Fernández et al., e-rheo.pt, 4 (2004) 21-28
YIELD STRESS AT DIFFERENT POTATO PUREES
C. Fernández, M.D. Alvarez* and W. Canet
Department of Plant Foods Science and Technology, Instituto del Frío-CSIC, José de Novaís nº 10, E28040 Madrid, Spain. Fax: +34 91 5493627; Phone: +34 91 5492300
e-mails: [email protected], [email protected], [email protected]
* -Corresponding author
Keywords: Steady shear, dynamic rheological test, flow curve, yield stress, freezing
Nomenclature: σ – Shear stress in eqs. (1) to (3)
.
γ − Shear rate eqs. (1) to (4)
σ0Β − Bingham yield stress in eq. (1)
η’ − Bingham plastic viscosity in eq. (1)
σ0C − Casson yield stress calculated as (K0c)2 from eq. (2)
Kc − Slope in eq. (2) used for calculating Casson plastic viscosity, ηCa
σ0H − Herschel-Bulkley yield stress in eq. (3)
KH − Consistency index in eq. (3)
nH − Flow behaviour index in eq. (3)
σ0BO − Yield stress from Bohlin option
σ0BM − Yield stress from Bingham method
G’− Storage modulus
G” − Loss modulus
σGe − Experimental yield stress
η*− Complex viscosity in eq. (4)
α − Shift factor for correcting the frequency in eq. (4)
ω − Frequency in eq. (4)
η − Apparent or steady viscosity in eq. (4)
σDRI − Dynamic yield stress from method I
σDRII − Dynamic yield stress from method II
Abstract: Seven methods for determining yield stress of concentrated suspensions were applied to fresh
and frozen natural and commercial purees at different temperatures. Since potato puree was consistent
with Herschel-Bulkley flow behaviour, yield stress was more reliably determined by extrapolation of the
flow curves assuming the Herschel-Bulkley model than Bingham and Casson models. Methods for
determining yield stress by dynamic rheological tests were tedious and are not always applicable. Given
the high correlation between Herschel-Bulkley yield stress and that as determined by Bohlin option (R2 =
0.8735), Bohlin’s “Yield stress option” appears to be highly useful for direct measurement of this
property in potato puree. Temperature influenced yield stresses more in frozen than in fresh purees,
both natural and commercial. At equal temperatures, processing reduced yield stresses in natural puree
but increased them in commercial puree, showing that their structures were not affected in the same
way.
21
Fernández et al., e-rheo.pt, 4 (2004) 21-28
1.
INTRODUCTION
Many commercially valuable foods like apple sauce and tomato paste are concentrated
dispersions of insoluble matter in aqueous media. Their rheological behaviour, especially
yield stress, is important for industrial handling, storage, processing and transport of
concentrated suspensions [1]. Yield stress means the stress that must be exerted simply to
move one fluid layer past another [2], and it plays a role in the coating of solid surfaces. In
terms of the strength of the coherent network structure, it is the force per unit area required
to achieve breakdown of the structure followed by the cleavage of network bonds or
linkages connecting the flow units [3], [4].
Several methods have been employed for the determination and comparison of the yield
stress of food suspensions, but most magnitudes of yield stress are determined by
extrapolation of shear rate-shear stress data according to several flow models such as those
of Casson, Herschel-Bulkley and Mizrahi-Berk [4], [5], [6]. With the availability of
automated rheometers, dynamic rheological tests can also be used to determine yield
stresses of food and non-food suspensions [4], [7], [8], [9], [10], [11].
The main objectives of the present study were (1) to determine, compare and correlate the
yield stresses of two different potato puree types obtained by seven established methods,
and (2) to study the effect of sample temperature and freezing on the magnitudes of the
yield stresses.
2.
MATERIALS AND METHODS
2.1. Preparation of samples
For preparation of natural puree, fresh tubers (cv. Kennebec) were selected. Tubers were
manually washed, peeled and diced. Natural potato purees were prepared from 395 g of
potatoes, 150 ml of milk, 100 ml of water and 5 g salt using a Thermomix TM 21. Ingredients
were cooked (20 min/100 °C), and the liquid evaporated was determined by weighing the
ingredients before and after boiling. This was compensated by addition of boiling water, and
the ingredients were again cooked (5 min/100 °C). The mash was triturated for 40 s. The
product was homogenised through a stainless steel sieve (diameter 1.5-mm).
