-]
shift
factor α
1.00
0.10
0.01
1.00
10.00
100.00
yield stress
Yield stress [Pa]
Figure 39. Factor ξ in the modified Cox-Merz rule,
η (γ& ) = η ∗ (ξω) , as a function of the yield stress for
HB (grey) and CB (empty) tomato paste suspensions at different concentrations.
62
These shift factors may allow the flow behaviour of the suspensions to be obtained using
oscillatory measurements, instead of the more common steady shear measurements,
which can be subject to a number of experimental errors. Dynamic data could then be
used in food processing design and engineering.
63
6. Conclusions
Processing of food materials, i.e. homogenisation and subsequent shearing, has a
considerable effect on the microstructure of the suspensions formed. These changes are
reflected in the textural and rheological characteristics of the processed foods. Structural
changes during processing seem to be related to the fractions of fine and coarse particles
present in the suspension, the viscosity of the suspending medium, and the
concentration.
The presence of fine particles results in marked time-dependent effects, which result
from the disruption of the network and the formation of elongated, densely packed flocs
of particles upon shearing. These effects are observed as rheopectic behaviour at low
deformations, caused by the tendency of the flocs to orient perpendicularly to the flow,
and as thixotropic behaviour at large deformations, with extensive disruption of the
network, densification of the flocs and an increase in the separation between them.
At high paste concentrations , the rearrangement of particles within the network induced
by processing is better reflected by values of the compressed volume fraction than the
magnitude of the elastic modulus obtained from small-amplitude oscillatory tests. The
relatively poor sensitivity of the elastic modulus to variations in the structure seems to be
a consequence of the suspensions being fully packed.
Tomato suspensions exhibit solid-like behaviour (G′>G′′), at concentrations as low as
10% tomato paste, which indicates the existence of a network, and the suspensions can
thus be described as weak gels. These suspensions are characterised by a yield stress,
below which the systems are found to deform elastically. Above the yield value, the
system begins to flow.
Tube viscometer measurements show that the flow behaviour of tomato paste is
substantially influenced by an apparent wall slip, which tends to disappear at lower
concentrations. Some difficulties are encountered in the extraction of the rheological data
using tube viscometers when wall slip is present.
65
7. Future Outlook
Basic knowledge on the mechanisms governing structural changes during processing and
their relationship to the textural and rheological properties of food suspensions is
desirable for the optimisation of industrial food processing. Some insights into these
relationships are given in this thesis, but further studies are required.
New approaches are needed, for example, to study and quantify the microstructure. The
use of confocal microscopy will allow the localisation of specific structural elements,
making it possible to follow their rearrangement in different stages of processing. In
addition, the visualisation of the material in three dimensions will be possible. Another
new technique, rheo-microscopy, may be useful to observe the structural changes taking
place on shearing and, at the same time, relate them to the rheological behaviour.
The process of homogenisation and its capacity to create different networks in the
material constitute an enormous field of investigation. The influence of the morphology
of the particles and the viscosity of the suspending medium requires further
investigation. Moreover, the investigation and understanding of the behaviour of
differently homogenised systems upon subsequent shearing are important in order to
prevent, or minimise, the loss of textural properties of products made using industrial
processes involving homogenisation.
The compressive volume fraction and its sensitivity in detecting small changes in the
microstructure of a suspension network should also be studied in greater depth, with the
aim of making it possible to measure the porosity of more concentrated suspension
networks.
Finally, the formation of slip at the wall in tube viscometers could be directly observed
and quantified using techniques such as magnetic resonance imaging (MRI) or
ultrasound. The comparison between direct observation of slip and the behaviour
predicted by Mooney and Mooney-Tikhonov analysis of the tube viscometer data will
give further insights into the “real” flow behaviour of these suspensions.
67
Acknowledgements
During the four years that it has taken to complete this degree, there have been many
people that have contributed in one way or another to this work. I would like to express
my gratitude to all of them.
I want to especially thank Eva Tornberg, my supervisor, for giving me the opportunity of
doing a PhD, and for her support and encouragement over the years, and her endless
enthusiasm about discussing every new result.
I want to thank also Ulf Bolmstedt, my second supervisor, for his positive and
supportive attitude over these years and for shearing his experience about the rheology
world. Fredrik Innings for good discussions and many comments that have made me
think about the results one more time. Also, for his invaluable help in the construction of
the rig equipment. Björn Bergenståhl, who gave me some interesting new thoughts for
interpreting the results in paper II. Petr Dejmek, always open for discussion, and I really
appreciate his help with the Matlab code used in the last paper. I would also like to thank
some undergraduate students that have helped me with part of the experimental work,
Pernilla Månsson and Peter Jansson.
The following companies are gratefully acknowledged for their financial support of this
work: Orkla Foods A/S, Tetra Pak Dairy & Beverage Systems AB and a number of
SMEs together with a regional EU fund. The SMEs are Sveriges Stärkelseproducenter,
Salico AB, Mariannes Farm AB, Kiviks Musteri AB and Reologica Instruments AB.
From them, I would like to thank Ene Pilman, for her support, and for bringing many
tomato samples to the department! Bengt Jakobsson, for revealing many secrets about
the potato fibres and bringing some samples every time I needed them. Mats Larsson,
who came over many times to check the rheometer, and answered all my questions about
it. And Anders Löfgren for shearing his experience about the rig with me. Many other
people from these companies, for many meetings and shearing of ideas.
69
Also, Mats Bergsten, who provided the pump for the rig measurements when I badly
needed it.
Many other people have contributed to this work in a more indirect way. My colleagues
at the department, especially my roommate Hanna, who insisted I could speak Swedish
and was very tolerant with my broken language, Carola for shearing the “writing a thesis
period” with me, Tomas who help me with some math problems, Mattias helping me
with some “tomato explosions” in the pilot plant, Margareta always knowinghow…mmmh well, I can not mention everyone, but all of you have contributed to create
a friendly and nice atmosphere at the department!
My lunch-mates, Roberto, Ramiro, Federico, Christine, and some other people that join
us from time to time, for these nice, relaxing breaks. Thanks also to all my friends for so
many parties, and Sunday brunches, and dinners…, in short, thanks for your friendship
and for making life so interesting! Maru, Mario, Laura, Eric, Jenny, Carol, Jamil and little
Erik, Roberto, Lotta, Christine, Lucho, Anders, Krike, Ramiro, and Javi. I would also like
to thank my friends in Barcelona, because no matter the time I have been away, I always
feel like nothing has changed when I’m back there.
I would also like to thank my parents, Arturo y Rosa, for their unconditional support and
love, despite they were not very sure what I was really doing in Sweden for such a long
period of time… Gracias por estar siempre ahí, tan cerca, a pesar de la distancia.
Thanks, Giuliano, for being you, always.
70
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76
I
Rheological and structural characterization of tomato paste and
its influence on the quality of ketchup
Bayod E., Willers, E. P., Tornberg E. (2007)
LWT - Food Science and Technology, In Press, DOI: 10.1016/j.lwt.2007.08.011
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Rheological and structural characterization of tomato paste and its
influence on the quality of ketchup
Elena Bayoda,, Ene Pilman Willersb, Eva Tornberga
a
Department of Food Technology, Engineering and Nutrition, Lund University, P.O. Box 124, SE-222 01 Lund, Sweden
b
Orkla Foods A.S, SE- 241 81 Eslöv, Sweden
Received 15 November 2006; received in revised form 27 August 2007; accepted 29 August 2007
Abstract
Three hot break tomato pastes were investigated to determine the effect of their characteristics on the properties of tomato ketchup,
processed in an industrial-scale facility (i.e. diluted, heated, homogenized and cooled). Pastes and ketchups were characterized by particle
size distribution, volume fraction, and rheological behavior in steady and dynamic shear. The ketchups were also subjected to sensory
assessment. The processing of pastes into ketchups induced large structural changes, which were reflected in all parameters studied. The
volume fraction of solids (f) accurately reflected the changes that the paste suspensions underwent during processing and it appeared to
be a good predictor of the flow behavior of both the pastes and the ketchups. The corresponding flow curves were found to be well
described by the Carreau model in a large range of shear rates and concentrations. However, the rheological characteristics of the
commercial pastes studied did not directly correlate to those of the corresponding ketchups. Instead, our results suggest that the change
in structure induced by processing might be governed by other properties of the paste, such as the fraction of small and large particles
and their sensitivity to breakage, together with the viscosity of the aqueous phase.
r 2007 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.
Keywords: Rheology; Structure; Tomato paste; Quality; Ketchup
1. Introduction
The viscosity of tomato ketchup is a major quality
component for consumer acceptance. Several parameters
contribute to the flow behavior of tomato ketchup,
including the quality of the raw material (i.e. tomato
paste) and the processing conditions. A high quality paste
and continuous control and adjustment of the variables for
processing it are thus required to achieve a constant and
desirable quality in the final product (i.e. ketchup).
Several researchers have shown that difficulties in quality
control arise from the great variation in flow behavior in
commercial tomato paste caused by different agronomical
and processing conditions (Sánchez, Valencia, Gallegos,
Ciruelos, & Latorre, 2002; Thybo, Bechmann, & Brandt,
2005). A number of studies have been conducted on the
rheological behavior of tomato products at low concentraCorresponding author. Tel.: +46 46 222 9808.
E-mail address: [email protected] (E. Bayod).
tions, resulting in evidence that many factors play a role in
determining the viscosity of tomato products, including the
degree of maturity, particle size and particle interactions,
content of solids as well as temperature of processing
(Beresovsky, Kopelman, & Mizrahi, 1995; Haley & Smith,
2003; Harper & El Sahrigi, 1965; Rao, Bourne, & Cooley,
1981; Sharma, LeMaguer, Liptay, & Poysa, 1996; Yoo &
Rao, 1994). However, for concentrated tomato products
such as tomato paste, few studies are available (Lorenzo,
Gerhards, & Peleg, 1997; Sánchez et al., 2002), probably
due to a number of measurement problems that occur
because of the high concentration of large particles, which
constitute the main structural component in the tomato
paste. Moreover, tomato paste exhibits complex rheological behavior, i.e. it is a non-Newtonian, shear-thinning and
time-dependent fluid that shows an apparent yield stress
(Abu-Jdayil, Banat, Jumah, Al-Asheh, & Hammad, 2004;
Rao et al., 1981).
Traditional devices used for quality control of tomato
products are the Bostwick consistometer and the
0023-6438/$30.00 r 2007 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.lwt.2007.08.011
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Brookfield viscometer. The former allows for an empirical
measurement of the distance that a specific volume of fluid
can flow under its own weight in a known interval of time.
This device provides a single point measurement and is
thus not suitable for concentrated products (Hayes, Smith,
& Morris, 1998; Marsh, Buhlert, & Leonard, 1980). The
Brookfield viscometer requires a discrete number of
measurements at different velocities to determine the
complete apparent flow curve. The measurements involve
a non-well-defined shear rate profile throughout the fluid
tested (Cullen, Duffy, & O’Donnell, 2001), which makes it
difficult to measure non-Newtonian fluids. However,
despite these problems, both methods are extensively used
by the food industry.
Although Bostwick and Brookfield readings successfully
predicted tube viscometry data according to Cullen et al.
(2001), it has been difficult to draw clear conclusions in
order to correlate consumer quality perception with data
obtained with these devices (Apaiah, Goodman, &
Barringer, 2001; Barret, Garcia, & Wayne, 1998). This
discrepancy has led to the use of a semi-empirical control
of tomato production that relies to a great extent upon the
experience of the operators.
An objective and well-defined method of quality control
would thus be highly useful in determining processing
parameters. For example, the extent of dilution can be
determined more accurately by having a better knowledge
of the effect of the flow behavior of the concentrated
tomato paste on the properties of the ketchup.
The goal of this study was hence to optimize tomato
paste processing into ketchup by improving the quality
control of both the raw material and the final product. In
this investigation the processing of tomato paste into
ketchup has been performed on an industrial-scale, which
makes the results immediately relevant for actual industrial
applications without any need for additional scaling-up.
Because the commercial tomato pastes used were similar
to and fulfilled the industrial specifications for the raw
material we were able to study the differences in the quality
of ketchups produced from slightly different raw materials.
This paper thus presents the results of a structural and
rheological study of tomato pastes and their processed
ketchups and of how these properties influence the
sensorial perception of the tomato ketchup.
2. Material and methods
2.1. Tomato paste
Three commercial hot-break tomato pastes purchased
from three Mediterranean producers were used in this
study. The commonly evaluated properties of the tomato
pastes are summarized in Table 1. All pastes fulfill the
specifications of quality for processed commercial ketchup.
The effect of the concentration on the rheological
properties of the pastes was studied in paste suspensions
of different concentrations, i.e. 1000, 400 and 332 g/kg. The
diluted suspensions were prepared by manually mixing
certain amount of paste in distilled water.
2.2. Processing of tomato paste into ketchup
The tomato paste was processed into ketchup in an
industrial-scale facility, with the paste content fixed to
332 g/kg suspension. The processing steps were (a) dilution
in water to the desired content of tomato paste, (b) mixing
with spices, vinegar, salt and sugar, (c) pasteurization,
(d) homogenization, (e) warm-filling into 1 kg-bottles and
(f) cooling to room temperature. The properties of the
tomato ketchups are also summarized in Table 1.
In order to study the effect of small variations in
concentration on the rheological properties of the ketchup,
the ketchups were further suspended in distilled water to
obtain a paste content of 300 and 265 g/kg suspension.
2.3. Dry-matter and water insoluble solids
Total solids (TS) were determined using a vacuum oven
at 70 1C (8 h). In order to determine the water-insoluble
solids (WIS), 20 g of product were added to boiling water
for the extraction of the soluble solids. The mixture was
centrifuged, and the supernatant filtered repeatedly until it
Table 1
The properties of the tomato pastes and ketchups, i.e. pH, soluble solids, Bostwick and Brookfield data, analyzed by the producers
pH
(–)
Soluble solids
(1Brix)
Bostwicka
(cm)
Brookfieldb
(cP)
Total solids
(g/kg wbc)
Water insoluble solids
(g/kg wbc)
Paste 1
Paste 2
Paste 3
4.2
4.3
4.2
22.870.3
23.270.8
22.570.9
4.570.1
3.470.2
4.170.2
–
–
–
245.074.5
257.071.5
237.078.1
55.870.8
62.673.1
65.574.2
Ketchup 1
Ketchup 2
Ketchup 3
3.8
3.8
3.8
26.270.1
26.570.6
27.170.4
3.170.1
2.870.1
2.870.2
237007141.0
241007141.0
2480071697
271.672.2
274.370.5
272.671.3
18.370.2
18.170.7
17.270.4
The total solids and water insoluble solids are also included.
a
Pastes were diluted to 8.31Brix, and the length of the measurement was 10 s; ketchups were non-diluted and measured for 30 s.
b
Brookfield viscometer, spindle no. 5, speed 10 rpm.
c
wb: wet basis.
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had reached a refractive index of about zero (Ouden, 1995).
The residue (WIS) was dried in an oven at 100 1C for 16 h.
2.4. Particle size distribution
The particle size distribution (PSD) was measured using
a laser diffraction analyser (Coulter LS 130, England),
applying the Fraunhofer optical model. Each sample was
run in duplicate. The area based diameter (d32) was defined
as
,
X
X
3
d 32 ¼
ni d i
ni d 2i ,
(1)
i
i
where ni is the percentage of particles with a diameter di.
The percentage of small (o10 mm) and large (4100 mm)
particles was obtained by integrating the particle size
distribution curve between the abovementioned limits. Cell
wall material distribution and form were studied using light
microscopy (Olympus BX50, Japan) with a magnification
of about 50, in at least six pictures for each sample.
2.5. Volume fraction
The samples were centrifuged at 110 000g for 20 min at
20 1C in an ultracentrifuge (Optima LE-80K, Beckman,
California) equipped with an SW41Ti rotor (tube diameter
d ¼ 2r ¼ 14 mm). The volume fraction of solids was
calculated as
f¼
Vs
,
Vt
(2)
2
where V s ¼ pr ð2=3r þ Ls Þ is the volume of solids and
V t ¼ pr2 ð2=3r þ Lt Þ is the total volume of the suspension.
The corresponding lengths (Ls and Lt, solids and total
length, respectively) were measured on the centrifuge tubes
using a vernier caliper.
The supernatant achieved was kept for further viscosity
measurements.
2.6. Steady-shear viscosity measurements
The viscosity of the supernatant was measured at 20 1C
in a controlled-stress rheometer (StressTechs, Reologica,
Sweden) equipped with a bob and cup concentric cylinder
(R0/Ri ¼ 27/25 mm).
The viscosity of the tomato pastes and ketchups was
measured at 20 1C in a controlled-stress rheometer
(StressTechs, Reologica, Sweden) equipped with a fourblade vane in order to eliminate the slip phenomenon. The
vane was 21 mm in diameter and 45 mm in height, and was
placed in a cup 27 mm in diameter. The vane was carefully
loaded at stresses below 0.8 Pa. Special care was taken to
minimize air inclusions in the sample.
All rheological measurements were carried out at least in
duplicate. The maximum relative standard error (RSE)
allowed between replicates was 5%, but in most of the
cases RSEE1%:
log Z log Z
1;_gi
2;_gi RSEð_gi Þ ¼ ,
ðlog Z1;_gi þ log Z2;_gi Þ=2
3
(3)
where Z is the viscosity and g_ is the shear rate of replicate
i ¼ 1,2.
To study the stress dependence of the viscosity, the
tomato suspensions were subjected to an increasing shear
stress in 100 intervals from 0.07 to 465 Pa. Each stress was
applied to the sample for 10 s to allow it to stabilize, and
then measurements were averaged during the following 10 s
of shearing. The flow curve measured in this way was
extrapolated to obtain the apparent yield stress. The
apparent yield stress was calculated using the mathematical
tool developed by Mendes and Dutra (2004), who defined
the apparent yield stress as the stress where the function
d ln s=d ln g_ reaches a minimum. Moreover, the apparent
viscosity (Za) of the suspension was described using the
Carreau model:
Z0
Za ¼
,
(4)
½1 þ ðlc g_ Þ2 N
where Z0 is the apparent zero-shear viscosity, lc is a time
constant and N is a dimensionless exponent. The parameters of the model were determined using the Matlab
function fminsearch, which performs a multidimensional
unconstrained nonlinear minimization (Nelder–Mead) of
the error (SSL), i.e. of the sum of squares of the logarithm
of the experimental and predicted values
SSL ¼
n
X
ðlog Zi log Zp Þ2 .
(5)
i¼1
2.7. Dynamic rheological measurements
Dynamic rheological measurement of tomato samples
was carried out in a controlled-stress rheometer (StressTechs, Reologica, Sweden) using the above-described
vane. The stress sweep tests at a frequency of 1 Hz were
carried out in order to determine the range of linear
viscoelastic response under oscillatory shear conditions.
The frequency sweep measurements under conditions of
linear viscoelasticity were performed at constant stress
amplitude (0.5 Pa in pastes and 0.1 Pa in ketchups) in the
range of frequencies 0.01–100 Hz. The measurements were
performed at least in duplicate.
2.8. Sensory analysis
The sensory analysis was performed by a non-trained
panel consisting of five females and three males. Each
tomato ketchup was subjected to evaluation of its textural
and sensorial (flavor and taste) properties. The descriptors
used in the evaluation, which are adapted from Tornberg,
Carlier, Willers and Muhrbeck (2005), are summarized in
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Table 2
Textural and sensorial parameters evaluated and descriptors used
Perception type
Attribute
Description
Texture before consumption
Spreadability
Elasticity
Grainy
Adherence
Color
Smoothness
Thickness
Tomato taste
Acceptance
The dish is bended to evaluate if the ketchup spreads quickly or slowly
Stickiness of the ketchup to a spoon when it is lifted from the plate
The product is spread in a thin layer to evaluate if dots occur
Adherence of the ketchup to the spoon when it is filled with product
Scale varying from yellow to red-brown
Surface smooth or rough
Thick or liquid texture based on pressing the ketchup on the palate
Scale varying from natural tomato taste to burned tomato taste
Evaluate if the ketchup is liked or not
Visual appearance
Texture after consumption
Overall acceptance
Table 2. All sensory attributes were evaluated in a scale
from 1 to 9 (low and high, respectively) on four samples,
consisting of three ketchups and one repetition. For
comparison, all four samples were served simultaneously
at room temperature.
2.9. Statistical analysis
An analysis of the variance (ANOVA) was performed to
evaluate the effects of processing and concentration on the
volume fraction and the rheological parameters (Minitab
v.14, 2003). The level of significance was set at po0.05.
Another ANOVA was carried out to assess the effect of
origin on the characteristics of pastes and ketchups. All
significant parameters were then analyzed by Pearson
correlation matrix to determine the independent variables,
which were further classified using principal components
analysis (PCA, Minitab v.14, 2003). The sensory data were
also analyzed using PCA (Minitab v.14, 2003).
3. Results and discussion
3.1. Changes in the structure, PSD and volume fraction
after processing tomato paste into ketchup
In Fig. 1, microscopic pictures show the structure of the
original paste and of the ketchup suspension after
processing. Fig. 1A reveals that the paste structure consists
mostly of whole cells with apparently intact cell walls,
along with some broken cells and cell wall material
suspended in an aqueous media. Fig. 1B shows that
processing the paste into ketchup induced significant
changes in the structure: few entire cells remained after
processing and those that did remain were generally small.
The ketchup suspensions mainly contain cell wall fragments and randomly distributed cellular material, and the
particles tend to aggregate becoming difficult to observe
them individually.
The PSD of both pastes and ketchups is shown in Fig. 2
as area-based diameter (d32). All samples of pastes and
ketchups exhibit at least a bimodal size distribution. In
tomato paste suspensions two main peaks are observed,
one at about 250 mm and the other at about 2 mm.
However, paste 1 appears to be differently structured
regarding the small particle fraction, with three peaks at 4,
8 and 27 mm, respectively. Concerning the ketchup suspensions, the PSD also shows two peaks, at about 75 mm and
at about 1 mm. While the PSD of the large particle region is
almost identical for the three ketchups, the small particle
region shows large differences between them, ketchup 3
being the one with the largest particles.
The percentage of large particles is shown to be
drastically reduced by homogenization. In the original
tomato pastes, the number of particles greater than 100 mm
was around 50% (determined as the area under the PSD
curve in Fig. 2), whereas in the ketchups this number was
reduced to about 20% by processing. In addition, the
percentage of small particles (o10 mm) was almost
doubled (Table 3). These changes appeared to be related
to the origin of the pastes (ANOVA, po0.03) in both
pastes and ketchups. For example, paste 2 has the highest
number of large particles, but its corresponding ketchup 2
shows few remaining large particles than the other
ketchups. These findings indicate that the different fractions (i.e. large and small particles) of the pastes have
different susceptibility to breakage during processing
depending on the paste origin. It has been reported in the
literature (Sánchez et al., 2002; Valencia, Sánchez, Ciruelos, & Gallegos, 2004) that the size of the particles in
ketchup did not depend on the screen size used during the
manufacture of tomato paste. As our findings indicated,
the size of the paste particles does not necessarily determine
that of the ketchup particles.
The volume fraction (f), determined by ultracentrifugation, is also reported in Table 3. Earlier results showed that
in paste suspensions the volume fraction was proportional
to the amount of paste (results not shown). However, in the
ketchups in the present study, f is higher than expected
according to the amount of paste, indicating that the
homogenization process has a large impact on the volume
occupied by the particles. Moreover, in pastes and
ketchups, the change in f was significantly different for
each origin (ANOVA, po0.03): i.e. while paste 2 showed
the larger f as a paste, its corresponding ketchup 2 resulted
in the lowest f. These findings thus indicate that processing
induces the particles to swell and also that the components
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Fig. 1. Microscopic pictures of typical suspensions of tomato paste (A) and tomato ketchup after homogenization (B). The bar is 150 mm.
of each paste have slightly different swelling properties.
The concentration of the suspensions was also calculated as
WIS (i.e. expressed as weight), but because the WIS value
resulted merely in a factor of dilution (Table 1) and did not
reflect the changes in structure after processing, we have
chosen to express concentration as f in the rest of this
study.
3.2. Changes in the rheological properties after processing
3.2.1. Viscosity of the supernatant
The supernatant of the pastes was non-Newtonian, and
thus their viscosity was calculated at 100 s1, being in the
range of 1.8–2.3 Pa s (Table 3). The continuous phase of the
ketchups was a Newtonian fluid, the viscosity of which
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significantly influence the value of the supernatant viscosity
(po0.04) in both pastes and ketchups.
4
3.5
diff. surf. area (%)
3
2.5
2
1.5
1
0.5
0
10-1
100
101
102
103
102
103
particle diameter (μm)
2.5
diff. surf. area (%)
2
1.5
1
0.5
0
10-1
100
101
particle diameter (μm)
Fig. 2. Particle size distribution of the original tomato paste (A) and the
corresponding ketchup after homogenization (B), for the three origins
studied: 1 (___), 2 (_ _) and 3 (. . . . . .). Two repetitions are shown.
Table 3
Volume fraction (f), percentage of small (o10 mm) and large particles
(4100 mm) and viscosity of the supernatant (Zs, RSEo1%) in both the
pastes and their corresponding ketchups
f
(–)
Particleso10 mm
(%)
Particles4100 mm
(%)
Zs
(Pa s)
Paste 1
Paste 2
Paste 3
0.5470.012
0.5970.003
0.5270.010
24.1970.08
27.9370.03
30.5370.04
51.4470.04
52.7370.08
47.0270.04
2.317
1.926
1.831
Ketchup 1
Ketchup 2
Ketchup 3
0.3770.017
0.3270.003
0.3470.002
46.4571.12
48.9870.06
46.2970.22
19.4070.39
16.4170.42
17.0370.74
0.015
0.012
0.012
ranged between 12 and 15 mPa s (Table 3). Since a sugar
solution of similar 1Brix would have 2.8 mPa s, the
increased viscosity must be due to other soluble components such as pectins. The origin of the paste does
3.2.2. The apparent shear-viscosity in pastes and ketchups at
different concentrations
The flow behavior of the suspensions is shown in Fig. 3
as the apparent shear viscosity as a function of the shear
rate. An initial Newtonian plateau is followed by a shearthinning region, which seems to change slope at shear rates
around 0.1–1 s1. According to Fig. 3 the apparent
viscosity (Za) of the suspension can be described using the
Carreau model (Eq. (3)). The parameters of the model are
summarized in Table 4. The viscosity data for both pastes
and ketchups could be acceptably predicted by the Carreau
model for various concentrations and a large range of shear
rates (Fig. 4), as shown in Table 4 the SSL being low.
Similar values for the Carreau parameters of tomato pastes
were reported by Valencia et al. (2003). It has to be noted,
however, that the Carreau model does not take into
consideration the second change of slope in the shearthinning region. This discontinuity of the flow curve, that
seems to be characteristic of concentrated suspensions, has
been discussed elsewhere (Tiziani & Vodovotz, 2005).
The apparent zero-shear viscosity Z0 is shown to be a
function of the concentration of the suspensions (f),
having a relationship of the type Z0 / f3:75 (R2 ¼ 0.92,
Fig. 4). The time constant l shows a weaker relationship
with the concentration (l / f1:49 , R2 ¼ 0.68). The N value,
which is related to the slope of the shear-thinning region, is,
however, independent of the concentration and is significantly lower for pastes (N ¼ 0.39) than ketchups
(N ¼ 0.41). No influence of the origin was reflected in
any of the Carreau parameters.
The results reported above are not consistent with either
Brookfield or Bostwick data (Table 1). For example, both
paste and ketchup 2 flow the shortest distance during the
Bostwick measurement, which only agrees with the Z0
determined in this study for paste 2 (being the highest), but
not for its corresponding ketchup (being the lowest).
Moreover, ketchup 1 has the lowest Brookfield viscosity,
which is the opposite of that observed by our rheological
measurements. As it has been discussed in the Introduction, these devices are not precise enough to notice small
differences of quality and should therefore only be used as
a gross test.
3.2.3. Effect of the concentration and processing on the
apparent yield stress
The yield stress is defined as the minimum stress required
by a material to initiate flow. The critical stress for the
onset of the shear thinning region (see arrows in Fig. 3) is
commonly used to characterize an apparent yield stress.
This parameter is related to the structure of the suspensions, and in gels it is an indicator of the strength of the
network. The apparent yield stress was plotted as a
function of the volume fraction in Fig. 4, showing a
relationship of the type sy / f2:06 (R2 ¼ 0.92). The yield
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106
105
Viscosity (Pa s)
104
103
102
101
100
10-1
10-6
10-4
10-2
100
102
Shear rate (1/s)
Fig. 3. Apparent steady-shear viscosity Za (Pa s) as a function of the shear rate g_ (s1) for a typical paste (filled symbols) and its corresponding ketchup
(empty symbols), at different concentrations (f): 0.54 , 0.21, ’, 0.18 m, 0.37 J, 0.33 x , and 0.26 }. The Carreau model (—) fitting is also shown.
Table 4
Carreau model parameters (apparent zero-shear viscosity Z0, time constant
lc, and exponent N) for pastes and ketchups at different concentration,
and estimation of the error of the fitting (SSL) based on Eq. (5)
Paste 1
Paste 2
Paste 3
Ketchup 1
Ketchup 2
Ketchup 3
f
(–)
Z0
(103 Pa s)
lc
(103 s)
N
(–)
SSL
(–)
0.54
0.21
0.18
0.59
0.23
0.19
0.52
0.21
0.17
486
11
3
742
23
11
662
21
9
11.5
2.7
1.6
26.8
4.5
4.9
18.4
4.8
4.2
0.41
0.40
0.40
0.37
0.41
0.40
0.38
0.40
0.40
1.6
0.6
0.4
0.7
0.7
0.6
0.2
0.3
0.1
0.37
0.33
0.26
0.32
0.29
0.23
0.34
0.31
0.24
50
40
28
43
29
26
43
42
30
4.4
4.5
3.1
4.4
4.3
3.6
4.7
5.3
3.4
0.41
0.42
0.43
0.41
0.42
0.43
0.41
0.41
0.43
0.3
0.3
0.4
0.3
0.3
0.2
0.2
0.2
0.3
The mean value of two replicates is given (RSEo5%).
value was significantly affected by processing and concentration (ANOVA, po0.05), i.e. it decreased by dilution
and, at the same paste content, increased by homogeniza-
tion. Regarding the origin, no differences were observed in
the case of pastes, but in the ketchups the yield value was
significantly different for each origin (ANOVA, po0.05),
being the higher value for ketchup 1 and the lowest for
ketchup 2.
3.2.4. Dynamic viscoelastic properties in the original pastes
and their corresponding ketchups
The linear viscoelastic region of the suspensions, i.e.
when G0 is independent of the stress, occurs in a range of
stresses between 0.01 and 20 Pa for pastes and 0.01 and
4 Pa for ketchups (Table 5). Under linear viscoelastic
conditions, the elastic modulus G0 is higher than the loss
modulus G00 for all the samples, indicating that the pastes
and ketchups behaved as gels. However, the pastes and
ketchups do not show the same trends with respect to their
origin (ANOVA, po0.05), i.e. paste 2 shows the highest
values for both moduli, but its corresponding ketchup 2
shows the lowest values. On the contrary, paste 1 shows the
lowest values as a paste, but its corresponding ketchup 1
results in the highest moduli. These facts might indicate
that different components in the paste behave slightly
differently under processing, giving rise to different networks. In addition, the phase angle shows no differences
between pastes and ketchups (ANOVA, po0.05) and the
average value was 11.871.31 for all concentrations, which
is low and indicates a strong network structure.
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8
1000000
0
100000
G'
10000
1000
100
y
10
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 4. Apparent zero-shear viscosity (Z0, Pa s), elastic modulus (G0 , Pa) and apparent yield stress (sy, Pa) as a function of the volume fraction (f) for
pastes (filled symbols) and ketchups (empty symbols) from different origins 1, 2 and 3 (J, &, W, respectively).
Table 5
Storage and loss moduli (G00 and G000 ), complex viscosity ðZ0 Þ and phase
angle (d), for both pastes and ketchups in the linear viscoelastic region,
determined during the stress sweep measurement (1 Hz)
f
(–)
G00
(Pa)
G000
(Pa)
Z0
(Pa s)
d
(1)
Paste 1
Paste 2
Paste 3
0.54
0.59
0.52
7124.2
10411.0
8817.7
1503.2
2363.9
2110.1
1160.1
1699.2
1475.3
12.0
12.8
12.5
Ketchup 1
Ketchup 2
Ketchup 3
0.37
0.32
0.34
732.9
526.7
565.7
184.9
118.7
130.7
120.3
86.1
92.4
14.2
12.7
12.6
Eqs. (6) and (7) are summarized in Table 6. At higher o,
the values of G0 and G00 were proportional to o0.1and o0.2,
in pastes and to o0.1 and o0.3 in ketchups. The behavior
observed in these suspensions seems to correspond to that
of ‘‘physical gels’’ or ‘‘weak gels’’, which falls between the
true gels characterized by covalent cross-linked materials,
and the concentrated suspensions, characterized by entanglement networks. Moreover, the ratio G00 =G 0 ¼ tan d is
in the order of 101 for both pastes and ketchups, whereas
that of true gels is in the order of 102 (Lizarraga, Vicin,
González, Rubiolo, & Santiago, 2006). The slope of log G0
vs. o hence indicates that the suspensions are strongly
aggregated gels (0.1on0 o0.2).
0
Both elastic (G0 ) and loss moduli (G00 ) as a function of the
frequency o (Fig. 5) indicate the same trends in pastes and
ketchups: G0 increased slightly with increasing frequencies,
whereas G00 remained constant or decreased slightly at low
frequencies (o), and then increased with o.
The mechanical spectra of model dilute solutions are
predicted by the general linear model to exhibit G 0 / o2:0
and G00 / o1:0 , with G00 4G0 and o-0. The mechanical
spectra of a gel, instead, are expected to be independent of
the o (Ferry, 1980; Ross-Murphy, 1988). Recently, it has
also been shown experimentally that during the sol–gel
transition, G 0 / o0:5 (Liu, Qian, Shu, & Tong, 2003). The
dependency of the moduli to the frequency seems to be
explained by a power-law relationship (Eqs. (6) and (7)).
However, in the systems studied here, at oo0.1 Hz, the
loss modulus G00 was almost independent of o and seemed
to show a minimum at low frequencies, in both pastes and
ketchups, which is typical of highly structured materials.
The power-law relationship is hence only valid at higher
frequencies, o40.1 Hz, and the parameters obtained from
G0 ¼ k0 ðoÞn ,
00
G00 ¼ k00 ðoÞn .
(6)
(7)
It can be seen, from Fig. 5, that the behavior of pastes is
different to that of the ketchups regarding the origin: once
again, paste 2 shows the highest G0 and G00 , whereas
ketchup 2 shows the lowest values of G0 and G00 . The value
of the power-law parameters in pastes (Table 6) are in
agreement with those reported by Rao and Cooley (1992).
3.3. A general description of pastes and ketchups by their
structural and rheological properties
In the previous sections we have described a number of
characteristics of the pastes and ketchups, such as the
particle size, volume fraction, and the rheological behavior
in steady and dynamic shear, and how these properties are
affected by concentration, processing and origin. Several of
these variables were significantly dependent on the origin
of the paste (ANOVA po0.05).
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9
A
100000
G’ and G’’
10000
1000
100
0.01
0.1
1
10
100
Frequency (ω)
10000
G’ and G’’
1000
100
10
0.01
0.1
1
10
100
Frequency (ω)
Fig. 5. Elastic G0 (Pa) (filled symbols) and loss modulus G00 (Pa) (empty symbols) as a function of the frequency o (Hz) in three tomato pastes (A) and its
correspondent ketchups (B), from different origins 1, 2 and 3 (J, &, W, respectively). Two repetitions are shown. Note that the scales are different.
Table 6
Power-law parameters for the correlation between the storage and loss
moduli (G0 and G00 ) and the frequency (o), according to Eqs. (6) and (7)
f
(–)
K0 0
(Pa sn )
n0
(–)
K00 00
(Pa sn )
n00
(–)
Paste 1
Paste 2
Paste 3
0.54
0.59
0.52
7556.4
11607.5
9763.3
0.1226
0.1399
0.1212
1659.9
2539.0
2156.5
0.2546
0.2077
0.2484
Ketchup 1
Ketchup 2
Ketchup 3
0.37
0.32
0.34
735.5
560.0
633.8
0.1084
0.1023
0.1064
159.5
106.6
125.1
0.3032
0.3313
0.3164
A Pearson correlation matrix was performed in order to
obtain those independent variables that could describe the
samples by their origin. The corresponding PCA of those
variables grouped the samples clearly by origin (Fig. 6),
where factors 1 and 2 explained 57.3% and 40.0%,
respectively, of the variation in pastes, and 65.5% and
33.3%, of the variation in ketchups.
The PCA describes, in a general picture (Fig. 6), pastes
and ketchups. Paste 1 is mostly characterized by the high
viscosity of the supernatant Zs and a low content of small
particles; paste 2 shows the largest f, which corresponds to
the highest amount of large particles and therefore, gives
the largest Z0. Paste 3 is characterized by a large content of
small particles and a low content of large particles. The
corresponding ketchup 1 shows higher Zs, a large increase
in small particles and the highest f. Ketchup 2 has the
larger decrease in large particles and the lowest f. Ketchup
3, finally, is characterized by the biggest size of the small
particles. Different variables were therefore chosen to
describe the pastes and the ketchups, for example
the apparent zero-shear viscosity is useful to describe the
pastes, whereas another variable such as the change in the
size of the particles is better in describing the ketchup
characteristics.
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10
Second factor (40.0 %)
1.0
0.5
s
small particles
0.0
-0.5
0
large particles
-1.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
First factor (57.3 %)
1.5
Second factor (33.3 %)
1.0
decrease large
increase small
0.5
0.0
s
-0.5
d32-I
-1.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
First factor (65.5 %)
Fig. 6. Principal components analysis (PCA) plots for the instrumental variables describing (A) pastes and (B) ketchups from different origins 1, 2 and 3
(, ’, ~, respectively).
3.4. Sensory assessment on ketchups based on different
pastes
Table 7
Sensory attributes of ketchups evaluated in an arbitrary scale 1 to 9 (mean
values and standard deviation of the assessors, n=8)
The ketchups were also subjected to sensory assessment.
The sensory characteristics of the three ketchups are
summarized in Table 7. No significant differences between
the ketchups were noticed (p40.05), probably because the
assessors were not especially trained for tomato products
and the differences between the ketchups were small.
Perception type
Attribute
Texture before
consumption
Spreadability 4.672.0
3.5. Does characterization of the pastes allow a prediction of
the quality of the ketchup?
In the previous sections we have shown that each paste
and ketchup is well-described by the particle size, volume
fraction, and the rheological behavior in steady and
dynamic shear. It has also been shown that the processing
of pastes into ketchups induces structural changes in the
suspensions. Moreover, the variations in the behavior of
Elasticity
Grainy
Adherence
Visual appearance
Color
Smoothness
Texture after consumption Thick
Tomato taste
Overall acceptance
Acceptance
Ketchup Ketchup Ketchup
1
2
3
5.372.3
2.971.6
4.071.8
4.870.9
5.771.2
6.171.8
5.571.2
6.571.7
6.071.6
6.070.9
5.071.8
3.871.7
3.871.8
5.570.9
5.671.3
5.671.1
5.470.9
6.971.1
3.671.6
4.671.8
4.671.8
5.571.1
5.871.3
4.871.3
5.370.5
7.070.8
the suspensions after processing are observed to depend on
the starting material, i.e. the paste origin. Considering that
pastes and ketchups, separately, are well-described by their
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steady and dynamic rheological properties, and that those
properties are closely related to f of the suspensions, it
seems plausible that knowing f the characteristics of the
ketchups can be predicted. However, it is noted that
the highest volume fraction in a paste does not imply the
highest volume fraction in its corresponding ketchup. The
origin of the paste seems thus to be responsible of
the differences from the expected behavior after processing.
Our study indicates that the volume fraction depends on
several factors such as WIS, fraction of small particles,
fraction of large particles, shape and aspect ratio of the
particles and viscosity of the supernatant, among others;
which is in agreement with a previous theoretical review by
Servais, Jones and Roberts (2002).
The changes in the fractions of small and large particles
are apparently related to the origin of the paste, i.e. the
components of that paste and their susceptibility to
breakage during processing. It is noted that the higher
the content of large particles, the higher the f of the paste
suspensions. In addition, it appears that the higher the
viscosity of the supernatant and the larger the increase in
small particles after homogenization, the higher the f in
the processed ketchups. Further research is hence needed in
order to discern between the effects of these parameters
and of processing on the structure of the suspensions and
their f.
4. Conclusions
The rheological characterization of each paste and
ketchup individually gives a good description of their flow
properties. However, the knowledge of the properties of
one paste is not sufficient to predict the properties of its
corresponding ketchup. The changes that each paste
undergoes during processing depend on a number of
parameters including the rheological properties but also the
particle properties such as their volume, size and shape,
and their susceptibility to breakage. The measurements
performed in the industry give only a ‘‘gross’’ estimation of
the viscosity under specific conditions. A better prediction
of the ketchup characteristics from the paste data is
industrially very interesting because it allows to control
and optimize the processing parameters, for example the
amount of paste added or the degree of homogenization
needed. Our results may then contribute to improve the
quality control performed during processing. Further work
is needed in order to define those properties that are able to
reflect the variation in the expected flow behavior after
processing.
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- Food Science and Technology (2007), doi:10.1016/j.lwt.2007.08.011
II
Low shear rheology of tomato products – Effect of particle
size and time
Bayod E., Månsson P., Innings F., Bergenståhl B., Tornberg E. (2007)
Food Biophysics, 2 (4), 146-157
Food Biophysics (2007) 2:146–157
DOI 10.1007/s11483-007-9039-2
Low Shear Rheology of Concentrated Tomato Products.
Effect of Particle Size and Time
Elena Bayod & Pernilla Månsson & Fredrik Innings &
Björn Bergenståhl & Eva Tornberg
Received: 16 March 2007 / Accepted: 10 August 2007 / Published online: 11 September 2007
# Springer Science + Business Media, LLC 2007
Abstract Time-dependent rheological properties of three
tomato paste suspensions in the concentration range of
200–1,000 g paste/kg suspension have been investigated by
using the vane geometry at shear rates g < 10 s1 . Creep
tests were conducted to analyze the influence of the level of
stress on the rheological behavior of the samples before and
after homogenization. The experimental results indicate that
the suspensions exhibit an elastic behavior at long times
and relatively low stresses, which proves that this type of
material can be characterized by a yield stress (σy).