For preparation of commercial puree, aseptically packed commercial dehydrated potato flakes
were used and mashed prepared according to label instructions. Following preparation, half of
each sample was packed in polyethylene plastic, sealed under light vacuum (-0.05 MPa) on a
Multivac packing machine and immediately frozen to –80 °C. The packs were then kept for 1
week in a freezer at –80 °C. Rheological measurements of frozen samples were made after
samples had been allowed to thaw overnight in a domestic refrigerator.
Rheological behaviour was evaluated on the samples with temperature ranging from 25 to 65
°C. Temperatures were reached in the fresh and frozen/thawed samples by placing them in a
CB60VS waterbath with a constant product weight:water volume ratio of 1:20. Water and
product temperatures were monitored by K-type thermocouples using a hardware and
22
Fernández et al., e-rheo.pt, 4 (2004) 21-28
software system developed with the LabWindows/CVI package for automation of the thermal
process control [12].
2.2. Rheological measurements
A Bohlin CVR 50 controlled-stress rheometer was used to conduct steady shear and small
amplitude oscillatory shear experiments (SAOS) using a plate-plate sensor system with 2-mm
gap (PP40, 40 mm) and a solvent trap to minimize moisture loss during tests. Samples were
allowed to relax for 5 min before conducting rheological measurements such as equilibration
time after loading the sample on the sensor system. Temperature control was carried out with
a Peltier Plate system (-40 to +180 °C). Each curve presented is a typical one out of two run.
2.3. Steady shear and yield stress data
Flow curves were obtained at shear rates of 0.1-100 s-1 approximately, which is the range of
interest in food texture studies [13]. Data were fitted to the Bingham (1), Casson (2) and
Hershel-Bulkley (3) models [4]. Bingham, Casson and Herschel-Bulkley yield stresses were
obtained respectively by extrapolation of shear rate-shear stress data according to flow models
(1)-(3).
.
σ − σ0Β = η’ γ
0.5
σ
(1)
.
0.5
= K0c + Kc( γ )
.
σ − σ0Η = ΚΗ( γ )
(2)
nH
(3)
1000
20000
15000
100
10000
5000
0
0
10
5 10 15 20 25 30 35 40 45 50 55 60
500
450
400
350
300
250
200
150
100
50
0
1000
Yield stress
10
1
0
0
time (s)
100
20
40
60
80
100
120
140
-1
Viscosity
Shear rate (s )
Shear Stress
Shear stress (Pa) - Frozen/thawed natural potato puree
Shear stress (Pa) - Frozen/thawed commercial potato puree
Apparent viscosity (Pas) - Frozen/thawed natural potato puree
Apparent viscosity (Pas) - Frozen/thawed commercial potato puree
Figure 1a - Yield from Bohlin “Yield Stress Option” Figure 1b - Yield from the Bingham Method
23
Appare nt v iscosity (Pas)
Yieldstress
25000
She ar stre ss (Pa)
30000
Shear stress (Pa)
Instantaneus Viscosity
(Pas)
Bohlin also obtained yield stress using Bohlin “Yield stress option” (σ0BO) through the
viscometry stress ramp test, which involves applying a gradually increasing stress and
monitoring the instantaneous viscosity for an inflexion of the curve: i.e. the onset of flow (fig.
1a.). Besides, yield stress was obtained by direct extrapolation of the straight-line portion of
shear rate-shear stress data (σ0BM) in accordance with Michaels and Bolger [14] (fig. 1b.).
This way of obtaining yield stress is known and is referred to as the Bingham method in this
work.
Fernández et al., e-rheo.pt, 4 (2004) 21-28
2.4. Yield stress from dynamic shear data
Magnitudes of storage modulus G’ and loss modulus G” were determined for each sample
from stress sweeps at 1 rad.s-1. As the strain was increased, G’ and G” remained relatively
constant until at a critical value of strain the magnitude of G’ decreased sharply and that of G”
increased sharply (fig. 2a.). The magnitude of G’ at the critical strain value was recorded as
the experimental yield value (σGe) [15].