Applying stresses just beyond the yield stress, an initial
rheopectic behavior appeared. This increase in viscosity at
low deformations was markedly larger after homogenization, and this difference was attributed to changes in the
aspect ratio, shape, and orientation of the particles induced
by homogenization. These structural changes were also
reflected in the transient viscosity when the samples were
subjected to larger stresses (σ>>σy): before homogenization the suspensions exhibited a steady-state viscosity at
large deformations, whereas after homogenization, the
transient viscosity continuously decreased. That behavior
was attributed to flocculation of the particles.
This work was partially presented at the “4th International Symposium
on Food Rheology and Structure” in February 19–23, 2006, Zürich,
Switzerland.
E. Bayod (*) : P. Månsson : B. Bergenståhl : E. Tornberg
Department of Food Technology, Engineering and Nutrition,
Lund University,
P.O. Box 124, 222 01 Lund, Sweden
e-mail: [email protected]
F. Innings
Tetra Pak Processing Systems,
221 86 Lund, Sweden
Keywords Tomato paste . Time-dependency . Yield stress .
Rheology . Homogenization
Introduction
Tomato paste is an important commercial product used in
the manufacturing of other tomato products, for example,
sauces and ketchup. It is the product resulting from the
concentration of tomato pulp by evaporation, after the
removal of skin and seeds, and contains 24% or more
natural tomato soluble solids.1 Tomato paste can determine
several characteristic properties of the food products where
it is included as an ingredient. These properties include
color, acidity, and consistency; all of them being major
quality aspects for consumer acceptance.
The rheological properties of tomato products depend on
a large number of parameters such as agronomic parameters
(i.e., variety and maturity), compositional parameters (i.e.,
soluble solids, acidity and pectin content), and processing
parameters (i.e., finisher screen and heat treatment).1
From a structural point of view, most tomato products
are dispersions consisting of aggregated or disintegrated
cells and cell wall material dispersed in an aqueous solution
of soluble tomato components. In these diluted regimes, the
viscosity of the system is mainly governed by the volume
fraction of the particles.2 Pure tomato paste is rather a
concentrated system full-packed by deformable particles
(i.e., cells). In such a system, the viscosity is largely
determined by the concentration and deformability of the
particles. The dispersed particles in a concentrated suspension form a network that determines its rheological
properties. In fact, displacing one particle within the
suspension requires large forces, which are, for example,
reflected in the large magnitudes of centrifugal forces
Food Biophysics (2007) 2:146–157
necessary to separate the dispersed phase from the
continuous phase (>100,000×g).3
Tomato products are known to exhibit strong shearthinning behavior (n<0.4) and appear to possess yield
stress.4,5 Different empirical flow models have been applied
to describe the rheological properties of tomato products
under steady shear;4–13 for example, the popular power law
equation or, when a yield stress is accounted for, the
Bingham plastic, Herschel–Bulkley. and/or Casson models.
There is, however, a large variation of data values depending on the experimental conditions, showing the difficulty
in obtaining general description of tomato products.
The preceding models all assume that the behavior of the
sample is time-independent. However, the rheological
behavior of complex foodstuffs might be influenced by
the shear history of the sample.14,15 In fact, earlier studies
have already suggested that the behavior of tomato
concentrates at low shear rates may be strongly influenced
by secondary effects such as yield phenomena, time
dependency, and wall effects, i.e., slippage.8 Those particular secondary effects are related to each other,16 and they
all complicate the measurement of the rheological properties in common rotational rheometers. The vane geometry
has been shown to considerably reduce these wall
effects,17,18 and simultaneously, it minimizes the amount
of disturbance when it is introduced into a complex fluid.
For this reason, the use of vane geometry in the yield stress
measurements of food suspensions has become increasingly
popular in the past few decades,19 and recently, its use has
also been extended to the measurement of other rheological
properties.20 A detailed review concerning the vane
geometry can be found elsewhere.21
The presence of the yield stress is a characteristic of
concentrated suspensions. It has been related to the strength
of the network structure, resulting from attractive particle–
particle interactions,22 and its magnitude is affected by a
number of factors, such as the density of the network,
particle concentration, and particle size and shape, among
others.23 It is commonly accepted that below the yield
value, the system deforms elastically, but when it is
exceeded, the structure begins to flow. However, there has
been a debate in the literature regarding the concept of the
yield stress, with Barnes18 claiming that the yield stress
does not really exist but is a consequence of the limitations
of the measurement system, and given the possibility of
measuring at very low shear rates, it is always found a large
but finite viscosity, i.e., zero-shear viscosity. Others authors
support the existence of the yield stress as a balance
between external and internal forces,24 i.e., the yield stress
exists when the external forces and internal fluctuations
(Brownian forces) are insufficient to significantly disrupt
the network (Eexternal +kT<<Enetwork). In fluids at rest, like
polymers and dilute suspensions (particle size<10 μm), the
147
Brownian forces dominate (kT), but their effect diminishes
with increasing particle number and size, as in concentrated
suspensions.
Some attempts have been made to describe the time
dependency of food suspensions. De Kee et al.14 proposed
a model based on the exponential decay of the viscosity
with time at a constant shear rate. However, in their study
on different food products, data for suspensions such as
tomato juice did not follow the proposed exponential decay.
Instead, tomato juice showed rheopectic (time-thickening)
behavior at shorter times and thixotropic (time-thinning)
behavior at longer times, which has been lately confirmed
by others.25
Recently, Marti, Höfler, Fischer, and Windhab26 have
studied the correlation between the time-dependent
rheological behavior and the well-defined structure of a
mixture of spheres and fibers in a suspension. They found
that these suspensions exhibit rheopectic behavior at short
times and thixotropic behavior at longer times, the former
being very pronounced only when fibers were present in
the suspension.
To the knowledge of the authors, the number of studies
regarding the time-dependence of the viscosity in concentrated tomato suspensions such as tomato paste are scarce.
The objectives of this work were thus to determine the
time-dependent rheological properties of tomato products at
low shear rates. The role of homogenization and concentration on both the structure and the time-dependent
behavior were systematically studied. Special attention
was also given to the yielding properties of this type of
materials.
Materials and methods
Tomato paste
Three commercial tomato pastes were used for the experiments: hot-break tomato paste 28–30°Brix (HB-28/30), hotbreak tomato paste 22–24°Brix (HB-22/24), and cold-break
tomato paste 36–38°Brix (CB-36/38). The properties of
these tomato pastes are summarized in Table 1. A series
of concentrations, 500, 400, 300, and 200 g of paste/kg of
Table 1 Properties of the three tomato pastes used in the experiment.
pH, total solids, and WIS are shown for the nondiluted tomato pastes,
before homogenization
Paste type
pH (–)
TS (%)
WIS (%)
HB-28/30
HB-22/24
CB-36/38
4.40
4.45
4.23
29.76±0.24
23.42±0.08
38.75±0.31
6.47±0.72
6.92±0.37
5.85±0.10
TS = total solids
148
Food Biophysics (2007) 2:146–157
suspension, was prepared in distilled water containing 0.1%
benzoate (as a preservative).
Homogenization
Homogenization of the suspensions was carried out at
90 bar using a ball-valve lab-scale homogenizer,27 where
the sample was recirculated until the desired particle size
was achieved, i.e., a volume-based diameter (d43) in the
range of 150<d43 <200 μm. The number of passages
through the homogenizer was thus adjusted for each sample
and is reported in Table 2. Note that fewer numbers of
passages were required when homogenising CB-36/38.
However, the possible causes for that behavior are out of
the scope of this paper. The samples were placed in a
refrigerator at 4°C and allowed to rest for at least 3 days.
Dry matter and water-insoluble solids
Total solids were determined using a vacuum oven (Forma
Scientific, USA) at 70°C (8 h) and 100 kPa of absolute
pressure. To determine the water-insoluble solids (WIS),
20 g of product was added to hot water for the removal of
the soluble solids. The mixture was centrifuged and then
washed repeatedly until the supernatant had reached a °Brix
value of about zero.28 The residue (WIS) was dried in an
oven (Termaks TS4057, Norway) at 100°C for 16 h.
Particle size distribution and particle shape
The particle size distribution (PSD) was measured using a
laser diffraction analyzer (Coulter LS 130, England)
applying the Fraunhofer optical model. Each sample was
run in duplicate. The volume-based and area-based diameter (d43 and d32, respectively) are defined as
,
X
X
4
d43 ¼
ni di
ni di3
ð1Þ
i
d32 ¼
X
i
ni di3
,
X
i
ð2Þ
ni di2
i
Table 2 Number of passages through the homogenizer for each paste,
adjusted according to the concentration, so that a comparable d43
(150–200 μm) was obtained in all samples
Paste type
HB-28/30
HB-22/24
CB-36/38
Concentration (g/kg)
1000
500
400
300
200
0
0
0
15
10
1
15
10
1
11
7
2
7
6
3
where ni is the percentage of particles with a diameter di.
Shape and structure of the cell wall material were studied
using light microscopy (Olympus BX50, Tokyo, Japan)
with a total magnification of about 50 times. The samples
were slowly diluted to 10% with distilled water and
examined directly after a gentle dispersion, i.e., the reduced
treatment was aimed to minimize the disruption of the
structure.
Rheological measurements
The viscosity of the suspensions was measured in a
controlled-stress rheometer (StressTech, Reologica, Lund,
Sweden) thermostatted at 20°C and equipped with a fourbladed vane tool to eliminate the slip phenomenon. The
vane was 21 mm in diameter (2r) and 5 mm in height (h)
and was placed in a cup 27 mm in diameter (2R). The vane
was carefully loaded at stresses below 0.5 Pa. Special care
was taken to minimize air inclusions in the sample.
The stress and shear rate calculations are based on20,21
s ¼ M sf ¼ M
g ¼ w gf ¼ w
1
2pr3
2R2
r2
R2
h 2
þ
r 3
1
ð3Þ
ð4Þ
The conversion factors from angular velocity (5) to
shear rate (g ), and from torque (M) to shear stress (σ),
respectively, depend on the geometry of the vane. These
equations are derived assuming that the material entrapped
between the blades of the vane tool forms a virtual inner
cylinder. In fact, the vane does not form a “perfect” cylinder
and, therefore, the calculated conversion factors have to be
slightly corrected. For this correction, Newtonian syrup
with a defined viscosity of 7.1 Pa s at 20°C was measured
using both the conventional concentric cylinder (d=25 mm)
and the vane tool. The corrected factors, obtained experimentally, were σf,exp =24,560 Pa/Nm (σf /σf,exp =0.9) and
+ f,exp =4.7 1/s ( + f / + f,exp =0.8) and were used throughout
this study. Finally, one paste sample was also measured in
both systems, the vane having a gap of 3 mm and the
concentric cylinder one of 1 mm. The viscosity curves
coincide in the low range of shear rates (10−4 to 10−2 1/s)
and clearly separate at larger shear rates, which was
probably due to slippage in the concentric cylinder.
To investigate the time dependence of the rheological
properties of the tomato suspensions, a creep test was
conducted. A constant stress was applied to the sample for
30 min, and the shear rate was recorded every 2.8 s. Each
measurement was conducted on a fresh suspension to avoid
any influence of the shear history.
Food Biophysics (2007) 2:146–157
149
For the study of the shear-rate dependence of the
viscosity, HB-28/30 tomato suspensions were subjected to
a logarithmic increase in shear stress (σ). The interval of
stresses was adjusted for each concentration (and particle
size) so that the shear rate was in the range 10−6 to 102 1/s
and about 90 measurement points were determined for each
sample. Each stress was applied to the sample for 10 s to
allow it to stabilize, and then measurements were averaged
during the following 10 s of shearing. The yield stress (σy)
was estimated at the beginning of the shear-thinning region,
using a procedure (Eq. 5) proposed by Mendes and Dutra,29
!
d ln s
) minimum:
ð5Þ
s y ¼ s where
d ln g
Various disturbing effects might develop during the
measurements, such as sedimentation and migration of
the particles. Moreover, the rheological properties of the
material are sensitive to the preparation procedure, which
may induce some structural changes. Therefore, we have
studied the reproducibility of the tests presented here in 12
rheological measurements that were run in duplicate. The
curves were compared in two different ways. Firstly, the
difference in the viscosity magnitude was studied by
comparing the obtained viscosity–deformation (η– + ) curves
and evaluating the relative standard error (RSE, Eq. 6)
between the viscosity values of two replicates as a function
of the deformation.
log η1 + log η2 +
.
RSEð + Þ ¼ log η1 + þ log η2 +
2
ð6Þ
Secondly, the shape of the curve was studied without
taking into account the viscosity magnitude; i.e., the curves
were forced to overlap by shifting one to the top of another
using a shift factor (x, y) that was able to reduce the
difference between the two curves (Δ, Eq. 7), and then the
remaining error was calculated according to Eq. 6.
Δ¼
X
i
!
!
X η1;i
+ 1;i
x þ
y
+ 2;i
η2;i
i
ð7Þ
The magnitude analysis showed that the average RSE
was somewhere between 1% (for high concentrations and/
or relatively low stresses) and as high as 20% (for low
concentrations and/or relatively high stresses, Table 3).
However, the remaining error after shifting the curves was
always below 2.2% for all samples, reflecting that the shape
of the two replicates was similar. In addition, the RSE did
not show any special trend with respect to the deformation.
It should be noticed that the results discussed in the
following sections were mainly derived from the shape of
the rheological curves, where the reproducibility was
always found to be acceptable.
Results and discussion
PSD and structural changes
The light microscopy pictures were taken on tomato
suspensions before and after the process of homogenization. Figure 1 reveals the drastic change in the physical
structure caused by homogenization in two suspensions
with the same chemical composition. Before homogenization, the tomato paste system consists mainly of large
deformable particles (i.e., whole cells) and a number of
small particles (i.e., other cellular material). During homogenization, these particles are strongly broken down,
Table 3 RSE % of various rheological measurements, considering the differences in magnitude and in shape between two replicates
Sample
H
Paste content (%)
σ (Pa)
RSE (%)
Shift factor (x, y)
Remaining error (%)
log + range (–)
HB-22/24
bh
100
50
89
400
7
5
6
1
40
15
20
10
5.2
1.1
15.9
3.4
9.7
14.8
18.1
0.7
0.5
8.7
1.0
(0.00,0.27)
(0.21,0.09)
(−0.30,−0.04)
(−0.04,0.03)
(0.23,−0.10)
(0.02,0.20)
(0.05,0.07)
(0.04,−0.03)
(0.10,0.01)
(0.09,−0.10)
(−0.03,0.03)
0.21
0.56
2.06
0.19
1.00
0.74
2.15
0.51
0.85
1.99
0.18
−2.5
−1.7
0.0
−1.7
0.0
0.0
1.2
−1.0
0.0
0.3
−0.7
40
30
HB-28/30
ah
bh
20
50
40
ah
30
−2.0
0.4
1.8
−1.0
2.1
1.6
3.5
2.2
2.3
3.2
2.3
The RSE was estimated using Eq. 6 in samples from two tomato pastes, at different concentrations, and before and after homogenization. The
RSE was averaged over a wide range of deformations ( + ). The remaining error was also estimated after forcing the curves to overlap, using a shift
factor (x, y) defined by Eq. 7
H = homogenization; bh = before homogenization; ah = after homogenization
150
Food Biophysics (2007) 2:146–157
the coarse fraction has a median diameter of 157 μm, with
about 50% of the particles being larger than 100 μm. In the
CB-36/38, however, only 36% of the particles have sizes
larger than 100 μm, and the median diameter for the coarse
fraction is 123 μm. Moreover, the cold-break paste has
notably finer particles (<10 μm), up to 37%, compared to
27–24% in the hot-break pastes.
The process of homogenization reduces the size of the
particles but also induces changes in the percentage of
coarse and fine particles. In the hot-break pastes, the
amount of particles having a diameter larger than 100 μm
is now reduced to 15 and 20%, whereas the fine fraction
represent up to 40–50% of all the particles. The median
diameter of the coarse fraction has also decreased to 55–
70 μm, whereas that of the fine fraction is about 2.5 μm.
The cold break paste has a coarse fraction with rather
similar median diameter (50–80 μm), but the fine particles
are smaller (0.5–1.0 μm) and represent about 60% of the
total particles. Note that, in this paste, only 5 to 15% of
the particles are larger than 100 μm. Figure 2 reflects the
changes caused by homogenization in the PSD of different
pastes (and concentrations).
Characterization of the time-dependent rheological
properties of tomato pastes subjected to different levels
of stress
Fig. 1. Typical light microscopy pictures of a diluted suspension of
tomato paste before (a) and after (b) homogenization. The bar is
150 μm
resulting in a system containing large numbers of small
particles such as fiber particles, cell and cell wall fragments,
and polymers, among others. The homogenization of the
suspension creates a different network, with different
rheological properties. Ouden and van Vliet30 showed that
higher values of yield stress and apparent viscosity were
found in homogenized samples than those achieved in
nonhomogenized samples with the same particle size.
The PSD, expressed as volume-based diameter (d43),
was similar in the three pastes, having a mean diameter of
about 320 μm before homogenization. The process of
homogenization decreased d43 to values comprised within
100 to 200 μm (Table 4). However, the PSD expressed as
area-based diameter (d32) does indicate some differences
between the three pastes, both before and after homogenization. Before homogenization, for the HB-28/30, the
fraction of coarse particles (>10 μm) has a median diameter
of 202 μm, and more than 50% of the particles in the
suspension have a size larger than 100 μm. For HB-22/24,
In this section, the typical time-dependent rheological
behavior of three tomato pastes is described. The results
obtained for the evolution of the shear rate as a function of
the time of shearing are presented in Figure 3 for three nondiluted tomato pastes. In general, the transient shear rate
shows a typical behavior for all paste samples. When the
applied shear stress is below a certain stress value, the
response of the system is an initial g < 102 s1 followed,
at longer times, by a marked decrease of the shear rate over
several decades down to g < 104 s1 , where the measurements become unstable (Figure 3). If the applied
shear stress is above a certain stress value, the system will
begin to flow, at initial shear rates ranging from
102 s1 < g < 101 s1 . The variation of the shear rate
with time will then be limited to values within the same
order of magnitude. If the shear stress is even higher, so
that it creates an initial shear rate in the range
101 s1 < g < 100 s1 , the response of the system at long
times is a sudden increase of the shear rate over one or
more decades, up to g > 101 s1 , where the vane measurements might lose reliability31 due to several causes such as
the formation of eddies, migration of particles, or slip
occurrence at the outer wall.
The range of stresses at which the different behaviors
occur slightly varies according to the microstructure of the
pastes, which is also reflected as different static yield values
Food Biophysics (2007) 2:146–157
151
Table 4 PSD of three types of tomato paste at different concentrations (200–1,000 g/kg), expressed as volume-based mean diameter
(d43) and standard deviation of the normal distribution, mass fraction
Paste type
HB-28/30
HB-22/24
CB-36/38
Conc. (g/kg)
1,000
500
400
300
200
1,000
500
400
300
200
1,000
500
400
300
200
of the very coarse (>100 μm) and fine (<10 μm) particles, and areabased median diameter (d32) for the two fractions
Mean diameter (μm)
Mass fraction (%)
Median diameter (μm)
d43
SD
Very coarse
(>100 μm)
Fine
(<10 μm)
d32 coarse
(>10 μm)
d32 fine
(<10 μm)
334
190
175
186
208
309
206
165
198
173
313
214
156
176
101
174
139
133
143
153
180
151
125
152
132
185
153
116
120
72
55
24
17
20
22
50
21
18
19
15
36
15
12
16
6
27
38
43
41
42
24
44
42
47
51
37
60
60
59
65
202
63
54
62
67
157
67
61
64
57
123
67
62
81
51
2.5
2.5
2.6
2.6
2.8
3.5
2.1
2.2
2.5
2.5
3.1
1.1
0.8
0.6
0.9
SD = standard deviation of the normal distribution
(see “Identification of yielding in tomato suspensions”
section and Table 5),
Identification of yielding in tomato suspensions
As has been shown above, the behavior of the tomato
suspensions, when a relatively low shear stress is applied
over long times, is that of the elastic deformation of a solid
with almost no movement of the vane, i.e., g < 104 s1 .
Increasing the magnitude of the applied stress above a
critical value will, however, force the system to flow. The
transition between elastic and viscous behavior apparently
takes place at a critical stress value that is suggested to be
identified as the static yield stress (σy). The behavior shown
in Figure 3 is thus interpreted as a proof of true yielding:
i.e., under the application of small stress the system
deforms elastically with finite rigidity, but when the applied
stress exceeds the yield value continuous deformation
occurs with the material flowing like a viscous fluid.22,23
To evaluate whether the static yield stress, determined by
the time-dependent rheological measurements, corresponds
to the critical stress normally obtained from the steadyshear curves (i.e., dynamic yield stress), further experiments were performed on one tomato paste (HB-28/30).
The flow properties of the suspensions are shown in
Figure 4 as the apparent shear viscosity as a function of
the shear rate. The curves are characterized by an apparent
Newtonian plateau at low shear rates, and a shear-thinning
behavior at high shear rates.
The stress at which the shear-thinning region begins is
commonly defined as the dynamic yield stress and, in this
work, it has been estimated using Eq. 5. The values of the
static yield stress and the dynamic yield stress are compared
in Table 5. According to these data, the dynamic yield
stress is comparable in magnitude to the static yield stress.
A number of studies have indicated that the static yield
stress can be significantly higher than the dynamic yield
stress, i.e., the shear stress required to initiate flow can be
larger than the shear stress required to maintain the flow at
slow motions. Our results showed slightly lower values of
yield stress in dynamic than in static measurements, but in
terms of magnitude, this type of suspension may be
characterized by a single yield value. The results from
Yoo et al.,19 for tomato puree and ketchup, also suggested a
slight difference in the values of static and dynamic yield
stresses.
There is a general agreement on the definition of the
yield stress at the beginning of the shear-thinning region.
Considering that the suspensions deform elastically below
the yield value, as stated above, it seems uncertain whether
the low shear-rate Newtonian plateau in the flow curves
(Figure 4) really exists for this type of suspension. The
shear rates measured in this region may instead be
interpreted as local rearrangement of the network structure32 (i.e., elastic deformation) rather than flow.
A discontinuity is observable in the shear-rate-dependent
flow curves in Figure 4 at shear rates ranging from
101 < g < 100 . Other authors have reported similar
152
Fig. 2. Frequency distribution of the cumulative surface area of the
particles as a function of the logarithm of the particle diameter (d32)
for a HB-28/30, b HB-22/24, and c HB-36/38, shown before (thick
solid line, 1,000 g paste/kg) and after homogenization of suspensions
in the concentration range 200–500 g paste/kg suspension (thin solid
line 200, dashed–dotted line 300, dotted line 400, and dashed line
500)
Food Biophysics (2007) 2:146–157
Fig. 3. Transient evolution of the shear-rate (s−1) as a function of the
time of shearing (s) at constant stress of shear for three nondiluted
tomato pastes before homogenization a HB-28/30, b HB-22/24, and c
HB-36/38. The different stresses used are shown in the legend (in Pa)
Food Biophysics (2007) 2:146–157
153
Table 5 Comparison between the values of the static and dynamic yield stress estimated by time-dependent and shear rate-dependent rheological
properties, respectively, on tomato paste suspensions (HB-28/30) in a concentration range 200–1,000 g/kg, before and after homogenization
Concentration g paste/kg suspension
1000
500
400
300
200
σy (Pa) before homogenization
σy (Pa) after homogenization
Static yield stress*
Dynamic yield stress
Static yield stress*
Dynamic yield stress
50–89
12–15
4–7
<5
1–1.73
49.8
8.9
–
2.6
0.5
–
15–30
20–23
8–10
4.6–5.0
–
–
17.0
9.8
4.1
*Interval of stresses where the transition between elastic to viscous behavior occurs, thus including the static yield value
discontinuities in the viscosity curves of concentrated
suspensions and food dispersions, which has been attributed to causes such as structural breakage or slip phenomenon.14,25,33 It is, however, interesting to notice that the
range of shear rates where the discontinuity occurs
101 < g < 100 corresponds, in the time-dependent
flow curves (Figure 3), to a drastic increase in the shear
rate due to the application of relatively high stresses under
long periods of time.
The dynamic yield values are represented as a function
of the concentration (WIS) in Figure 5. The relationship
between the yield stress and WIS is described by Eqs. 8
and 9 for samples before and after homogenization,
respectively.
s y ¼ 0:47 WIS2:5 R2 ¼ 0:99
ð8Þ
s y ¼ 2:59 WIS2:0 R2 ¼ 1:00
ð9Þ
The yield stress can be considered as the result of the
particle–particle interactions, leading to a network structure,
which can be described as a colloidal glass or jammed
state,34,35 i.e., the particles are not exposed to sedimentation
or Brownian motion. Several factors may affect the
magnitude of the yield stress, for instance, the particle
concentration, size, shape, and size distribution, among
others.23,30 The yield stress is a power law function of the
particle concentration.22 For the tomato suspensions in this
study, the power-law exponents were 2.5 before homogenization and 2.0 after homogenization. The power-law
exponents are an indication of the type of network structure
that constitutes the suspension and have been derived from
theories modeling the gel as a network of interconnected
fractal clusters.36–38 These observations, together with
microscopy (Figure 1), suggest that the homogenization of
tomato products increases its fibrous nature and gives rise
to a different type of network, accompanied by an
enhancement of the rheological properties, as after homogenization, σy becomes higher (at a given WIS content).
Time-dependent flow behavior of tomato suspensions
before and after homogenization
At stresses just beyond the yield stress
Fig. 4. Shear-viscosity as a function of the shear rate for tomato paste
HB-28/30 in a concentration range 200–1,000 g paste/kg suspension
before and after homogenization (bh and ah, respectively; see legend)
The time-dependent flow behavior of the tomato suspensions has been studied by applying a stress just beyond the
yield stress (Table 6). The samples were sheared at a fixed
stress during a certain length of time, as described in the
“Rheological measurements” section, and the results are
presented in Figure 6 as the transient viscosity as a function
of the deformation, for three tomato pastes in the
concentration range 200–1,000 g paste/kg suspension,
before and after homogenization. Note that each displayed
curve corresponds to a measurement on an unsheared
suspension. The data exceeding 10 s−1 in shear rate were
not included to ensure the reliability of the results.
The transient viscosity as a function of the deformation,
when the flow is initiated, is characterized by rheopectic
154
Food Biophysics (2007) 2:146–157
Fig. 5. Dynamic yield stress (Pa) as a function of the concentration
(WIS, %) for tomato paste (HB-28/30) suspensions, before (bh) and
after homogenization (ah). The yield stress was determined at the
beginning of the shear-thinning region by Eq. 5
behavior at low deformations, i.e., an initial rise in
viscosity, which is followed by a later decrease of viscosity
(i.e., thixotropic behavior), whereas at larger deformations,
the transient viscosity tends to level off to a steady-state
value. In the suspensions before homogenization, the
increase in viscosity is less pronounced than it is after
homogenization, and generally at low concentrations no
peak is observed, but the viscosity directly reaches a
steady-state value, at + <5. On the contrary, a peak is
observed after homogenization at high concentrations, and
the steady-state viscosity is achieved at relatively larger
deformations, i.e., + >10. This initial rheopectic behavior of
the viscosity is characteristic of fiber suspensions and has
been attributed to a combination of causes; according to
Marti et al.,26 those causes might be (1) the formation of
slip layers that lead to very low-start up viscosity readings,
(2) the hindering of fiber rotation by neighboring fibers,
and (3) the delay response of the sheared material due to the
elastic properties of the fiber network.
The deformation at which the transient viscosity
achieves the maximum value is summarized in Table 6 for
all the suspensions studied. Before the homogenization
process, the maximum in viscosity may be observed at
rather variable degrees of deformation. After homogenization, on the contrary, this maximum is found in a narrow
range of deformations, generally at + <1. It is noted that the
position of the peak is weakly dependent on the magnitude
of the stress applied, which in turn is dependent on the
concentration; i.e., the lower the concentration, the larger
the deformation required to reach the peak.
The differences in the time-dependent behavior due to
the homogenization process might be explained by the
influence of several factors, such as the volume fraction,
aspect ratio, shape, size, and size distribution, as well as
orientation, deformability, and number of particles. Indeed,
all geometrical characteristics of the particles are drastically
altered by homogenization, as it is obvious from Figure 1,
where nonhomogenized suspensions consisted of a mixture
of whole cells and dispersed cell wall material having a
rather spherical shape, and homogenized suspensions
consisted of smashed cellular material that tend to aggregate forming fibrous-like particles.
Table 6 Deformation at which the maximum in viscosity is observed ( + at max), when applying a constant stress just beyond the static yield value
(σy), in three tomato pastes in a concentration range 200–1,000 g paste/kg suspension, before and after homogenization
Paste
HB-28/30
HB-22/24
CB-36/38
Concentration (g paste/kg suspension)
1,000
500
400
300
200
1,000
500
400
300
200
1,000
500
400
300
200
Before homogenization
After homogenization
σy (Pa)
+ at
89
15
7
5
1.7
89
15
11
5
0.4
211
15
11
8
3
0.065
1.272
1.355
16.016
11.008
0.075
0.947
3.532
10.224
6.835
2.401
0.680
6.128
15.798
4.815
max
(–)
Note that when no peak is observed (Figure 6), the maximum viscosity corresponds to the steady-state viscosity
σy (Pa)
+ at
–
30
23
10
5
–
35
30
20
10
–
30
20
15
15
–
0.465
0.421
0.871
0.745
–
0.117
0.546
0.751
1.584
–
0.481
0.338
0.907
2.584
max
(–)
Food Biophysics (2007) 2:146–157
155
Fig. 6. Transient viscosity as a
function of the deformation in
three pastes HB-28/30 (a, b),
HB-22/24 (c, d), and CB-36/38
(e, f) in a concentration range
from 200–500 g of paste /kg
suspension (solid line 200,
dashed–dotted line 300, dotted
line 400, and dashed line
500 g/kg), before and after homogenization (a, c, and e and b,
d, and f, respectively).
Experimental results were
obtained at the first stress where
the material was observed to
flow; those stresses are summarized in Table 6
In general, marked time-dependent properties are characteristic of suspensions having high particle concentration
and fibrous nature,26 which is probably the case in the
homogenized suspensions, where the rheopectic increase in
viscosity at low deformations is enhanced by the higher
content of fibrous particles. The initial distribution of
orientations of the fiber particles also has an important
impact on the rheopectic behavior of the suspensions.
Barbosa, Ercoli, Bibbó, and Kenny39 have shown that
uniform initially distributed systems result in a greater
magnitude of transient viscosity and that the maximum
peak in these systems is achieved at lower deformations. In
this study, the suspensions were stirred before the measurements to obtain homogeneous samples, hence, with more
random distribution of the orientation of the particles.
However, the homogenization process could induce some
other preferential direction in the fiber orientation that may
be irreversible and, thus, affect the results but this has not
been taken into account in this study.
As has been stated above, the transient viscosity reaches
a steady-state value at certain deformations. This steadystate might be caused by the alignment of the particles with
the flow direction. The rotation of the particles in laminar
flow can be described by geometrical considerations as,40
+t
tan θ ¼ p tan
p þ 1=p
!
þ tan θ0 ;
ð10Þ
where θ is the averaged orientation angle (note that the
angles in this equation are given in radians and θ=π/2
156
Food Biophysics (2007) 2:146–157
Table 7 Deformation at alignment + θ¼π=2 calculated using Eq. 10 for different aspect ratios (p)
Aspect ratio (p)
Deformation + θ¼π=2
0.1
0.5
1.0
1.5
3.0
10
30
50
70
100
15.9
3.9
3.1
3.4
5.2
15.9
47.2
78.6
110.0
157.1
means parallel and θ=0 means perpendicular to the flow
direction, respectively), p is the aspect ratio (p<1 for oblate
and p>1 for prolate particles), and θ0 is the initial averaged
orientation angle of the particles. For p=1, the rotational
angle is thus proportional to half the deformation g ¼ g t ,
i.e., θ θ0 + =2. Using Eq. 10, it is possible to estimate
the deformation at which the alignment of the particles
occur for any aspect ratio p, i.e., where θ=π/2, which also
correspondsto the first rotation period. The deformation at
alignment + θ¼π=2 is shown to be independent of the
initial orientation angle for any θ0 ≠π/2 and, hence, only
dependent on p. According to Eq. 10, for large aspect
ratios, the rotation of the particles is slowed down and
the alignment with the flow direction occurs at larger
deformations (Table 7).
In the tomato suspensions studied here, the steady-state
viscosity is normally reached at + <5 before homogenization and at + >10 after homogenization, which, according to
Table 7, would correspond to aspects ratios of the order of 1
to 3 and 10 to 30, respectively. These ranges of aspect
ratios seem realistic for these systems. Note also that, for
p values as large as 50, the alignment is still reached at
rather low deformations ( + <100). These estimations suggest that the time to reach the steady-state viscosity is
mainly due to the alignment of the particles with the flow
direction. Moreover, the alignment of the particles may
cause the system to become anisotropic.
Equation 10 was first derived by Jeffery40 to describe the
orientation distribution of spheroids in diluted systems in a
shearing flow. It is noted that interactions between particles
can produce deviations from this equation and also that the
flow behavior of concentrated suspensions is in part
determined by particle interactions. However, in laminar
flow, the particle network deforms following the streamlines, which leads to its alignment along the flow lines at
certain deformations.
viscosity before and after homogenization at different levels
of stress. The data exceeding 10 s−1 in shear rate were not
included to ensure the reliability of the results.
Before homogenization, the transient viscosity seems to
level off at large deformations, whereas after homogenization, the viscosity tends to decrease continuously. In the
first case, the response of the viscosity is stable at large
deformations, which suggests that the system becomes
At stresses much larger than the yield stress
The time-dependent results discussed in the previous
section were obtained by applying a stress just beyond the
yield value. To further study the influence of the stress level
on the time-dependent properties, the suspensions were also
subjected to shearing at higher stresses σ>>σy. The results
in Figure 7 show different behaviors of the transient
Fig. 7. Typical behavior of the transient viscosity as a function of the
deformation when applying stresses above the yield stress (σ>>σy),
on tomato samples (HB-28-30) in the concentration range 300–1000 g
of paste /kg suspension, a before and b after homogenization. The
different stresses used are shown in the legend (in Pa)
Food Biophysics (2007) 2:146–157
stable (i.e., time-independent) when the particles are
aligned into the flow, and thus, the steady-state viscosity
is attained. In the second case, the constant decrease in
viscosity at large deformations gives indication of particle
rearrangements (i.e., instability of the system), which is
suggested to be caused by flocculation. As the system
flows, the network is gradually disrupted into apparent
aggregates, consisting of densely packed particles. This
result suggests that homogenization increases the susceptibility of the structured suspensions to disrupt into smaller
aggregates under shear; we have further analyzed this
phenomenon in another study.
Conclusions
In this paper, we have measured the yield value of tomato
suspensions as a function of the concentration taking into
account the time-dependent rheological properties. At
stresses below the yield values, the system exhibits an
elastic behavior at long time periods, and as the stress is
increased above the yield value, the system begins to flow.
This elastic behavior at low deformations proves that this
type of suspension cannot be characterized by a zero-shear
viscosity, at least within the time limits of the experiments
performed in this investigation.
At stresses just beyond the yield stress, the timedependent flow behavior in tomato suspensions exhibits
rheopectic behavior at low deformations, followed by
steady-state viscosity at large deformations. The rise in
the transient viscosity was more pronounced after homogenization of the suspensions, and the maximum was
achieved at lower deformations. The differences in the
time-dependent rheological behavior due to homogenization were attributed to a number of geometrical characteristics, such as the aspect ratio, shape, and orientation of the
particles.
The application of stresses much larger than the yield
stress showed different behaviors at large deformations
before and after homogenization; whereas the nonhomogenized suspensions become stable (i.e., time-independent),
in homogenized suspensions the transient viscosity continuously decreases at large deformations. The results of this
study might be used to improve the design of processing
operations where the transient rheological properties might
come into play.
Acknowledgments The authors wish to thank Orkla Foods A.S. for
providing the tomato paste samples.
157
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III
Microstructure of highly concentrated tomato suspensions
during homogenisation, and after subsequent shearing
Bayod E., Tornberg E. (2008)
Submitted for publication, 2007
Microstructure of highly concentrated tomato suspensions
during homogenisation, and after subsequent shearing.
Elena Bayod*, and Eva Tornberg
Department of Food Technology, Engineering and Nutrition, Lund University,
P.O. Box 124, SE-222 01, Lund, Sweden
*
Corresponding author: Elena Bayod, e-mail: [email protected]
Abstract
The changes in the microstructure of tomato paste suspensions have been investigated
during homogenisation and subsequent shearing in suspensions with similar
composition, at three tomato paste concentrations 10, 30 and 40 %. The suspensions
were characterised by the particle size distribution (PSD), volume fraction (ø), and
dynamic rheological properties (G’,G’’). All suspensions exhibit a solid-like
behaviour with G’>G’’. Micrographs indicate that the process of homogenisation
creates a smooth network of finer particles, that is easily disrupted by prolonged
shearing, giving rise to the formation of densely packed flocs that become clearly
oriented in the direction of the shearing. At high concentrations, these changes in the
microstructure on homogenisation and subsequent shearing were better reflected by
differences in ø than in G’. The rheological behaviour of the suspensions exhibits a
power-law dependence on ø, over a large range of PSD and for 0.05<ø<0.55. Finally,
an experimental equation, including ø and the size of the coarse particles in the
surface-weighted PSD, is found to accurately estimate G’ (R2>99.3%, p<0.001).
Keywords: particle size distribution, viscoelastic properties, tomato suspensions,
rheology, flocs and aggregates, morphology, network, homogenisation, shearing.
1. Introduction
Tomato products generally form structured suspensions consisting of cells and/or cell
wall material dispersed and arranged in a liquid matrix phase, which comprises
1
soluble materials such as polysaccharides, i.e. pectins and sugars, and some proteins.
Processing of tomato products includes dilution of tomato paste to the desired tomato
concentration, mixing with other ingredients, thermal treatment and, frequently,
homogenisation. The study of the effect of paste concentration (Tanglertpaibul & Rao,
1987a), origin (Sánchez, Valencia, Gallegos, Ciruelos & Latorre, 2002) and breaktemperature (Fito, Clemente & Sanz, 1983, Xu, Shoemaker & Luh, 1986), added
hydrocolloids and other ingredients (Sahin & Ozdemir, 2004, Tiziani & Vodovotz,
2005), and combined pressure and thermal treatment (Verlent, Hendrickx, Rovere,
Moldenaers & van Loey, 2006) on the properties of the final tomato products have
been previously reported in the literature. Particle size influence on the rheology of
tomato concentrates has also been considered to some extent (Tanglertpaibul & Rao,
1987b, den Ouden & van Vliet, 1997, Valencia, Sánchez, Ciruelos, Latorre, Madiedo
& Gallegos, 2003).
Homogenisation of tomato juice enhances the structure of the product, increasing its
viscosity and prevent synerisis to some extent (Thakur, Singh & Handa, 1995, den
Ouden, 1995, Bayod, Månsson, Innings, Bergenståhl & Tornberg, 2007a), and hence
it is a key processing step in the production of ketchup and other tomato sauces. This
process does not only decrease the average particle size of the tomato suspensions,
leading to a smoother texture and higher viscosity, but also induces changes in the
nature of the network, causing an enhancement in the viscosity of the suspensions,
compared at the same particle size (den Ouden & van Vliet, 1997) and at the same
WIS (Bayod et al., 2007a). Homogenisation may also affect the molecular weight
distribution of the soluble pectins, decreasing the viscosity of the solution (Corredig &
Wicker, 2001). In order to better design structured foods, such as tomato suspensions,
a better knowledge of the influence of the dispersed material, the liquid matrix as well
as the processing steps on the structure formation is desirable.
Food processing involves often intense or prolonged shearing of the food material in
distinct unit operations, for example in mixing, homogenising and pumping.
However, a systematic investigation on the influence of the degree of homogenisation
on the particle size distribution (PSD), and consequently, the effect of the different
PSD achieved, on the rheological properties of this food suspension is lacking in the
2
literature. Besides, the influence of prolonged shearing on the microstructure of
tomato homogenates, exhibiting different PSD, has not yet been reported.
Tomato concentrates exhibit pronounced non-Newtonian effects: e.g. yield stress,
shear-thinning behaviour, and shear history dependence (Rao, 1999). Besides,
rheological measurements of homogenised tomato products have revealed rheopectic
behaviour at low deformations (De Kee, Code & Turcotte, 1983, Bayod, et al.,
2007a), and thixotropic behaviour at large shear deformations (Harper & Sahrigi,
1965, Tiziani & Vodovotz, 2005). The thixotropic behaviour has been attributed to the
breakdown of the network structure into smaller flocs or aggregates (Bayod, et al.,
2007a), which decreases the viscosity of the suspension. With regard to the liquid
phase, a previous investigation of model solutions of pectins has shown that while low
shear rates induce gelation and shear-thickening, intense shearing may cause the
disruption of intermolecular junctions leading to a decrease in viscosity (Kjøniksen,
Hiorth, Roots & Nyström, 2003). The understanding of the mechanisms of network
breakage and consequent formation of flocs is relevant in the design of production
processes, where the effect of prolonged shearing on the food structures should be
prevented or minimised.
It is assumed that the viscoelastic behaviour of suspensions is determined by the
particle size distribution and shape as well as the volume fraction of particles
(Nakajima & Harrell, 2001, Servais, Jones & Roberts, 2002) and the particle-particle
interactions (Shah, Chen, Schweizer & Zukoski, 2003), and the influence of these
parameters on the rheological properties of food suspensions has been reported
previously. However, for highly concentrated suspensions the influence of the
microstructure on the rheology of the suspensions is less well understood (Wyss,
Tervoort & Gauckler, 2005). This is probably due to the fact that the number of
techniques available to investigate the microstructure of highly concentrated
suspensions are rather limited (Wyss, et al., 2005), and also because there is a lack of
standardised ways of quantifying microstructure.