2E+00
10000
1E+00
1E+00
G' (Pa)
100
Strain ( )
G', G" (Pa)
Experimental
Yield value
1000
G" (Pa)
1E+00
8E-01
6E-01
Yield stress
4E-01
2E-01
10
0,00
1E-05
0,00
0,01
0,10
1,00
0
10,00
20
40
60
80
100 120 140 160 180 200
Shear stress (Pa)
Strain, γ ( )
Figure 2a - Yield from dynamic rheological test, Figure 2b - Yield from dynamic rheological test,
Method I
Method II
For some of the potato purees studied, a modified Cox Merz rule was found to be applicable
to:
.
.
η* (αω) = η ( γ )ω = γ
(4)
In separate experiments, frequency sweeps over the range 0.1-100 rad.s-1 were conducted in
the linear viscoelastic domain, and shift factors (α) for Cox-Merz plots were determined from
plots of steady shear viscosity shear rate and complex viscosity frequency data as described
earlier [15]. The product of the Cox Merz shift factor (α) and σGe was calculated to obtain the
corrected dynamic yield stress, which in this study is designated dynamic yield stress from
method I, σDRI. It is also possible to determine yield stresses from dynamic tests by plotting
strain versus shear stress (fig. 2b.). The shear stress corresponding to the intersection of the
tangents and the two distinct segments of the strain-shear stress curve is considered to be the
yield stress and in this study is called the dynamic yield stress from method II, σDRII.
Therefore, a total of seven different methods were applied to obtain yield stresses for the two
types of potato purees studied.
3. RESULTS AND DISCUSSION
Tables 1 and 2, respectively, show the magnitudes of yield stresses obtained for fresh and for
frozen/thawed natural and commercial potato purees using the different methods applied at
the different sample temperatures studied.
In fresh natural puree, the temperature did not appear to affect the yield stress values obtained
from the Bingham model, σ0B. However, in frozen/thawed natural potato puree, σ0B was
clearly higher at 25 °C than at the other sample temperatures. In natural potato puree, except
for 25 °C, σ0B values were lower in the processed than in the fresh samples, indicating that
24
Fernández et al., e-rheo.pt, 4 (2004) 21-28
freezing decreased the strength of the network structure of the samples. The effects of both
temperature and processing on Casson yield stresses σ0C were similar to those found for
Bingham yield stresses.
Table 1 - Magnitudes of yield stress (Pa) in natural potato puree using different methods.
Fresh natural potato puree
Bingham
yield
stress,
Temp
σ0B
(°C)
25
201.7
35
169.0
45
169.7
55
127.0
65
182.4
25
35
45
55
65
226.6
74.6
68.9
113.4
84.7
Yield stress Yield stress
Casson Herschel
from
from
yield
Bulkley
Bohlin
Bingham Experiment Cox-Merz Dynamic
Dynamic
Stress, yield stress,
Option,
Method, al
yield rule shift yield stress yield stress
σ0C
σ0H
σ0BO
σ0BM
stress, σGe factor, α
(I), σDRI
(II), σDRII
9089.4
0.008
164.1
105.5
32.6
345
72.7
200
11930
0.005
147.6
111.2
60.7
228
59.6
199
10305
0.009
166.0
117.8
61.4
175
92.7
167
10899
0.005
116.5
100.9
33.0
145
54.5
240
14076
0.007
164.1
151.8
33.5
215
98.5
193
Frozen/thawed natural potato puree
211.1
56.3
51.1
73.8
63.9
75.9
11.1
25.8
33.5
41.4
12.9
8.3
8.0
11.9
8.4
302
120
116
217
121
6406.6
2397.6
2287.2
3785.3
2282.8
0.008
0.014
30.3
31.9
250
39
29
40
37
For natural puree exhibiting non-linear plastic behaviour (fig. 1b.), the correlation coefficients
of the fits to the Casson model were higher than those corresponding to the Bingham model
for all temperatures. In fresh natural puree, Herschel-Bulkley yield stress values, σ0H,
exhibited a non-identifiable trend with sample temperature, whereas in processed samples, the
σ0H value was higher at 25 °C than at the other temperatures. From the σ0B, σ0C and σ0H yield
stresses, it would appear that the effect of temperature was more pronounced in processed
than in fresh samples. In natural puree, σ0H values were also lower in the processed than in the
fresh samples at all temperatures, more clearly evidencing fluidification of the product with
processing. As was to be expected from the shape of the flow curves of potato puree (fig. 1b.),
of the models used, the Herschel-Bulkley equation was the one for which fits gave the highest
correlation coefficients.