Scaling laws relating the fractality of the networks (as a measure of the
microstructure) to the rheological properties have been developed, mainly on model
colloid suspensions and gels (Buscall, et al., 1987, Buscall, Mills, Goodwin &
3
Lawson, 1988) at relatively low concentrations and with monodisperse particle size
distributions. The fractal description of microstructures is argued not to hold at high
concentrations (Wyss et al., 2005), and other explanations, such as the formation of
interconnected fractal aggregates, have been suggested as a cause to the strong powerlaw dependence of the rheological properties to the particle concentration (see for
example Buscall et al., 1987 and Brown & Ball, 1985). But still the fractality of the
network structure is one of the few existing ways to relate microstructure and
rheology.
The effect of shearing on the microstructure has also been studied to some extent on
model colloid systems at relatively high concentrations (Mills, Goodwin & Grover,
1991). Those authors concluded that prolonged shearing caused a rearrangement of
the network, forming tightly packed aggregates with a characteristic size. Buscall et
al. (1987) and Channell, Miller and Zukoski (2000) have studied the rheology of
highly flocculated dispersions of colloidal particles forming a network, using uniaxial
compression (in centrifugation) and shear. They arrived to some interesting
conclusions that uniaxial compression is more sensitive to heterogeneities in the
flocculated network than shearing, and the latter authors derived a model based on the
size of heterogeneities that qualitatively agrees with experimental data.
The structure formation by homogenisation, and its subsequent disruption by shearing
need to be studied with techniques that cause a minimum disruption in the sample
under examination. Microscopic observation is the most direct way of obtaining
valuable information on the shape and arrangement of the particles in diluted and
semi-diluted systems, but it is not suitable for highly concentrated suspensions. Small
amplitude oscillatory shearing has successfully been applied to explore the
microstructure of complex materials, even at high concentrations, and a number of
models have been developed relating the storage (G’) and loss moduli (G’’) to
structural features such as the onset of gel formation, the number of junction points in
a network, the strength of the gel, and the network fractality (Larsson, 1999).
The objective of this experimental study is to investigate the mechanisms of formation
and disruption of structures in tomato products with similar chemical composition, by
considering the effect of concentration, homogenisation and subsequent shearing. We
4
will focus on the influence of the particle size distribution and the arrangement of
particles in the suspensions on the rheological properties of tomato concentrates. The
study of tomato concentrates instead of model suspensions involves some challenges,
such as the polydisperse nature of the particle size distribution of the suspension
consisting of relatively large particles (100-200 µm).
2. Material and methods
2.1 Composition of tomato concentrates
Tomato suspensions were prepared from cold-break tomato paste 36-38°Brix (Alsat,
Spain), dispersed in an aqueous solution containing sodium benzoate (0.1 %), salt (10
%), sugar (23 %) and acetic acid (0.4 %). Three concentrations of paste (10, 30 and 40
% w/w) were used in the experiments. The suspensions were prepared by gently
mixing the paste in the solution by hand. The composition of the tomato suspensions
are summarized in Table 1. Total solids (TS) were determined using a vacuum oven at
70ºC (8 h). In order to determine the water-insoluble solids (WIS), 20 g of the sample
was added to boiling water for the extraction of the soluble solids. The mixture was
centrifuged, and the supernatant filtered repeatedly until it had reached a °Brix value
of about zero (den Ouden, 1995). The residue (WIS) was dried in an oven at 100ºC for
16 h. pH was also measured. All measurements were carried out at least in duplicate.
Table 1. Composition of the tomato paste suspensions, including pH, total solids (TS), and water
insoluble solids (WIS).
Concentration
% tomato paste
10
30
40
pH
[-]
3.56
3.66
3.62
Total Solids
[%]
37.8
45.8
48.4
± 0.0
± 0.1
± 0.4
Water Insoluble Solids
[%]
0.5
± 0.08
1.3
± 0.31
2.4
± 0.03
2.2 Mechanical treatment of the suspensions
The tomato suspensions were homogenised at room temperature in a lab-scale
homogeniser at 90 bars (Tornberg & Lundh, 1978). The samples were subjected to
different number of passages (~1, ~2 and ~3) in order to obtain different degrees of
homogenisation. The samples were then allowed to rest at 4°C for at least 3 days. The
different samples were afterwards subjected to shearing using a magnetic stirrer
5
during 1 h at room temperature. All samples were sheared under similar conditions
(~750 rpm, beaker diameter: 5.7 cm, magnet length: 3.5 cm, ~50 ml sample) and left
to rest at 4°C for at least 2 days.
2.3 Experimental design
The experimental design followed in this study is specified in Table 2, where three
factors are studied: a) the variation in concentration (3 levels), b) degree of
homogenisation (4 levels) and c) the effect of prolonged subsequent shearing (2
levels), giving rise to 24 independent samples. In this paper the samples are
designated by H0, H1, H2, and H3 for the different degree of homogenisation, where
H0 stands for the non-homogenised sample and H3 for samples that have been
subjected to 3 passages through the homogeniser. Finally, SH means sheared samples.
For example, “H1SH” is a sample subjected to 1 passage through the homogeniser,
and subsequently sheared for 1 h.
Table 2. Overview of the experimental plan.
Concentration
Degree of homogenisation
% tomato paste
H0
H1
H2
H3
10
NO/SH
NO/SH
NO/SH
NO/SH
30
NO/SH
NO/SH
NO/SH
NO/SH
40
NO/SH
NO/SH
NO/SH
NO/SH
H0: before homogenisation, H1: after 1 passage, H2: after 2 passages, H3: after 3 passages.
NO: non sheared SH: sheared
2.4 Particle size distribution
The particle size distribution (PSD) was measured using a laser diffraction analyser
(Coulter LS 130, England) and applying the Fraunhofer optical model (Annapragada
& Adjei, 1996). Each sample was run in duplicate. The area based diameter (d32) is
defined as d 32 = ∑ ni d i3
i
∑n d
i
2
i
, where ni is the percentage of particles with a
i
diameter di. The percentage of fine (< 10 µm) and coarse (> 10 µm) particles was
obtained by integrating the particle size distribution curve between the above
mentioned limits. The PSD was stable at least for the following three weeks after
homogenisation.
6
2.5 Microscopic observations
To analyse the microstructure of the suspensions, 10 % tomato samples were observed
using light microscopy (Nikon Optiphot, Japan) at a magnification of about 25x.
Around 10 µl of each suspension was placed on a slide and the cover glass was
carefully placed over the specimen, thereafter it was rotated ~45° in all the samples to
minimise the effect of uncontrolled shearing during the preparation of the samples.
Three preparations were made for each suspension and at least five pictures were
taken in different areas of each preparation. The images were acquired using a Sony
digital camera (CCd-IRIS/RGB) and the program Image-Pro-Plus (v. 4.0). The images
were recorded as 8-bits greyscale, at a resolution of 720 x 576 pixels and saved as
JPEG-files.
2.6 Image analysis
Image analysis was performed on 124 microscopic pictures. The free available
software ImageJ (vs. 1.38r) was used to convert the images to binary, first correcting
for an inhomogeneous lighting by subtracting the background with a rolling ball (30
px), then reducing the noise by applying a mean filter (1.5 px) and finally adjusting
the threshold automatically at a value of 137, which was observed to give a similar
visual appearance as that of the original images. The percentage area occupied by the
particles and the fractal number derived from the image (fractal based on box
counting, box sizes: 2–124) were estimated on these binary images using ImageJ
algorithms. To estimate the size of the pores or distance between the particles (i.e. the
voids of the image), a macro was written in ImageJ, where a series of binary
operations (close, open) were applied on the images to identify the particles and
separate them from the background. The images were then inverted, and a Euclidian
distance map (EDM) was generated on the voids of the image. The minimum distance
between the particles was characterised at several points on the skeleton of the voids.
2.7 Volume fraction determination
The volume of particles was determined by subjecting the samples to centrifugation at
~110 000 g for 20 min at 20ºC in an ultracentrifuge (Optima LE-80K, Beckman,
California) equipped with a SW41Ti rotor (tube diameter d = 14 mm). The volume
fraction of wet solids was calculated as φ = Vs Vt , where Vs is the volume of wet
7
solids and Vt is the total volume of the suspension. The volume fraction determination
was performed at least in duplicate.
2.8 Rheological measurements
Dynamic rheological measurement of tomato samples was carried out in a controlledstress rheometer (StressTech, Reologica, Sweden) using a four-blade vane geometry
(for calibration procedure, see Bayod et al., 2007a) in order to eliminate the slip
phenomenon and reduce the influence of large particles. The stress sweep tests (0.03100 Pa), at a frequency of 1 Hz, were carried out to determine the range of linear
viscoelastic response under oscillatory shear conditions. The frequency sweep
measurements under conditions of linear viscoelasticity were performed at a constant
stress amplitude of 0.3 Pa in the range of frequencies 0.01–100 Hz. All oscillatory
measurements were performed at least in duplicate.
2.9 Statistical analysis
Analysis of the variance (ANOVA) was carried out to evaluate the effects of
concentration, homogenisation and shearing, on the measured properties of the tomato
suspensions, using Minitab (Minitab v.14, 2003).
3. Results
3.1 Microscopic observations
The light microscopy pictures were taken on 10 % tomato suspensions subjected to
different degree of homogenisation, and subsequent shearing. The suspensions were
stable under at least three weeks after preparation. The series of images in Fig. 1
reveal the successive creation of an evenly distributed network by passing the
suspension through the homogeniser several times. An evident decrease of the particle
size is noticed, which is accompanied by an increase in the surface area covered by
the particles from an initial 20 % up to 50 % in the most homogenised samples (Table
3). Posterior shearing of the suspensions had no visible influence on the surface area
covered at low degree of homogenisation, but the structure of the suspensions become
distinctly different after shearing, for the well homogenised suspensions. In fact, in
the homogenised-and-sheared suspensions (H3-SH) the individual particles tend to
aggregate forming heterogeneous regions with densely packed flocs, resulting in a
8
Non sheared
Sheared
H0
H1
H2
H3
Figure 1. Binary images of 10 % tomato paste suspensions at different degrees of homogenisation (H0,
H1, H2, H3), before and after subsequent shearing (SH). The bar is 250 µm.
9
different type of network. From this series of pictures, it is therefore deduced that
homogenisation creates a network that is disrupted by shearing, depending on the
degree of homogenisation.
The apparent fractal number (Df), derived from the images, shows similar trends,
initially it is 1.5 increasing up to 1.8 as a result of the homogenisation, and decreasing
down to 1.6 due to the subsequent shearing of the structure. Note that the images are
2-D, and therefore the fractal number is comprised within 1 ≤ Df ≤ 2. If the 3-D
network is considered to be isotropic, i.e. it has the same properties in all directions,
the Df values will approximately correspond to 2.3 at H0, 2.8 at H3, decreasing to 2.5
at H3-SH, which indicates a high degree of fractality of the network.
Table 3. Percentage of area covered by the particles in 10 % tomato paste suspension, at different
degrees of homogenisation (H), before and after prolonged shearing (SH). The fractal number
representing the microstructure of the suspension is also reported. The pore size distribution is given as
average pore sizea (µm), and as the percentage of small (< 45µm) and large pores. All the data was
obtained by image analysis. All factors (H, SH, H*SH) had a significant influence (p<0.03, ANOVA)
on the variables shown here, except for the minimum pore size (min.), where only the interaction
(H*SH) was significant.
Shearing
H
Non sheared
H0
H1
H2
H3
H0
H1
H2
H3
Sheared
a
Covered
area [%]
18
33
40
46
21
25
33
27
Fractal
number
1.55
1.74
1.81
1.85
1.61
1.66
1.73
1.68
Pore size [µm]
average min.
135
15
78
13
59
12
54
12
111
12
109
15
96
13
106
16
max.
417
279
241
188
375
320
326
318
Pores [%]
< 45 µm
20
37
46
52
25
25
30
19
> 45 µm
80
63
54
48
75
75
70
81
Note that pore size is used as a wide definition and includes the separation between particles
The average separation between particles or aggregates, as well as the porosity of the
network, is of interest to understand the rheological behaviour and the microstructure
of the suspensions. The distance between the particles and/or the distribution of pores
in the network is observed to change on homogenisation, and successive shearing. In
the non homogenised samples, the average distance between the particles (i.e. whole
cells) is around 135 µm, for the 10 % tomato suspension. During homogenisation, the
microstructure of the network changes, and this change is accompanied by the
10
formation of smaller pores. At low degree of homogenisation (H1) only 40 % of those
pores are below 45 µm, having an average size around 80 µm. In the highly
homogenised system (H3), the averaged pore size has decreased to 54 µm and more
than 50 % of the pores are now below 45 µm. Successive shearing of this network
leads to the formation of aggregates/flocs, with a distance between them of the order
of 100 µm (H3-SH). Note however that in the sheared samples, the distance between
particles, i.e. whole cells or aggregates, seems independent of the degree of
homogenisation, although the shape, size and distribution of the particles have
drastically changed.
Finally, a rough estimation of the aspect ratio was performed on the micrographs,
giving for the individual particles (whole cells or fragments) a value close to 1.5. The
flocs formed after prolonged shearing show, however, higher aspect ratios, in the
order of ~10, and were observed to orient easily in the shearing direction (~45º).
3.2 Particle size distribution
The particle size distribution (PSD) of the non homogenised tomato suspensions
(lower curve in Fig. 2) exhibits a bimodal distribution with a prevailing very coarse
fraction (> 100 µm, Table 4). The relative concentration of coarse and fine fractions
changes with the homogenisation degree, which tends to increase the amount of finer
particles. Also, prolonged shearing has an effect on the PSD of the particles with the
coarse fraction that tends to increase, probably due to the aggregation of the fine
particles forming densely packed flocs, as suggested from the microscopic pictures
(Fig. 1).
The efficiency of homogenisation was different at different concentrations of tomato
paste (10, 30 and 40 %), as is reflected in the different PSD curves obtained at the
same degree of homogenisation (H0, H1, H2, or H3). The coarse fraction of particles
was significantly lower after just one passage through the homogeniser (H1) in 10%
suspensions, whereas in the more concentrated suspensions (30 and 40 %) there was
almost no effect of this first passage. Moreover, the highly homogenised 10 % sample
(H3) contains a larger proportion of fine particles, i.e. < 10 µm, compared to the 30
and 40 %.
11
cumulative area mass [%]
100
h0
h1
h2
h3
h0sh
h1sh
h2sh
h3sh
80
60
40
20
A
0 3
10
2
1
0
−1
10
10
10
10
equivalent spherical diameter [µm]
10
−2
cumulative area mass [%]
100
h0
h1
h2
h3
h0sh
h1sh
h2sh
h3sh
80
60
40
20
B
0 3
10
2
1
0
−1
10
10
10
10
equivalent spherical diameter [µm]
10
−2
cumulative area mass [%]
100
h0
h1
h2
h3
h0sh
h1sh
h2sh
h3sh
80
60
40
20
C
0 3
10
2
1
0
−1
10
10
10
10
equivalent spherical diameter [µm]
10
−2
Figure 2. Particle size distribution expressed as cumulative area mass (%) as a function of the
equivalent spherical diameter (µm) for A) 10 %, B) 30% and C) 40 % tomato paste suspensions, at
different degrees of homogenisation (H0, H1, H2, H3), before and after subsequent shearing (SH).
12
Table 4. Morphological properties of the tomato fibre suspensions based on their area-based particle
size distribution. Percentage of particles with sizes larger than 10 µm and ratio between fine and coarse
particles (f/c), i.e. those below and above 10 µm, respectively. The median diameter for those size
fractions is also given. All the factors (concentration, homogenisation and shearing) and their
interactions had a significant influence (p<0.001, ANOVA) on the variables, except for the size of fine
particles, where SH and SH*CONC were non-significant.
Shearing
Conc.
H
Non sheared
10%
H0
H1
H2
H3
H0
H1
H2
H3
H0
H1
H2
H3
H0
H1
H2
H3
H0
H1
H2
H3
H0
H1
H2
H3
30%
40%
Sheared
10%
30%
40%
Size fraction
Coarse
> 10 µm
[%]
73
47
28
25
73
74
40
38
73
75
63
37
72
50
37
34
67
75
36
39
68
76
68
41
Median diameter (d32)
f/c
Coarse
Fine
[-]
0.4
1.1
2.6
3.0
0.4
0.4
1.5
1.6
0.4
0.3
0.6
1.7
0.4
1.0
1.7
1.9
0.5
0.3
1.8
1.6
0.5
0.3
0.5
1.4
[µm]
177
119
72
54
177
141
80
63
177
148
115
59
175
114
72
57
179
145
98
57
176
159
126
67
[µm]
3.1
1.2
0.8
0.7
3.1
4.0
0.7
0.5
3.1
4.0
2.2
0.7
3.5
1.5
0.8
0.8
2.4
4.0
0.7
0.9
2.4
4.0
3.0
1.0
For the diluted 10 % suspension, the coarse component (> 10 µm) has a median areabased diameter of 177 µm before homogenisation and represents about 73 % of the
particles in the suspension. The amount decreases to 47 % after 1 passage through the
homogeniser, and to 28 and 25 % after 2 and 3 passages, respectively. The median
diameter of the larger fraction of particles progressively decreases with the process of
homogenisation to 119, 72 and 54 µm for H1, H2 and H3, respectively. The fine
fraction of particles (< 10 µm) varies its percentage in an inverse way. Initially it has a
median diameter of approximately 3 µm, and represents 27 % of the particles,
whereas after homogenisation (H3) the median diameter decreases to 0.7 µm and
characterizes nearly 75 % of the particles.
13
Prolonged shearing of the tomato suspensions shows little or no effect on the PSD at
low degrees of homogenisation, and strongly influences it at high homogenisation
degrees. For the highly homogenised 10 % suspensions (H3-SH), shearing increases
the amount of coarse particles from 25 to 34 % and slightly augments the median
diameter to 57 µm. The changes in the coarse and fine fraction of the PSD in the more
concentrated suspensions (30 and 40 %) are also shown in Table 4 and Fig. 2(b-c),
and can be interpreted in the same way as for the more diluted suspensions.
3.3 Volume of particles and gel strength
The volume ( φ ) that the particles occupy in suspension depends also on
morphological factors such as the PSD and the particle shape, as well as on their
packing capacity and deformability. In this work, φ
was determined by
ultracentrifugation and is shown in Fig. 3(a) as a function of the degree of
homogenisation. Breaking the cells into smaller particles by homogenisation results in
an increase of the volume occupied by those particles in the suspension. Prolonged
shearing of highly homogenised suspensions results in a decrease in φ , whereas no
changes are observed at low degree of homogenisation. Similar trends are observed
for all concentrations considered in this study.
In a suspension, it is assumed that the volume fraction occupied by the particles
determines its rheological properties, and then changes in φ due to formation
(homogenisation) and disruption (shearing) of the structure might be reflected in the
strength of the network formed by the suspended particles. Small amplitude
oscillatory shearing is used here to monitor the structural changes induced by
homogenisation and shearing.
Firstly, the linear viscoelastic (LVE) region was determined for the suspensions using
a stress sweep. At low concentrations (10 %) and low degrees of homogenisation, the
linear region was difficult to achieve due to limitations of the measuring equipment,
where the minimum possible stress was defined at 0.03 Pa. At that concentration, the
end of the linear region, in some samples (H0, H0SH, H1SH), was therefore assumed
to be at this minimum stress value, and the elastic (G’) and loss (G’’) moduli
discussed below were determined at that stress (0.03 Pa). For the rest of the samples,
14
the linear region was clearly found, and the limiting stress at the end of the LVE was
observed to vary between 0.7 and 3.5 Pa, for 10 % samples, between 2.4 and 13.6 Pa,
for 30 % samples, and between 4.3 and 17.6 Pa in 40 % samples, increasing with
homogenisation within each concentration.
0.6
Figure 3. A) Changes in the
volume fraction ( φ ) and B) in
Volume fraction, ø [-]
0.5
the linear elastic modulus (G’,
0.4
ω=1Hz) with the degree of
homogenisation for 10, 30 and
0.3
40 % tomato paste suspensions
0.2
(■, ▲, ●, respectively). Filled
symbols
0.1
A
represent
samples
before shearing and empty
symbols are samples that have
0.0
h0
h1
h2
h3
been subjected to prolonged
10000
Elastic modulus, G’ [Pa]
shearing.
1000
100
B
10
h0
h1
h2
h3
degree of homogenisation
All samples behave as gel-like materials, where G’>G’’ at all frequencies
(0.01<ω<100 Hz). For the 10 % suspension, the elastic modulus (G’) in the LVE is
observed to increase with the degree of homogenisation (Fig. 3(b)) and shearing
decreases the G’-value to a great extent. For the 30 % suspension, a slight increase in
G’ with the degree of homogenisation is noticed, followed by a small decrease after
shearing. However, for the 40 % suspensions, the elastic modulus is almost constant,
and both homogenisation and shearing seem to have a negligible effect on the strength
15
of the network. These results seem to be in contradiction with the changes in the
volume of the particles reported previously and will be further considered in the
discussion.
The oscillatory data as a function of the frequency (ω) was measured in the LVE at
constant stress (σ = 0.3 Pa). Only the samples that exhibit a linear region at that stress
are reported here. The strain (γ) was always kept below 10-2 (Fig. 4(a)). The strain as a
function of the frequency showed a minor decrease until a certain frequency was
reached, after which γ decreased sharply. This limiting frequency seems to depend on
the concentration of paste, being lower at low concentrations. The sudden decrease in
γ might be related to an apparent shear thickening behaviour at high frequencies. The
large particles probably have more difficulties to follow the sinusoidal motion,
contributing in this way to an increase in the rigidity of the system. A similar
phenomenon has been observed by Nakajima and Harrell (2001).
The storage (G’) and loss moduli (G’’) as a function of the frequency are shown in
Fig. 4(b-c). The elastic modulus (G’) results in a smoother curve with better
reproducibility than G’’, probably due to the more solid nature of the suspensions
(G’>G’’). Both moduli seem to be sensitive to the degree of homogenisation, i.e. to
different PSD, but the effect of concentration is clearly dominant. Besides, shearing
has a slight effect on the values of the moduli (data not shown). At high frequencies
all curves seem to converge into one, which might be due to the apparent
immobilization (or increased rigidity) of the particles, as explained above. The
mechanical spectra of all the suspensions follow some general trends that are
characteristic of concentrated suspensions: the elastic modulus G’ increases slightly
with increasing frequencies, whereas the loss modulus G’’ shows a minimum at low
frequencies 10-2 < ω < 10-1, thereafter it gradually increases with ω (Ferry, 1980,
Ross-Murphy, 1988). The observed curves were fitted to the empirical
equations, G ' = k ' ω m ' and G ' ' = k ' ' ω m '' , in the range of frequencies comprised between
the minimum in G’’ and the upper limiting ω, where γ decreased drastically. The
fitted parameters k’ and k’’ are mainly related to the magnitude of G’ and G’’, which
is governed by the concentration (data not shown). The exponents m’ and m’’ are
related to the solid-liquid behaviour of the suspension, being G ' ∝ ω 2.0 and G ' ' ∝ ω 1.0
16
−2
10
Figure 4. Oscillatory rheological data as
a function of the frequency, measured in
−3
10
γ [−]
the linear viscoelastic region (σ =0.3
Pa): A) strain (γ), B) elastic modulus
−4
10
(G’) and C) loss modulus (G’’). Solid,
long-dashed and dashed lines represent
−5
10
10, 30
suspensions,
A
−6
10
−2
10
10
−1
0
10
ω [Hz]
1
2
10
and 40
10
%
tomato
respectively.
For
paste
each
concentration, each line indicates a
different degree of homogenisation; in
5
10
general, the higher G’ and G’’, the more
homogenised the sample.
4
10
G’ [Pa]
3
10
2
10
1
10
B
0
10 −2
10
10
−1
0
10
ω [Hz]
1
2
10
10
5
10
4
10
G’’ [Pa]
3
10
2
10
1
10
C
0
10 −2
10
10
−1
0
10
ω [Hz]
10
1
2
10
characteristic for an ideal liquid, whereas the mechanical spectra of an ideal gel is
expected to be independent of ω (Ferry, 1980, Ross-Murphy, 1988). In tomato
concentrates, we have previously shown that 0.1<m’<0.2 and 0.2<m’’<0.3 (Bayod,
Willers & Tornberg, 2007b) at 0.05< φ <0.6, which is characteristic of strongly
aggregated gels. In this investigation, even lower m’ were obtained, with values
17
varying between 0.08 and 0.14, suggesting an even more solid-like network
suspension.
4. Discussion
In this paper, we consider structured suspensions as those exhibiting solid-like
network behaviour or, in other words, having a storage modulus (G’) rather
independent of the frequency (ω) and always higher than the loss modulus (G’’). This
was the case in all studied suspensions, showing m’~ 0.1 and G’ > G’’, even at the
lowest concentration (10 %). However, the concentration regime had a strong impact
on the rheological behaviour of the suspensions and on the processing effectiveness.
In semi-diluted regimes, such as 10 %, the particles are swollen to equilibrium
(Steeneken, 1989) and form a more heterogeneous network consisting of a collection
of particles or aggregates/flocs, with large pores in between (Fig. 1). The rheological
properties (G’) and the volume fraction ( φ ) of this type of suspension depend linearly
on f/c , whereas this does not seem to be the case for the more concentrated
suspensions, being more independent on f/c (Fig. 5). We suggest that the 30 and 40 %
tomato paste suspensions form instead a continuous particulate network, where the
particles fill up all the available space and probably are not swollen to equilibrium but
exist as more deformed particles (Steeneken, 1989). Such networks exhibit a yield
stress (Buscall, et al., 1987 and Bayod et al., 2007a). In this study, an indicator of the
yield stress is given by dynamic measurements as the limiting stress at the end of the
linear viscoelastic region and we observed that this type of yield stress was negligible
at the lowest concentration of 10%.
The existence of a continuous network seems to have an impact on the efficiency of
the homogenisation process, i.e. the ability to break down the particles. As the PSD
indicates (Fig. 2), changes were only noticed after 2 passages through the
homogeniser in 30 %, and after 3 passages in 40 %, and when breakage does occur,
the decrease of particle size is rather extensive. This behaviour is also visualised in
Fig. 5. It seems that a gradual decrease of the particle size occurs upon
homogenisation of semi-diluted systems, whereas a minimum number of passages
18
seem to be required to begin breaking down the particles in systems having a spacefilling network. We suggest that on homogenisation of highly concentrated
suspensions, the network should first be broken into smaller aggregates, creating
heterogeneities, before individual particles can also begin to be broken down.
0.6
Figure 5. A) Volume fraction
(φ )
0.5
B)
linear
elastic
modulus (G’, ω=1Hz) as a
0.4
ø [-]
and
function of the fine to coarse
0.3
ratio (f/c) for 10, 30 and 40 %
tomato paste suspensions (♦, ▲,
0.2
●, respectively). Filled symbols
0.1
represent
A
0.5
1.0
1.5
2.0
2.5
3.0
before
shearing and empty symbols are
0.0
0.0
samples
3.5
f/c [-]
samples
that
have
been
subjected to prolonged shearing.
10000
The lines are a guide to the eye.
G' [Pa]
1000
100
B
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
f/c [-]
The rheological behaviour of the more concentrated suspensions does not seem to be
dependent on φ and PSD (f/c) to the same extent as in the semi-diluted suspensions
(Fig. 5). In fact, φ was found to be more sensitive to changes in the microstructure of
highly concentrated suspensions, changes that, however, were not noticed in the
elastic modulus (G’) (Fig. 3 and 5). This might be explained by the fact that in more
concentrated suspensions the deformability of the particles comes more into play, as
pointed out by Steeneken (1989). Channell et al. (2000) found that the presence of
heterogeneities in the microstructure of aggregated aluminia suspensions could be
measured using compressive yield stress (by centrifugation), whereas the shear
19
modulus G could not differentiate between these different type of microstructures. In
our study, large particles, aggregates or flocs and large pores or voids in the network
are causing heterogeneities in the microstructure of the suspensions. Since φ has been
determined by ultracentrifugation, i.e. uniaxial compression at a given speed
(~110.000 g), it can be affected by the compressive strength of the different networks,
i.e. by the heterogeneities induced by homogenisation and subsequent shearing.
However, those changes introduced by processing may not alter the number of
junction points in the network, especially in the more concentrated suspensions where
particles are physically touching each other and space-filling, giving for this reason
similar G’ values in the dynamic shear measurements.
The volume fraction of the particles is partially determined by the maximum packing
fraction ( φmax ), which in turn is affected by particle shape, size and PSD, the latter
parameters being subjected to changes during homogenisation. The method of
packing (regular or random) has also an influence on the maximum packing fraction,
and the initial random packing in the homogenised suspensions is probably modified
due to the densification of the particles inside the aggregates/flocs on shearing. It is
therefore expected that each sample in this investigation exhibits different φmax . The
PSD has in some cases been used to calculate the maximum packing of particles in
unimodal and bimodal particle size distributions (Farris, 1968, Lee, 1970, Bierwagen
& Saunders, 1974) and recently also in a continuous PSD, when it exhibits a powerlaw distribution (Brouwers, 2006). The cumulative finer fraction as a function of the
particle size (Fig. 2), as suggested in Brouwers (2006), might be an indicator of the
ability of the particles how to pack in a suspension. To our knowledge, however, no
methods are available so far to determine φmax for more complex PSD such as those
studied in this paper.
Rheological data and morphological features derived from the PSD, as well as φ
obtained by ultracentrifugation, were considered for regression analysis. An
experimental equation was found to accurately describe the whole set of data
(R2>99.3%, p<0.001), including the size of the coarse fraction (d32, coarse, in meters)
and the compressed volume φ occupied by the particles, being the most relevant
parameters determining the elastic and loss moduli.
20
4
10
3
G’ [Pa]
10
2
10
1
10
0
0.1
0.2
0.3
φ [−]
0.4
0.5
0.6
Figure 6. Linear elastic modulus (G’, ω=1Hz) as a function of the volume fraction ( φ ) in suspensions
with predominant coarse (f/c<1, ●) or fine (1<f/c<3, ○) particles. The fitted values using Eq. 1 are also
β
shown (x). The dotted lines represent the fitting to G ' = αφ , and the fitted parameters (α and β) are
given in the text.
log G' = 3.75 + log φ 2.47 + 4120d 32,coarse ,
(1)
log G ' ' = 3.08 + logφ 2.52 + 4660d 32,coarse .
(2)
The importance of the particle size (d43) in the determination of the viscoelastic
properties of tomato products was also experimentally observed by Sánchez et al.
(2002), who found an experimental equation describing G ' = f (WIS , d 43 ) .
The oscillatory shear data obtained in the linear region (G’) was plotted against the
volume fraction of the particles ( φ ) in Fig. 6. The elastic modulus estimated by Eq. 1
is also included for comparison and very good agreement between the experimental
and calculated data according to Eq. 1 is obtained. The data indicates that suspensions
with predominantly coarse particles (f/c<1) exhibit higher G’-values than suspensions
with predominantly fine particles (f/c>1) at a given φ . We have applied the fractal
approach, according to Eq. 3, to describe the rheological behaviour of the
21
suspensions, in those size fractions: the coarse (f/c<1) having a median diameter of
approx. 100 µm, and the fine (f/c>1) having a median diameter of approx. 30 µm. The
elastic modulus (G’) of a particulate network (or gel) is related to the volume of
particles in the network by the following relationship, proposed by Narine and
Marangoni (1999),
G ' = αφ β ,
(3)
where α is a constant that depends on the size of the particles and on the interactions
between them, φ is the volume fraction of particles and β = 1 ( d − D f ) is an exponent
that depends on d, the Euclidean dimension of the network (usually d=3), and Df, the
fractal dimension of the network. These authors used this equation to describe the
behaviour of fat crystal networks at φ up to 0.7. In our case, the parameters α and Df
were determined by fitting the data to Eq. 3. The constant α here has a corresponding
value of α ~ 20000 for f/c<1, and α ~ 10000 for 1<f/c<3. The fractal number was not
substantially different in the coarse and fine fractions, having a value of Df~2.58,
which is comparable to the averaged Df obtained from the image analysis of the 10 %
tomato paste suspensions. From table 3, the averaged Df value for fine and coarse 10
% suspensions can be calculated and converted to 3-D, by assuming that the
suspensions are isotropic. This gives a value of 2.41 for the coarse suspensions (f/c <
1) and 2.64 for the finer suspensions (1<f/c<3), which are in qualitatively agreement
with the fitted value.
The fractal description in 3-D is based on the assumption that the microstructure is
randomly distributed in three dimensions, but subsequent shearing orients the flocs or
aggregates in a 2-D plane, and the fractal approach might then be less valid.
Moreover, it is not possible to confirm the fractal behaviour of the highly
concentrated space-filling suspensions, and extrapolating the results from the semidiluted regime alone to higher concentrations is not accurate enough. Moreover, the
determination of the volume fraction involves some compression of the network, and
φ is then the volume of the deformed particles and not necessarily the cumulative
volume of primary fractal elements. But, even with the limitations described above, it
is unambiguously concluded that the power-law scaling holds for a large range of φ ,
22
PSD and particle shapes. In strongly flocculated colloidal suspensions, Buscall et al.
(1987) suggested that the strong power-law dependence on concentration in such
systems supports the idea that those networks have a heterogeneous structure
comprising a collection of interconnected fractal aggregates.
Finally, some practical implications of our findings are to be mentioned. In the
determination of rheological properties of this type of suspensions, it is common to
pre-shear the sample as a way to establish a controlled and known shear history,
avoiding in this manner the possible time effects. The result of this pre-treatment, in
suspensions like those studied here, would rather lead to the formation of irreversible
flocs and other structural rearrangements that significantly change the microstructure
and the nature of the suspensions, giving rise to misleading rheological data.
5. Conclusions
Tomato paste suspensions undergo pronounced microstructural changes on
homogenisation, and subsequent shearing. Strong variations in the particle size
distribution and shape as well as changes in the arrangement of particles in the
suspension occur upon processing, and have a substantial influence on the rheological
properties of such suspensions. The formation of flocs consisting of densely packed
particles appears on shearing suspensions containing large amounts of fine particles.
Moreover, these flocs have a tendency to orient in the direction of the flow, hence
decreasing the viscosity of the fluid, leading to a decrement of several quality
parameters in the suspension. The results of this investigation may be used to enhance
industrial processing of food suspensions, where homogenisation takes place, to
prevent the deterioration of the quality of the network by prolonged shearing (e.g.
mixing, or pumping).
Acknowledgements
The authors wish to thank VINNOVA, Orkla Foods AB and TetraPak AB, for their
financial support. Comments on the manuscript and helpful discussions with Prof.
Petr Dejmek are also gratefully acknowledged.
23
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26
Rheological behaviour of concentrated fibre suspensions in
tube and rotational viscometers, in the presence of wall slip.
Bayod E., Jansson P., Innings F., Dejmek P., Bolmstedt U., Tornberg E.
(2008)
Manuscript
IV
Rheological behaviour of concentrated fibre suspensions in tube and
rotational viscometers, in the presence of wall slip.
Bayod E.1*, Jansson P.1, Innings F.2, Dejmek P.1, Bolmstedt U.1,3, Tornberg E.1
1
Department of Food Technology, Engineering and Nutrition,
Lund University, P.O. Box 124, 222 01 Lund, Sweden
2
Tetra Pak Processing Systems, 221 86, Lund, Sweden
3
Tetra Pak Processing Components, 221 00 Lund, Sweden
*corresponding author: [email protected]
Abstract
The rheological behaviour of concentrated fibre suspensions, i.e. dried potato fibres and
tomato paste, has been studied in a tube viscometer with three diameters, and in a rotational
rheometer, using different geometries: concentric cylinder, vane in a smooth cup and vane in
a vane cup, in order to create different slip conditions. The occurrence of slip has been
evaluated in the tube viscometer data using the classical Mooney method and a numerical
Mooney-Tikhonov method, but the solutions given by these methods were found to be
unrealistic when the reproducibility of the data was poor. Dynamic measurements are
suggested as an alternative to obtain the “true” flow behaviour of the suspensions, but, in
yield stress fluids, the Cox-Merz rule should first be modified to include a shifting factor on
the frequency. In tomato suspensions, this factor is found to be independent of both the
concentration and the yield stress value.
Keywords: Wall slip, tomato paste, fibre suspensions, Cox-Merz rule, Mooney, Tikhonov,
tube and rotational viscometers
1. Introduction
Determination of the rheological properties of food materials is carried out for a variety of
purposes, ranging from quality control, to engineering and process design. Many foodstuffs
can be described as concentrated suspensions, e.g. emulsions, pastes, foams, and they are
found to exhibit a complex rheological behaviour. Rheological measurements made on
complex materials are then complicated by their viscoelasticity, the possible occurrence of
slip at the walls of the measuring instrument, and by the possible migration of particles and/or
structural degradation and rearrangements (Kalyon 2005). Measurements performed under
similar experimental conditions, but in different geometries, do not always superpose
1
(Plucinski et al., 1998), and hence the comparison and/or prediction of rheological properties
from one instrument to another are difficult to achieve. These difficulties become a major
problem for food engineers when designing industrial equipment based on rheological data
obtained for example in rotational rheometers.
Rotational rheometers are convenient because of their small dimensions, thereby requiring
less sample amount. However, in complex materials with large particles (> 100 µm) the
number of applicable geometries is limited. The vane geometry has become popular to
explore the rheological behaviour of complex food such as tomato products (Yoo, Rao and
Steffe, 1995, Bayod et al., 2007a), and yogurt (Krulis and Rohm, 2004), because it reduces or
prevents the slip at the wall, and causes minimum disturbance when it is load into a complex
fluid. Nevertheless, the shear rates that can be investigated using the vane geometry are rather
low, γ& < 10 s-1, in most cases (Dzuy and Boger, 1983). Hence, it might not be relevant in
estimating the flow behaviour of food materials during processing, for example in a tube,
where the typical shear rates are 100 < γ& < 1000 s-1.
Using a tube viscometer is an alternative that allows to measure particulate suspensions in this
range of shear rates, but it requires large floor space and a substantial amount of sample. In
addition, wall slip is likely to occur and should be corrected for, particularly if the data needs
to be scaled to different diameters, which is often the case in food process design. The
classical method for slip correction in tube viscometer was proposed by Mooney (1931) for
capillary flow, involving measurements in at least three capillary diameters. He divided the
measured flow in two parts; one due to the slip velocity (Qs) and the other caused by the shear
rate in the fluid (Qws), and developed a graphical method to determine the slip velocity, which
was assumed to be only a function of the wall stress, vs = f (σ w ) . This analysis was found to
fail in some cases, and Jastrzebski (1967) proposed a modification of the method, where he
suggested the slip velocity to be inversely proportional to the capillary radius,
vs = f (σ w ,1 R) . However, this approach has no theoretical justification and has been
discussed to give incorrect slip velocities (Martin and Wilson, 2005).
Yeow et al. (2000) have developed a new numerical method to extract rheological data from
the tube viscometer for yield stress fluids, using inverse problem solution techniques and
Tikhonov regularisation, which was reported to work on fruit purees (Yeow, et al., 2001).
Later, they have extended the method to cope with the presence of wall slip (Yeow et al.,
2003), based on the Mooney analysis, with the advantage that it does not require the
assumption of any rheological or slip model. Martin and Wilson (2005) applied this numerical
2
method on published data of polymers, foams and pastes, finding that the method works well
on polymers and foams, but its performance was not as good on paste materials. This
Mooney-Tikhonov method has not yet been applied to interpret the flow data of highly
concentrated food suspensions, such as tomato paste, which is known to exhibit both yield
stress and wall slip. Wall slip effects in tomato paste account for 70-80 % of the measured
flow using the Mooney-Jastrzebski analysis (Kokini and Dervisoglu, 1990), and tomato
concentrates at concentrations of 12ºBrix exhibited slip velocities from 2 to 12 cm/s at wall
shear stresses below 20 Pa. The flow rate governed by the slip was as high as 80% of the total
flow, as measured by magnetic resonance imaging (Lee et al., 2002).
The apparent slip is caused by the migration of the liquid phase towards the fluid-wall
interface (Martin & Wilson, 2005), because the particles can not physically occupy the space
adjacent to the wall (Kalyon, 2005). This leads to the formation of a thin layer of less
concentrated suspension at the wall, with a thickness of the same order of magnitude as the
particle size (Yilmazer & Kalyon, 1989). The slip layer has a lower viscosity than the bulk
fluid and distorts the velocity profile in the tube, and might lead to an incorrect interpretation
of the flow data.
The aim of this work was hence to understand more the prerequisites for slip to occur, to find
ways to quantify it and to extract the flow behaviour of concentrated suspensions in a tube
viscometer. Therefore a relatively large variation in the rheological properties of the studied
suspensions was chosen. Two series of suspensions with different low deformation
viscoelastic properties were compared, i.e. one exhibiting liquid-like (G''>G') behaviour, and
the other one a solid-like (G'>G'') behaviour. For the concentrated suspensions having G''>G'
not only the concentration of particles was varied, but also the viscosity of the continuous
phase. With regard to the quantification of the wall slip the classical Mooney graphical
approach and the new numerical Mooney-Tikhonov method were evaluated and compared.
The rheological data generated from the tube viscometer was also compared to steady and
dynamic measurements obtained in a rotational rheometer, and the validity of the Cox-Merz
rule was investigated.
2. Material and methods
2.1 Fiber suspensions
Commercial syrup donated by Danisco AB was used in the experiments. The syrup was
diluted to viscosities of 860 and 68 mPa s, respectively, at 20ºC. Potato dried fibers (provided
by Lyckeby Culinar) were added to the two sugar solutions in the concentration of 4.5, 5.6
3
and 6.5 % (w/w), to obtain a highly viscous non-Newtonian fluid. The series of
concentrations will be referred to as Fiber A (high suspending medium viscosity) and Fiber B
(low suspending medium viscosity). The particle size distribution (PSD) and the volume
fraction of the suspensions were determined, after pumping, as described in Bayod et al.,
2007a. The PSD is given in Table 1.
Table 1. Particle size distribution (PSD) of the material used to prepare the suspensions, given as the
fraction of fine (<10µm) and coarse (>10 µm) particles, the ratio fine to coarse (f/c) and the median
diameter for these two fractions.
Suspended particles
Dried potato fibre
HB tomato paste
CB tomato paste
Mass fraction (%)
Fine
Coarse
(< 10 µm)
(> 10 µm)
47.2
52.8
34.1
65.9
25.3
74.7
Median diameter (µm)
Fine
Coarse
(< 10 µm)
(> 10 µm)
3.73
36.8
2.63
192.6
3.85
153.5
f/c
0.89
0.52
0.34
2.2 Tomato paste suspensions
Two commercial tomato pastes were used for the experiments: hot break tomato paste 2830°Brix (HB) and cold break tomato paste 36-38°Brix (CB) kindly donated by Orkla Foods
AB. The total solids content (TS) was 29.3 and 36.8 %, respectively. The water insoluble
solids (WIS) content was 6.5 % for both pastes. A series of concentrations 500, 400, 300 g/kg
was prepared in distilled water with 0.1 % benzoate added as a preservative. The particle size
distribution (PSD) and the volume fraction of the suspensions were determined, after
pumping, as described in Bayod et al., 2007a. The PSD of the two tomato pastes is given in
Table 1.