In both fresh and frozen/thawed natural purees (Table 1), yield stresses obtained from the
Bohlin option, σ0BO, followed a non-identifiable trend with sample temperature and, as was
found for σ0H, σ0BO values were also clearly lower in frozen/thawed than in fresh samples at
all temperatures. Bingham method yield stresses, σ0BM, decreased with sample temperature up
to 55 °C in fresh natural puree, whereas in frozen/thawed natural puree, σ0BM decreased with
temperature up to 45 °C. Except for 55 °C, σ0BM values were lower in frozen/thawed than in
fresh samples. It must be considered that even if the extrapolation is performed carefully, the
yield values obtained by the Bingham method are somewhat uncertain for potato purees that
exhibit a pronounced non-linear shear stress-shear rate ratio.
In frozen/thawed natural puree at 25, 35 and 45 °C, σDRI could not be obtained; relationships
between complex and steady viscosities in these samples were non-linear and therefore it was
not possible to multiply experimental yield stresses by the Cox-Merz rule shift factor for these
temperatures. In contrast, in fresh natural puree, relationships between complex and steady
viscosities were linear at all temperatures. σDRI values in fresh natural puree exhibited a non25
Fernández et al., e-rheo.pt, 4 (2004) 21-28
identifiable trend with sample temperature. In natural puree, dynamic yield stresses (II), σDRII,
were lower in processed than in fresh samples for all the temperatures except 25 °C. In fresh
samples, temperature had a non-identifiable influence on σDRII values, while in processed
samples the values corresponding to 25 °C were higher than those for other temperatures.
In fresh commercial puree (Table 2), σ0B was lowest at 65 °C, while in frozen/thawed
commercial puree, σ0B at 25 °C was clearly higher than at other temperatures. At 35, 45 and
55 °C, σ0B values were lower in processed than in fresh samples. As in the case of natural
puree, the effect of both temperature and processing on σ0B and σ0C yield stresses in
commercial puree was similar. Again, correlation coefficients were higher in the Casson
model fits than those corresponding to the Bingham equation, indicating that a non-linear
model is more suitable for characterization of potato puree flow behaviour. σ0H was higher in
the frozen/thawed samples than in the fresh samples at all temperatures, indicating that the
processing of commercial puree led to the formation of a coarsely aggregated structure.
Table 2 - Magnitudes of yield stress (Pa) in commercial potato puree using different methods.
Fresh commercial potato puree
Bingham
yield
Temp Stress,
σ0B
(°C)
25
193.9
35
237.0
45
167.7
55
232.2
65
58.4
25
35
45
55
65
629.4
199.1
65.0
126.9
121.3
Casson Herschel
yield
Bulkley
Yield stress
Yield stress
Experiment
stress, yield stress, from Bohlin
from Bingham al
yield
Option, σ0BO Method, σ0BM stress, σGe
σ0C
σ0H
2705.6
159.8
20.7
62.6
311
2163.8
185.9
22.6
49.1
395
1611.8
124.2
19.6
11.9
268
1721.5
156.1
29.0
12.9
463
1233.2
43.7
5.7
8.1
96
Cox-Merz
rule shift
factor,
α
-
Frozen/thawed commercial potato puree
564.2
174.7
47.0
94.2
87.6
387.6
38.6
23.6
30.8
30.6
212.0
37.5
8.0
9.7
8.7
750
261
120
190
203
15552
4944
1517.5
1766.8
13956
0.020
0.015
0.020
0.020
Dynamic Dynamic
yield
yield
stress (I) stress (II)
σDRI
σDRII
300
97
62
123
53
311
74.2
35.4
279.1
590
267
45
70
59
The temperature effect was more clearly apparent in the processed samples where σOBM was
higher at 25 °C than at other temperatures. In fresh commercial puree at all temperatures, and
in frozen/thawed puree at 45 °C, it was not possible to obtain dynamic yield stresses (I), σDRI,
since in these samples the relationships between complex and steady viscosities were also
non-linear. In frozen/thawed commercial puree, σDRI was much lower at 55 °C than at 25 °C,
indicating a temperature effect.
In order to quantify the differences between the magnitudes of the yield stresses obtained by
the different methods, linear correlations from data for both puree types were established
between the yield stress values produced by the six applied methods (Table 3). There was
very good linear correlation (R2 = 0.9913) between Casson and Bingham yield stresses.