Table 2. Main characteristics of the geometries used in the rheometer: concentric cylinder (CC), vane
in a smooth cup (V) and vane in a vane cup (VV). Stress and strain conversion factors (σcoef , γcoef), bob
and cup radius (Rb and Rc, respectively), height of the bob and gap are given.
Type of
Geometry
CC
V / VV
σcoef
Pa/Nm
24998
24560
γcoef
1/s
12.25
4.7
Rb
mm
12.5
10.5
Rc
mm
13.6
13.6
H
mm
37.5
45.0
Gap
mm
1.1
3.1
2.3 Rotational rheometer
Steady-shear rheological measurements were determined in a stress-controlled rheometer
(StressTech, Reologica, Sweden) using different geometries in order to prevent or reduce the
formation of a slip layer: concentric cylinder (CC), four-blades vane in smooth cup (V) and
four-blades vane in vane-cup (VV) (A, B and D in Fig. 1, respectively). The vane-cup was
constructed in such a way that the virtual cylinder formed by the outer blades had the same
diameter as the smooth cup, giving rise to a gap of about 3 mm. The vane and vane-cup were
calibrated as is described in Bayod et al., 2007b; and the main characteristics of the
4
geometries are specified in Table 2. The tomato suspensions were subjected to a logarithmic
increase of the shear rate ( γ& ) from 10-4 to 102 1/s and about 50 measurement points were
determined. At low shear rates, the samples were allowed to stabilize during 40 s and the
measurements were collected during the following 40 s of shearing to avoid time-dependence
effects. At higher shear rates, those times were reduced to 25+25 s. The suspension samples
were collected after pumping them in the tube viscometer. All measurements were run in
duplicate in the three geometries. The supernatants of the suspensions, obtained by
centrifugation, were also subjected to viscosity measurements, using concentric cylinder
geometry only.
A
B
C
D
Figure 1. Schematic illustrations of A) a concentric cylinder, B) the vane geometry C) the previous
geometries inside a smooth cup, and D) the vane geometry in a vane-cup.
Small-amplitude oscillatory measurements were performed on the tomato suspensions after
pumping in the tube viscometer. Stress-sweep test at a frequency of 1Hz was carried out in
order to determine the range of linear viscoelastic (LVE) response under oscillatory shear
conditions. The apparent yield stress was determined from the stress sweep data, according to
Wyss et al., 2005. Frequency sweep measurements were performed at a constant strain (0.01
%) in the range of frequencies 0.05-100 Hz. All oscillatory measurements were run in
duplicate using only the vane geometry (V).
2.4 Tube viscometer.
The rheological measurements were performed in a tube viscometer, kindly constructed by
Tetra Pak Processing Systems AB, consisting of three pipes with different outer diameters, d0
= 20, 25, and 38 mm. The pressure drop was determined over a length L=3.42 m in each pipe,
using two pressure gauges. The transmitters used were of two types Wika P-11 (0-10, 0-16
and 0-25 bars), and Keller PR-35 (0-10 bars). The pressure drop per unit length (dP/L) was
5
checked to be constant for given flow rates over different tube lengths, and hence the entrance
pressure losses were assumed to be negligible. The volumetric flow was determined using an
electromagnetic flow meter (Endress+Hauser, Promag 53, 1.5-75 l/min). A schematic diagram
of the experimental setup is shown in Fig. 2. The system was first calibrated with a
Newtonian syrup (1 Pa s). Then the feeding tank was filled with potato fiber or tomato paste
suspensions. They were pumped through each pipe during 5 min, to fill the system, thereafter
all the valves were opened and the fluid was recirculated during 10 min at low flows (~5
l/min) in the whole system. Finally, the fluid was pumped through one pipe at the time, for 5
min, to ensure that all pipes were filled with exactly the same product. Previous pumping of
the samples was also performed to avoid any time-dependent effects during the
measurements.
P
ø 25
P
P
ø 20
P
P
ø 38
P
3420 mm
Figure 2. Schematic diagram of the experimental setup for the determination of rheological properties
in tube flow.
Each measurement run consisted of pumping the suspension at six selected flow rates, in one
pipe at the time. The sequence of pipe diameters and flows was randomly selected. Before
data was collected, the sample was allowed to flow at the set flow rate for 60 s, to stabilize the
system. The flow rate and pressure drop data were collected during the following 60 s using
the software DaisyLab 9.0, with a sampling rate of 10 s-1. The temperature of the fluid was
manually measured for each flow rate with a thermocouple at the exit of the system (at the
feeding funnel). The experiments were performed in triplicate.
2.5 Evaluation of wall slip in the tube viscometer
2.5.1
Mooney method
The shear stress distribution in the pipe can be obtained from the equation of motion,
assuming the fluid to be incompressible (the viscosity being independent of pressure), and
6
that the motion only takes place in the x direction. The shear stress at the wall of the tube is
then defined as
σw =
RdP
2L
(1)
where R is the tube radius, and dP is the pressure drop over a length L. Assuming fully
developed, isothermal and laminar flow, with velocity only in the x direction, the measured
volumetric flow rate (Qm) is defined as,
R2
R
Qm = 2π ∫ vx (r )rdr = π ∫ vx (r )dr 2
0
(2)
0
where v x (r ) is the velocity profile along the radius of the tube. Equation 2 can be solved with
the boundary condition vx = vs at r = R, to consider possible wall slip velocity (vs). When vs =
0, the non slip condition is fulfilled, and the volumetric flow without slip (Qws) reduces to the
well-known Weissenberg–Rabinowitsch equation,
σw
πR 3
Qws = 3 ∫ σ 2 f (σ )dσ
σw 0
(3)
Equation 3 can be solved analytically for some simple rheological models (Steffe, 1996). In
table 3, some of the analytical solutions are summarised. The apparent wall shear rate ( γ&a )
generated from the volumetric flow in Eq. 3 has generally the form,
γ&a =
Qws ⎛
d ln Qws
⎜3 +
3 ⎜
d ln σ w
πR ⎝
⎞
⎟⎟
⎠
(4)
and for Newtonian fluids, Eq. 4 takes the form of
γ&a =
4Qm
πR 3
(5)
and it is known as the apparent Newtonian shear rate.
σw
Table 3. Analytical solution of
Fluid
model
πR 3
Qws = 3 ∫ σ 2 f (σ )dσ
σw 0
γ& = f (σ )
Newtonian
σ /μ
Power law
(σ / K )1/ n
, for some common fluid models.
Analytical solution
Q=
πR 4 dP
8 Lμ
1/ n
HerschelBulkley
⎛σ −σ y
⎜⎜
⎝ K
1/ n
⎞
⎟⎟
⎠
⎛ dP ⎞ ⎛ n ⎞ (3n +1) / n
Q =π⎜
⎟ ⎜
⎟R
⎝ 2 LK ⎠ ⎝ 3n + 1 ⎠
Q=
1+1 n
2+1 n
3
2
2σ w (σ w − σ y )
π ⎛ 2L ⎞ ⎡σ w (σ w −σ y )
⎜ ⎟⎢
K 1 n ⎝ dP ⎠ ⎣⎢
1 +1 n
−
(1+1 n)(2 +1 n)
2(σ w − σ y )
⎤
⎥
(1+1 n)(2 +1 n)(3 +1 n)⎦⎥
3+1 n
+
If vs ≠ 0, the measured flow (Qm) comprises the contribution of the slip (Qs) and the
contribution of the fluid itself (Qws),
7
Qm = Qs + Qws ,
(6)
where Qs = vsπR 2
(7)
Mooney (1931) suggested a method for the correction of wall slip based on the assumption
that the slip velocity is only a function of the wall shear stress, i.e. vs = β (σ w )σ w . Thus
combining equations 3 and 7 and dividing by 1 σ wπR 3 , he obtained,
σ
Qm
β 1 w 2
=
+
σ f (σ )dσ
σ wπR 3 R σ w4 ∫0
(8)
Generally, the Mooney graphical correction requires measurements in at least three diameters.
At a constant wall shear stress, the slope of a plot of Qm σ wπR 3 against 1/R is equal to the
slip coefficient β. After determining the flow caused by the fluid (Qws), the rheological data
can be extracted using Equation 4. In practice, it is difficult to obtain data in different tube
diameters at the same wall shear stress. In this study, the data from three replicates was
averaged into one curve, for each diameter, and the rheological behaviour of the suspensions
was interpolated and/or extrapolated, assuming a power law behaviour, to a set of values of
wall shear stresses, comprised between the minimum and the maximum σw present in the set
of data.
2.5.2
Mooney-Tikhonov method
The problem of generating shear rate and shear stress data from capillary data (i.e. from
pressure drop and volumetric flow) is formulated, in Equations 3 and 8, as an integral
equation of the first kind, and the solution might not be unique and might not depend
continuously on the data. This is an example of an ill-posed inverse problem and their
mathematical treatment can be complicated (Yeow et al., 2000). Common non linear methods
are difficult to apply because many local minima might exist and the result is then very
dependent on the initial conditions.
Yeow et al. (2000, 2003), has worked out a new method of processing tube viscometer data in
the presence of wall slip. The method essentially takes into account the ill-posed nature of the
problem using Tikhonov regularization and improves the convergence of the solution when
noise is present in the data. The model was slightly modified by Martin and Wilson (2005).
The procedure has the advantage that it does not require the assumption of a rheological
model to relate the shear rate and the slip velocity to the local shear stress, and it uses all the
set of measured data without need of extrapolation. It solves the Mooney equation put in the
form,
8
γ&a =
4Q 4vs (σ w ) 4
=
+ 3
πR 3
R
σw
σw
∫σ
'
γ& (σ ' )σ ' dσ '
(9)
For yield stress fluids, the lower integration limit σ’ is replaced by the unknown yield stress
σy. The condition that at the yield stress the shear rate is zero should also be satisfied, and is
( )
solved iteratively for γ& σ y = 0 . The first part of Equation 9 is the contribution of the wall
slip to the shear rate, and the second part is that of the shear flow. To apply the MooneyTikhonov method, the interval between the minimum and maximum values of σw in the set of
data is divided into Nj uniformly spaced points, and the unknown slip velocities at these
points are represented by a vector vs=[v1, v2,…vNj]. In the same way, the integration interval
(σy to σw) in Equation 9 is divided into Nk uniformly spaced points, and the unknown shear
rates at these points are represented by the vector γ& =[ γ&1 , γ&2 ,… γ& N k ]. The precision of the
solution is evaluated by the sum of the squares of the deviation between the calculated shear
rate (superscript c) and the experimental measured data (superscript m),
⎡ γ& m − γ& c ⎤
S1 = ∑ δ = ∑ ⎢ a ,i m a ,i ⎥
i =1
⎢⎣ γ&a ,i ⎥⎦
ND
2
2
i
(10)
To ensure that the shear rate γ& (σ ) and the slip velocity vs (σ ) functions varied smoothly
with the local stress, the sum of the squares of the second derivatives of these two functions,
at the internal discretization points, is also minimised,
4
S2 =
Rmin
⎛ d 2 vs
⎜⎜
∑
2
p = 2 ⎝ dσ w
N j −1
N k −1
⎞
⎛ d 2γ& ⎞
⎟⎟ + ∑ ⎜⎜
⎟ .
2 ⎟
⎠ p q = 2 ⎝ dσ ⎠ q
(11)
Tikhonov regularization minimises a linear combination of these two quantities,
R = S1 + λ S 2 ,
(12)
where λ is an adjustable numerical factor. For example, a large value of λ favours the
smoothness conditions over the goodness of the fit.
2.5.3
Synthetic data for method verification
The performance of the above described methods in extracting rheological data from tube
viscometer data was first tested on synthetic data. The data was generated from the Power
Law (PL) and Herschel Bulkley (HB) rheological models, σ = Kγ&
n
n
and σ = σ y + Kγ& ,
respectively. The parameters used in the models were K = 50 Pa sn, n = 0.25 and σy = 100 Pa.
9
The shear stress was set between 105 and 500 Pa. The flow rate (Qws) was calculated using
the equations presented in Table 3 for PL and HB fluids. Slip is also synthetically generated,
using the model vs = βσ wα , where β = 10-5, and α = 1.4 or α = 2.0. Two different levels of
noise were randomly added to the data, 1 and 10 %, to evaluate the effect of poor
reproducibility on the extracted slip and fluid models. The data was generated in three tube
radius R=8.7, 11.5 and 18.1 mm, and the apparent Newtonian shear rate and the wall shear
stress were calculated using Eq. 1 and 5, respectively.
3. Results and discussion
3.1 Verification of Mooney’s and Mooney-Tikhonov’s method on synthetic data
For the verification of the Mooney and Mooney-Tikhonov methods, the synthetic data is
represented, in Fig. 3 to 5, on a linear scale, to better visualize the differences between the
expected and the calculated behaviour. Note also that the rheological models (HB, PL) were
only used to generate the synthetic data. The models have not been used when applying the
Mooney or the Mooney-Tikhonov methods to process these synthetically generated data.
6000
Fitted shear rate [1/s]
Fitted shear rate [1/s]
12000
8000
4000
4000
2000
A
B
0
0
0
4000
8000
12000
0
Apparent shear rate [1/s]
4000
6000
6000
Fitted shear rate [1/s]
12000
Fitted shear rate [1/s]
2000
Apparent shear rate [1/s]
8000
4000
4000
2000
D
C
0
0
0
4000
8000
12000
Apparent shear rate [1/s]
0
2000
4000
6000
Apparent shear rate [1/s]
Figure 3. Performance of the classical processing of capillary data (A, B) and the Mooney-Tikhonov
method (C, D) applied on synthetically generated data, using the power law (A, C) and the HerschelBulkley (B, D) models, with no wall slip and 10% noise added to the data. The Mooney-Tikhonov
parameters are Nk=101, and λ=0.1, 0.01, 0.001 and 0.0001, the lower the λ, the better the
approximation.
10
3.1.1
Data with and without yield stress. No slip considered. 10 % noise added.
Processing tube viscometer data, i.e. Qm and ΔP, into shear rate ( γ& ) and shear stress (σ), is
performed on synthetic data for fluids with and without yield stress, assuming no slip
conditions, i.e. power law (PL) and Herschel Bulkley (HB) fluids. In the Mooney-Tikhonov
approach, the number of integration points was set to Nk=101 and the fitting parameter λ was
varied: 0.1, 0.01, 0.001 and 0.0001.
The classical approach using Eq. 4 gives a perfect fit using the power law data, and it slightly
deviates when the yield stress is present (Fig. 3A, B). The Mooney-Tikhonov method,
however, underestimates the shear rate to some extent, in both sets of data especially at high
shear rates (Fig. 3C, D). Decreasing λ, the fitting approximates better the expected shear rate,
but the result is not as smooth, especially at low shear rates.
4000
Fitted shear rate [1/s]
Fitted slip velocity [m/s]
0.12
0.08
0.04
3000
2000
1000
A
0.00
0.00
B
0
0.04
0.08
0
0.12
Apparent slip velocity [m/s]
2000
3000
Fitted shear rate [1/s]
0.08
0.04
3000
2000
1000
C
0.00
0.00
4000
4000
0.12
Fitted slip velocity [m/s]
1000
Apparent shear rate [1/s]
D
0
0.04
0.08
Apparent slip velocity [m/s]
0.12
0
1000
2000
3000
4000
Apparent shear rate [1/s]
Figure 4. Performance of Mooney (A, B) and Mooney-Tikhonov (C, D) methods in obtaining the
apparent slip velocity (A, C), and the apparent shear rate after slip correction (B, D), on synthetic data
generated using the Herschel-Bulkley model, with 10% added noise, and with moderate slip conditions
(β=10-5, α = 1.4). Mooney-Tikhonov method with λ=0.01, Nj=501, Nk=1001.
11
3.1.2
Data with yield stress. Different slip conditions. 10 % noise added.
The classical Mooney and the Mooney-Tikhonov method have also been applied to synthetic
data generated with the Herschel-Bulkley model, with different slip conditions: moderate wall
slip and intense wall slip. In the Mooney-Tikhonov approach, the fitting parameter λ was set
to 0.01, and Nj=501, and Nk=1001.
4000
Fitted shear rate [1/s]
Fitted slip velocity [m/s]
4.00
3.00
2.00
1.00
3000
2000
1000
A
0.00
0.00
B
0
1.00
2.00
3.00
4.00
0
Apparent slip velocity [m/s]
2000
3000
4000
4000
Fitted shear rate [1/s]
Fitted slip velocity [m/s]
4.00
3.00
2.00
1.00
C
0.00
0.00
1000
Apparent shear rate [1/s]
1.00
2.00
3.00
4.00
Apparent slip velocity [m/s]
3000
2000
1000
D
0
0
1000
2000
3000
4000
Apparent shear rate [1/s]
Figure 5. Performance of Mooney (A, B) and Mooney-Tikhonov (C, D) methods in obtaining the
apparent slip velocity (A, C), and the apparent shear rate after slip correction(B, D), on synthetic data
generated using the Herschel-Bulkley model, with 10% added noise, and with strong slip conditions
(β=10-5, α = 2.0). Mooney-Tikhonov method with λ=0.01, Nj=501, Nk=1001.
The results of this test are shown in Fig. 4 and 5. The performance of both methods in
extracting the slip velocity is better when wall slip contributes in a substantial amount to the
measured volumetric flow (compare Fig. 4a, 4c with Fig. 5a, 5c) and when the level of noise
is low (1 %, not shown). Slip data generated by the application of Mooney method gives
almost exact values with strong slipping conditions (Fig. 5a), but the effect of adding noise
into the data alters somewhat the goodness of the fit. The Mooney-Tikhonov procedure
approximates well the real slip data when Qs/Qm ≥ 60 %, i.e. at low shear rates (Fig. 4c, 5c).
At higher shear rates the contribution of Qs to the total flow is considerably smaller and the
fitted model deviates from the real one.
12
Regarding the extraction of the rheological data (in this case, the Herschel Bulkley data), the
performance of each method is reported in Fig. 4b,4d and 5b,5d, as the calculated shear rate
as a function of the real shear rate. It is observed that the Mooney method combined with Eq.
4 is useful in approximating the rheological fluid model in the case of low slip conditions, but
deviates when the slip dominates the flow. Mooney-Tikhonov method gives rather good
results in all slip conditions and noise levels at relatively low shear rates, but underestimates
the shear rate at high shear rate values.
Both the Mooney and the Mooney-Tikhonov are approximations to the real behaviour of the
suspensions. Some of the tests run on synthetically generated data gave rise to negative values
in the shear rate and/or slip velocities, which reflects the approximate nature of the solutions.
Negative values of the shear rate are a consequence of too high fitted slip velocities. Negative
values in the slip velocity are found when there is no slip at all or when the contribution of
slip to the total flow is very small.
The Tikhonov regularization, as expressed by Yeow et al. (2003), consists in the minimization
of Eq. 12. The parameter λ is adjusted to give more or less weight to the smoothing equation
(Eq. 11), i.e. the second derivatives of the slip and shear rate functions. The use of only one
fitting parameter implies that these two second derivatives have similar shapes, which is
probably not the case. It might be more appropriate to use two parameters, λs and λf , which
allows to treat each second derivative function separately. With this modification, the
Mooney-Tikhonov regularization might be less sensitive to the presence of noise, and
smoother slip velocity functions might be obtained.
3.2 Characterization of potato fibre and tomato suspensions
All suspensions used in these experiments exhibit a bimodal particle size distribution (Table
1), with a predominantly fraction of coarse particles. The dried potato fibre had the smallest
particles, with a median diameter of 36 µm), whereas the HB tomato paste had the largest
particles (193 µm).
Four series of concentrations were prepared: potato fibers in high (Fiber A) and low viscous
syrup (Fiber B), hot break (HB) and cold break (CB) tomato paste suspensions. Their main
characteristics are summarized in Fig. 6. The volume fraction, determined by
ultracentrifugation, was found to be 0.2<ø<0.7 in hot break, and 0.1<ø<0.7, in cold break
suspensions. In potato fiber suspensions, ø was found to vary between 0.2<ø<0.4, and was
larger in the series of Fiber A than in series Fiber B, at the same WIS content, which is caused
by the higher supernatant viscosity in the former series. The added fibers or pastes had soluble
13
substances such as starch in potato fibers and pectins in tomato pastes that contributed to the
increase in the supernatant viscosity (ηs) with the volume fraction of the suspensions. The ηs
was substantially higher for hot break tomato paste suspensions than for those made with cold
break.