However, Bingham yield stresses were higher in magnitude than Herschel-Bulkley yield
stresses, and were higher by a factor of 2.5 than the yield stress values obtained from the
Bohlin option. This would indicate that, if the flow curves for potato purees do not follow
Bingham behaviour, yield values would be seriously overestimated by use of this model. In
26
Fernández et al., e-rheo.pt, 4 (2004) 21-28
certain cases, the Bingham yield value can be higher by a factor of 4-5 than the value obtained
by non-linear extrapolation [16].
Table 3 - Equations and R2 for linear correlation between yield stresses of potato purees obtained
by six different methods.
Bingham yield
stress, σ0B
Casson yield
stress, σ0C
Herschel Bulkley yield
stress, σ0H
Yield stress from
Bohlin
Option, σ0BO
Yield stress from
Bingham
Method, σ0BM
σ0B
1
σ0C
σ0C = 0.91σ0B – 13.96
(R2 = 0.9913)
1
σ0H
σ0H = 0.63σ0B – 29.11
(R2 = 0.7978)
σ0H = 0.70σ0C – 21.94
(R2 = 0.8447)
1
σ0BO
σ0BO = 0.36 σ0B – 23.08
(R2 = 0.9147)
σ0BO = 0.40σ0C – 18.13
(R2 = 0.9422)
σ0BO = 0.50σ0H – 1.51
(R2 = 0.8735)
σ0BM
σ0BM = 1.16σ0B + 44.63
(R2 = 0.9376)
σ0BM = 1.23σ0C + 67.55 σ0BM = 1.35σ0H + 133.67
(R2 = 0.8905)
(R2 = 0.6268)
σ0BM = 2.81σ0BO + 133.50
(R2 = 0.7867)
1
σDRII
σDRII = 0.97σ0B – 19.02
(R2 = 0.8157)
σDRII = 1.08σ0C – 8.00
(R2 = 0.8643)
σDRII = 2.64σ0BO + 46.96
(R2 = 0.8486)
σDRII = 0.73σ0BM – 30.02
(R2 = 0.6593)
σDRII = 1.41σ0H + 36.32
(R2 = 0.8459)
Dynamic
yield stress
(II), σDRII
1
1
There was good linear correlation (R2 = 0.9422) between Casson yield stresses and yield
stresses from the Bohlin option. The highest magnitudes of yield stress were clearly produced
by the Bingham method. These were almost 3 times higher than those obtained from the
Bohlin option. The highest linear correlation of Herschel-Bulkley yield stresses was with
yield stresses from the Bohlin option (R2 = 0.8735), the former being nearly twice the latter.
Although yield stresses from the direct Bohlin option were the lowest, the Herschel-Bulkley
model was the one that best characterised the flow behaviour of potato puree, and so this
direct method would appear to be a reliable technique for measuring yield stresses in potato
puree.
We certainly think that if linear correlations between different yield stresses were established
between different potato puree groups separately (that is, between fresh and frozen natural
and commercial potato puree, or between fresh natural and commercial puree and frozen
natural and commercial puree, or even between fresh natural puree, frozen natural puree, fresh
commercial puree and frozen commercial puree, separately), comparisons of the ratios
between different yield stresses could help us understand the differences between potato puree
structures and how they are affected by processing.
4. CONCLUSIONS
The experimental results indicated that the methods applied to the determination of yield
stress constitute a complementary set of techniques that are useful in studying the rheology of
natural and commercial potato purees, either fresh or frozen/thawed. The effects of sample
temperature and freezing on yield stresses as determined by different methods are
comparable. The influence of sample temperature on yield stresses was greater in the
processed purees. In natural potato purees, yield stresses decreased with processing,
indicating a weaker structure, whereas in commercial potato purees yield stresses increased
with processing, indicating greater strength.
The behaviour of potato puree was consistent with the Herschel-Bulkley model, which is
therefore more reliable for determination of yield stress than the Bingham and Casson models.
Determination of yield stress from dynamic rheological tests is extremely tedious, is not always
27
Fernández et al., e-rheo.pt, 4 (2004) 21-28
applicable and is more uncertain. Nevertheless, the high linear correlation found between
Bohlin and Herschel-Bulkley yield stresses would suggest that the Bohlin “yield stress option”
is a suitable tool for the direct measurement of yield stress in potato puree.
5.
ACKNOWLEGEMENTS
The authors wish to thank the CICyT for financial support with projects (AGL2001-2290) and
(AGL2004-01780).
6.
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