0.8
10000
0.7
0.6
1000
ηs [m Pa s]
ø [-]
0.5
0.4
0.3
0.2
100
10
0.1
A
0.0
0.0
2.0
4.0
6.0
B
1
8.0
0.0
0.2
WIS [%]
0.4
0.6
0.8
ø [-]
100000
100
1000
σy [Pa]
G' [Pa]
10000
100
10
10
C
1
0.0
0.2
0.4
ø [-]
0.6
0.8
D
1
0.0
0.2
0.4
0.6
0.8
ø [-]
Figure 6. Characterization of the four series of suspensions, fiber suspensions on high viscosity syrup
(◊), on low viscosity syrup (■), hot break tomato paste (▲) and cold break tomato paste (○). A) The
volume fraction (ø) as a function of the water insoluble solids (WIS), and different rheological
parameters as a function of volume fraction (ø) are shown, in B) viscosity of the supernatant (ηs) , C)
elastic modulus (G’) obtained in the linear region at ω=1 Hz, and D) the yield stress (σy). Error bars are
included.
In all potato fibers samples, the elastic modulus was lower than the loss modulus, G'<G'' in
the frequency range 1<ω<100 Hz, which indicates that the solution behave as a liquid.
14
Moreover, there was no indication of yield stress in those samples. The tomato paste series
exhibit a solid-like behaviour, G'>G'', at all frequencies and concentrations studied, and the
values of the elastic modulus were similar for hot and cold break samples. However, the yield
stress associated with the tomato paste suspensions was considerably different for the hot
break and the cold break series, the former being higher at all concentrations.
3.3 Tube viscometer data
3.3.1
Uncorrected rheological data obtained in tube viscometer
3.3.1.1 Potato fibre series
The uncorrected rheological data generated from the tube viscometer is shown in Fig. 7 for
Fiber A and B at three concentrations, in the form of the shear wall stress as a function of the
apparent Newtonian shear rate. The fibres suspended in high viscous syrup (Fig. 7a) gave
similar results in the larger and medium diameters, but during the experiments in the smaller
tube, the pressure in the system became rather high, and it was difficult to pump the
suspensions thorough the smaller pipe, the system stopping in some occasions. This data has
therefore not been included. Both series of suspensions, A and B, exhibited a rather linear
relationship between the wall shear stress and the apparent shear rate, suggesting the flow
behaviour to be almost Newtonian.
3.3.1.2 Tomato paste series
The uncorrected rheological data generated from the tube viscometer is shown in Fig. 8 for
tomato paste suspensions at different concentrations, in the form of the shear wall stress as a
function of the apparent Newtonian shear rate. The hot and cold break 100% pastes exhibited
clear non-Newtonian behaviour, and they flowed as a plug (Fig. 9). After dilution, the
viscosity of the suspensions markedly decreased.
3.3.1.3 Determining the reproducibility of the experiments and the presence of slip
The error between replicates was also determined, for a given shear rate, Eq. 13, and the
maximum and minimum error of each series of suspensions are summarized in Table 4.
ε γ& =
SD(σ )
σ
(13)
γ&
The error between replicates was found to be acceptable, and usually, it was found to be
below 10%, but in some cases it was as high as 17%. Moreover, the error was not random, but
appeared to be a complex function of the wall shear stress and the radius of the pipe. Note that
poor reproducibility is a inherent characteristic of concentrated suspensions (Larsson, 1999)
and variability up to 50% has been reported in the rheological properties of wheat starch at
15
1200
1600
A
A
Wall shear stress [Pa]
Wall shear stress [Pa]
1400
1200
1000
800
600
400
1000
800
600
400
200
200
0
0
0
100
200
300
400
0
Apparent Newtonian shear rate [1/s]
1600
200
300
400
500
600
1200
B
1400
B
1000
Wall shear stress [Pa]
Wall shear stress [Pa]
100
Apparent Newtonian shear rate [1/s]
1200
1000
800
600
400
800
600
400
200
200
0
0
0
100
200
300
400
0
Apparent Newtonian shear rate [1/s]
Figure 7. Tube viscometer data plotted as wall
shear stress as a function of the apparent
Newtonian shear rate for 4.5 (◊), 5.6 (□) and 6.5
% (Δ) A) high syrup viscosity (860 mPa s) and
B) low syrup viscosity (68 mPa s) suspensions,
obtained in three tube diameters d=20, 25 and 38
mm, corresponding to black, grey and empty
symbols, respectively. Three replicates are
shown.
100
200
300
400
500
600
Apparent Newtonian shear rate [1/s]
Figure 8. Tube viscometer data plotted as wall
shear stress as a function of the apparent
Newtonian shear rate for tomato suspensions of
100 (◊), 50 (□) 40 (Δ) and 30 % (○) paste A) hot
break and B) cold break tomato paste
suspensions, obtained in three tube diameters
d=20, 25 and 38 mm, corresponding to black,
grey and empty symbols, respectively. Three
replicates are shown.
high concentrations (Steeneken, 1989), and between 15 and 30% in the determination of yield
stress in model colloidal suspensions (Buscall, et al., 1987).
In order to determine whether slip affected the measurements, the mean value of the wall
shear stress in one pipe diameter was compared to the mean value of σ w (γ& ) at a different
pipe diameter using a t-test (p<0.05, Table 4). If the mean values were significantly different
in different pipes, slip was assumed to be present. Strong wall effects have been previously
reported in tomato pastes (Cooley and Rao, 1992) and in tomato paste suspensions (Lee, et
al., 2002), representing about 70 % of the measured flow in a tube viscometer. In the present
study, rheological measurements performed in a rotational rheometer using the vane geometry
give rise to higher stresses than using smooth concentric cylinders, which is an indication of
16
the presence of slip. Wall slip in rotational rheometers has previously been identified in
tomato suspensions (Grikshtas and Rao, 1993).
Figure 9. Hot break tomato paste (100%) flowing as a plug.
In general, it seems that a low viscosity of the continuous phase gives rise to a higher
probability for slip to occur, which in turn increases with the concentration of particles (Table
4). In this case the slip decreases with wall stress, whereas for the dispersions with a high
yield stress (for example 100 % paste) the slip increases with wall stress.
3.3.2
Extraction of rheological data: flow behaviour and quantification of slip.
The applicability of the Mooney method and the relative contribution of the slip to the
measured flow are summarized in Table 4. The results indicate that this classical approach
works relatively well for the fibre suspensions, but in the paste it seems not to apply in most
of the cases, because it results either in non linear slopes or in unrealistic slip flow,
Qs/Qm>100%. There is a notable exception, in hot break tomato paste at 50 and 100%
concentrations. The graphical analysis for the latter is shown in Fig. 10a. An example of non
linear slope encountered in the Mooney graphical procedure is also shown in Fig. 10b for
100% cold break paste. The problem of non linear slopes probably arises from the relatively
poor reproducibility of this sample (Table 4).
In Fig. 11a, the slip velocity as a function of the wall stress is shown, and it exhibits a
surprising strong dependence on the wall stress, v s = 3 ⋅10 −14 σ w4.29 . This might indicate the
existence of a slip threshold, which can not be modelled by the assumption of power law slip
velocity. The slip velocity function of this hot break paste is in the same order of magnitudes
as that found by Kokini and Dervisoglu (1990) using the Jastrzebski-Mooney method. The
slip flow represents between 30 and 70% of the total measured flow (Fig. 11b). If slip is not
taken into account in the extraction of the flow curves, errors of up to 70% in the shear rate
17
Table 4. Summary of the analysis performed in each of the suspensions. Interval between the minimum and maximum measured wall shear stress (σw). Error between
replicates (%). Determination of the presence of slip by comparing the mean data between different pipe diameters using a T-test. Ratio of slip to total flow (Qs/Qt)
determined by Mooney and Mooney-Tikhonov methods, and observed variation of Qs/Qt as a function of the wall shear stress.
Suspensions
Dried potato fibre
A-4.5 %
A-5.6 %
A-6.5 %
Measured
wall shear stress
interval
min
max
Error between
replicates (%)
min
max
T-test between pipe
diameters
d 20-25
d 20-38
d 25-38
b
b
-
b
b
b
b
-
0.15
0.06
0.67
Predicted
behaviour
MooneyTikhonov
Mooney
Qs/Qt (%)
f(σ )c
No slip
No slip
No slip
1.4 – 14 b
6.9 – 15 b
6.3 – 20 b
↑
→
↓
5 – 23
3 – 43
0 – 15
↓
↑↓
↑↓
Qs/Qt (%)
f(σ )c
213
182
437
825
1375
1197
0.8
1.9
1.5
3.6
3.8
3.6
15
33
60
128
249
330
3.1
1.7
1.1
11.6
6.4
8.2
0.03*
0.01*
0.00*
0.03*
0.07
0.04*
0.04*
0.36
0.65
Slip
Slip
Slip
8 – 27
0 – 37
1 – 65
↓
↓
↓
vs<0
vs<0
1 – 17
x
x
↓
14
40
82
119
42
88
130
517
4.5
0.9
1.0
1.3
16.5
10.6
4.0
3.9
0.01*
0.61
0.67
0.09
0.93
0.85
0.02*
0.02*
0.37
0.08
0.00*
0.00*
Slip
No slip
Slip
Slip
>100
>100
7 – 86
27 – 69
x
x
↓
↑
vs<0
vs<0
vs<0
3 - 88
x
x
x
↑↓
CB-30 %
20
46
0.3
5.3
0.00*
0.02*
0.27
Slip
σ >32 Pa
n.l.
vs<0
CB-40 %
44
94
0.3
2.3
0.02*
0.00*
0.00*
Slip
σ >77 Pa
n.l.
vs<0
CB-50 %
91
160
0.8
5.7
0.00*
0.16
0.79
Slip
σ >130 Pa
n.l.
0 - 23
CB-100 %
438
774
2.1
13.2
0.01*
0.05
0.09
Slip
>100
x
3 - 119
a
level of significance p<0.05*
b
only two diameters were used
c
variation of Qs/Qt as a function of the wall shear rate σ, ↑ increases, → no variation, ↓ decreases, x non physical meaning, n.l. non linear slope in Mooney plot
x
x
↓
↑↓
B-4.5 %
B-5.6 %
B-6.5 %
Tomato paste
HB-30 %
HB-40 %
HB-50 %
HB-100 %
18
component can thus be expected. The flow curve after slip correction, using the classical
Mooney, is given in Fig. 11c. Note that at σw~1100 Pa, the uncorrected shear rate was slightly
more than 200 s-1, whereas after correction it is only ~50 s-1. This might lead to the
underestimation of the viscosity when using uncorrected tube viscometer data.
0.08
517
651
785
919
1053
Q/πR3σw [1/Pa s]
0.07
0.06
584
718
852
986
1119
Figure 10. Mooney graphical method for the
determination of the slip coefficient (β)
applied on the tube viscometer data of A) 100
% hot break tomato paste and B) 100 % cold
break
tomato
paste.
The
interpolated/extrapolated wall shear stresses
are given in the legend in Pa.
A
0.05
0.04
0.03
0.02
0.01
0.00
50
60
70
80
90
100
110
120
1/Radius [1/m]
0.08
438
513
587
662
737
Q/πR3σw [1/Pa s]
0.07
0.06
0.05
476
550
625
699
774
B
0.04
0.03
0.02
0.01
0.00
50
60
70
80
90
100
110
120
1/Radius [1/m]
The Mooney-Tikhonov approximation was also applied to the tube viscometer data for each
suspension. The parameters used in the fitting were Nj=Nk=101, and λ=10. The value of λ was
chosen after Yeow et al. (2001), who showed that values of this order of magnitude were
appropriate for fruit purees. In the present study, values of λ<10 resulted in non-smooth flow
curves. The fact that the noise in the data (replicates error) is not random might cause the need
of using such high λ compared to that used in the synthetic generated data with 10% added
noise.
The Mooney-Tikhonov approximation gives rise to lower slip velocities than those derived
from the classical Mooney analysis (Fig. 11a), and in the suspensions were no slip was
expected, the slip velocity had negative values. The underestimation of the slip velocity give
too high shear rate values, as can be seen in Fig. 11c, because the fitted shear rates are larger
than the measured ones, which is physically unrealistic. It is interesting to note the different
19
behaviour of the Qs/Qm ratio as a function the wall shear stress (σw) in the Mooney and the
Mooney-Tikhonov methods (Fig. 11b). In the former, it either increases or decreases over the
wall stress interval, whereas in the Mooney-Tikhonov, more complex behaviours are allowed.
0.35
A
Slip velocity [m/s]
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
200
400
600
800
1000
1200
1000
1200
Wall shear stress [Pa]
1.0
B
0.9
Qs/Qt ratio [-]
0.8
0.7
Figure 11. Comparison between the
classical method of processing tube
viscometer data with Mooney (M)
correction for slip, and the MooneyTikhonov (M-T) numerical method,
applied on data of 100 % hot break
tomato paste. A) Slip velocity as a
function of the wall stress (σw), given
by M ( ) and M-T (solid line). B)
Ratio of slip flow over the total
measured flow Qs/Qm as a function of
wall shear stress (σw) for each tube
diameter (d=20, 25, 38) given by M
( , , , respectively) and by M-T
(dotted, dashed and solid line,
respectively). C) Flow curves, as wall
shear stress as a function of the shear
rate, uncorrected data for different
diameters (20 , , 25, , 38, ,), after
slip correction by Mooney (dashed
line), and extracted using MooneyTikhonov (thick line).
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
200
400
600
800
Wall shear stress [Pa]
1200
Wall shear stress [Pa]
1000
800
600
400
200
C
0
0
100
200
300
400
Apparent shear rate [1/s]
20
3.4 Comparison between tube viscometer and rotational rheometer data
A comparison between the tube viscometer data and rheological data measured in a rotational
rheometer using different geometries might give some insight into the “real” flow and slip
behaviour of these suspensions. In the rotational rheometer, different geometries were used in
order to get different degrees of slippage in the rheometer walls. The concentric cylinder had
smooth walls and the tomato paste was expected to exhibit wall slip. The vane was expected
to avoid slip in the inner wall of the cylinder, whereas it might occur in the outer wall (i.e. at
the cup-wall) when high stresses were applied. The vane-vane geometry was constructed to
prevent the slip in the outer wall. For the cold break tomato paste, measurements in the
rotational rheometer, at shear rates higher than γ& >3 s-1, were difficult to achieve because the
sample tended to climb out of the cup. The phenomenon was observed in all the geometries.
10000
Wall shear stress [Pa]
Wall shear stress [Pa]
10000
1000
100
A
10
1
10
100
Apparent Newtonian shear rate [1/s]
100
B
10
1000
10000
1
10
100
Apparent Newtonian shear rate [1/s]
1000
100
Wall shear stress [Pa]
Wall shear stress [Pa]
1000
1000
100
C
10
1
10
100
Apparent Newtonian shear rate [1/s]
1000
10
1
D
0.1
1
10
100
1000
Apparent Newtonian shear rate [1/s]
Figure 12. The flow curves of A) Fiber suspension A-6.5 %, B) Fiber suspension A-4.5 %, C) hot break
tomato paste (100%) and D) hot break tomato paste (30%). The data was obtained using tube
viscometer with different diameters (d=20 ( ), 25 ( ) and 38 ( ), uncorrected data), and rotational
rheometer using different geometries: concentric cylinder (-), vane (x), vane-vane (*). The classical
Mooney correction ( ) and the Tikhonov-Mooney correction are included ( ).
21
In Fig. 12, the flow curves of 4.5% and 6.5% Fiber A suspensions, as well as 100% and 30%
hot break tomato paste, expressed as shear stress as a function of the shear rate, are shown for
each of the measurements systems used. The flow curves corrected for slip by the classical
Mooney and Mooney-Tikhonov methods are also included. In the fibre suspensions, the data
obtained in different geometries superpose rather well, and the differences observed are
probably due to slightly different temperatures during the pumping experiments. In 100%
tomato paste, the tube viscometer data corrected for slip by the classical Mooney method
correspond rather well with the rheological data obtained using the vane and vane-vane
geometries. The concentric cylinder with smooth walls gave rather similar values at very low
shear rates, γ& <2.5 s-1, but deviates considerably at higher shear rates, giving values even
lower than those from the uncorrected data in tube viscometer, which seems to indicate that
the slip in the concentric cylinder is substantially larger than in tube viscometer. In 30% hot
break suspensions, the tube viscometer and the rheometer data are found to superpose,
indicating that there is no slip. However, the application of the Mooney procedure
overestimated the slip velocity in this sample, which might be caused by the relatively poor
reproducibility (Table 4).
From these results it is concluded that the comparison between the tube viscometer and the
rheometer data is of great importance to be able to verify the correct performance of the slip
correction methods.
3.5 Dynamic and steady measurements. Cox-Merz rule
In highly concentrated suspensions, dynamic oscillatory measurements are easier to perform
experimentally (Doraiswamy, et al., 1991) and show better reproducibility than steady shear
measurements. Moreover, dynamic experiments on food materials such as mayonnaises,
which often exhibit apparent wall slip in steady-shear, were found to give true material
properties when small strain amplitudes <1% were used, with no detectable wall slip
distorting the results (Plucinski et al., 1998). It is therefore interesting to investigate the
validity of the Cox-Merz rule on the suspensions studied here. The Cox-Merz rule establishes
a simple and empirical relationship between the steady shear viscosity η (γ& ) and the complex
viscosity η * (ω ) ,
η * (ω ) = η (γ& = ω ) .
(14)
Is the Cox-Merz rule appropriate for yield stress fluids?
In Fig. 13, the complex and the steady-shear viscosity are plotted together as a function of the
frequency and the shear rate, respectively. In the potato fiber suspensions the Cox-Merz rule
22
is observed to hold relatively well for low and high fiber concentrations, whereas in the
tomato suspensions, the complex viscosity is about one order of magnitude higher than the
100
10
A
1
1
10
100
Dynamic and steady-shear viscosity [Pa s]
Dynamic and steady-shear viscosity [Pa s]
steady-shear viscosity, for concentrations of paste between 30 and 100 %.
100
10
B
1
1000
1
10000
1000
100
10
C
1
1
10
100
1000
Apparent shear rate or frequency [1/s or Hz]
10
100
1000
Apparent shear rate or frequency [1/s or Hz]
Dynamic and steady-shear viscosity [Pa s]
Dynamic and steady-shear viscosity [Pa s]
Apparent shear rate or frequency [1/s or Hz]
100
10
1
0.1
D
0.01
1
10
100
1000
Apparent shear rate or frequency [1/s or Hz]
Figure 13. Application of the Cox-Merz rule on potato fiber suspensions in 860 mPa s syrup A) 6.5 %
and B) 4.5 % and on hot break tomato paste at C) 100 % and D) 30% paste concentration. The viscosity
measurements were performed on different systems, tube viscometer with d= 20, 25 and 38 ( , , ,
respectively), rotational rheometer using concentric cylinder (-), vane (+) and outer vane (*), and shear
oscillatory measurements (Δ).
Small amplitude oscillatory measurements tend to preserve the microstructure of the material
being tested, whereas steady shear measurements can induce changes in the microstructure of
the suspensions (Bayod et al., 2007b), disrupting the network to some extent. This difference
in the conservation of the microstructure might explain the lack of superposition of both types
of data in complex structured food materials.
The dried fibre suspensions exhibit a liquid-like behaviour at all frequencies (G'<G'') and
have no yield stress. On the contrary, tomato paste suspensions exhibit solid-like behaviour
over all the studied range of frequencies (G'>G''), and had a yield stress. Hence, the lack of a
network structure in the suspensions seems to be hence a key factor for the Cox-Merz rule to
23
apply. In cases were the Cox-Merz rule does not apply, a shifting factor (ξ) with the frequency
can be used (Doraswamy et al., 1991), and the modified Cox-Merz rule takes the form,
η * (ξω ) = η (γ& = ξω ) .
(15)
In Fig. 14, the shifting factors used to superimpose the complex and the steady-shear
viscosities, in hot and cold break tomato pastes and in the interval of concentrations between
30 and 100%, are plotted as a function of the yield stress of the suspensions. The reference
steady-shear viscosity was that measured with the vane-vane geometry, which is free of wall
effects. However, vane-vane, evaluated as Couette flow between cylinders defined by vane
tips, does not yield true viscosity, because the channel is on average wider in vane-vane. In
addition, vane-vane might be affected by extensional viscosity, which is unknown but could
be significant. The yield stress is taken as a measurement of the structure in the material.
Interestingly, the shifting factor on the frequency is found to be about 0.1 for all the
suspensions studied, independently of the concentration or the yield stress of the suspensions.
These values were somewhat higher than those found by Rao and Cooley (1992) on tomato
pastes.
1.00
Figure 14. Factor ξ of the
modified
Cox-Merz
rule,
Shift factor [-]
η (γ& ) = η ∗ (ξω ) , as a function
of the yield stress for hot break
(grey) and cold break (empty)
tomato paste suspensions.
0.10
0.01
1.00
10.00
100.00
Yield stress [Pa]
These shifting factors will allow us to use dynamic, rheological data, which are more easily
obtained and have better reproducibility, instead of steady-shear data, which can be subjected
to a number of experimental errors. Dynamic data could then be used in food processing
design and engineering, provided an independent method is found to predict and quantify slip.
24
Conclusions
This study shows that substantial wall slip effects can occur in steady-shear measurements of
concentrated fibre suspensions at relatively high shear rates. The existing correction methods
for slip, i.e. the classical Mooney and the Mooney-Tikhonov method, however, lead to
unrealistic results when the reproducibility of the suspensions is poor, which is a
characteristic of this type of suspensions. Comparison with rheological data obtained in
rotational rheometers is then useful to verify the performance of the correction methods.
Dynamic measurements are proposed as an alternative to estimate the “real” flow behaviour
of yield stress fluids, upon the application of a shifting factor on the frequency, which seems
to be independent of the concentration of the suspension.
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