Effect of temperature on the density of whole milk under high pressure
Bérengère Guignon, Iván Rey, Pedro D. Sanz
MALTA Consolider Team, Department of Processes. Food Science Technology and Nutrition Institute
(ICTAN – CSIC), c/ José Antonio Novais 10, 28040 Madrid, Spain ([email protected])
ABSTRACT
High pressure processes is emerging as an effective preservation technology. Food shelf-life is prolonged
while its organoleptic and nutritive qualities are kept close to those of the fresh product. Modelling and
numerical simulation are employed to check and optimize treatment uniformity. These calculations require
the input of food properties like density. The lack of such data at high pressure for different temperatures has
led to the measurement of density of whole milk between 0 and 60 ºC at pressures up to 350 MPa. A
variable-volume piezometer with a solid-piston volumeter was employed for that purpose. Due to the
presence of solutes, the density of milk was about 3 % higher than that of water for a given pressure and
temperature condition. The density of whole milk increased with pressure in a similar way to water.
However, the temperature dependency observed was irregular in the case of whole milk compared to that of
water from 150 MPa. This behaviour is probably linked to the known effects of pressure and temperature on
milk lipid and protein fractions: fat crystallization, whey protein denaturation, casein micelle size
modification, interactions between fat globule and proteins and so on. The sensitivity of modelling
predictions to such small changes in density should be estimated. The study of the volumetric behaviour with
pressure and temperature of individual milk components should provide new insights on how to use high
pressure processing to modify technological properties of milk.
Keywords: High pressure processing; engineering properties of food; volumetric properties; modelling; whole milk.
INTRODUCTION
More and more consumers look for safer, nutritional added value and extended shelf-life food. In this way,
many beneficial effects of both high hydrostatic pressure and dynamic high pressure on dairy products have
been observed [1]. However, several hurdles have to be overcome in order to bring those technologies to the
current state of the thermal treatments in the industry. One of the most important facts hampering the
progress of both high hydrostatic pressure and dynamic high pressure is the lack of knowledge about
thermophysical properties of food in the high pressure domain. Investigating these properties, it will be
possible for example to model the behavior of density as a function of pressure and temperature that is
required for process simulation. Water density values as a function of temperature and pressure are used in
calculations as an approximation of food density behavior with pressure. Also approximations from
compositional models based on water density behavior with pressure and solute density at atmospheric
pressure can be employed [2]. This is reasonable for food with high moisture content but the uncertainty
generated by these assumptions has not been assessed yet. This would be made possible by providing such
density data for food and analyzing differences with water data. Besides, milk components undergo
modifications under pressure: protein denaturations, casein micelles dissociation, fat solidification and so on.
Macroscopic properties like density could be influenced by these modifications. In the literature, there is no
information to our knowledge about such effect on density of milk under pressure. Thus, the purpose of this
work was to determine the difference of density behavior between water and whole milk in a wide range of
pressure and temperature.
MATERIALS & METHODS
Raw whole bovine milk was provided by a local dairy (CLESA, Madrid, Spain) with its corresponding
compositional analysis. Mean values with standard deviations for sample composition in mass percentage
were 3.44±0.14 % for fats, 3.06±0.04 % for proteins and 4.63±0.03 % for lactose. The milk was stored at
0 ºC and used within 48 hours. It was manually mixed prior to sampling and care was taken to avoid
introducing air in the sample. Density at 0.1 MPa was measured with the vibrating tube method (Anton Paar
DMA5000, Graz, Austria) between 0 and 90 ºC. This apparatus provides density measurements for
substances with a density between 0 and 3000 kg·m-3. Measurements were carried out by cooling (mainly) or
heating by 5 ºC steps and repeated with the different milk samples that were provided (between four and
eleven measurements were obtained). The standard uncertainty of our measurements was at most 0.003 ºC
for temperature and 0.6 kg·m-3 for density. At high pressure, the density was determined using a variable
volume piezometer introduced in a high hydrostatic pressure equipment (U111, Institute of High Pressure
Physics - UNIPRESS, Warsaw, Poland). The standard uncertainty on specific volume change measured by
this device was estimated to be at most 3·10-7 m3·kg-1. The complete set-up and procedure were the same as
described in [3]. Briefly, it consists in measuring the volume changes determined by the displacements of a
piston in a cylindrical sample holder; displacements are detected by a linear variable differential transformer
associated to the piston. Pressure is increased to 70 MPa, 100 MPa and by 50 MPa steps up to the maximal
working pressure of the volumetric device (350 MPa), waiting for the temperature stability between each
compression (at least 10 min). The sample initial volume is about 17 mL. The density at a given pressure is
calculated as the sample mass divided by the sum of sample volume at atmospheric pressure and of the
volume change with pressure increase. Sample volume at atmospheric pressure is obtained from the sample
mass and from the density measured in the vibrating tube densimeter at the initial temperature condition of
the high pressure experiment. Volume changes with pressure are corrected due to a slight deformation of the
volumetric device with pressure by using a calibration performed with water. Volume changes were
measured for all the pressures mentioned above and at temperatures between 0 and 60 ºC each 10 ºC.
Experiments were repeated at least three times.
RESULTS & DISCUSSION
From the milk densities measured at atmospheric pressure between 0 and 90 ºC, the following relation was
developed:
 0 (T )  1017.23  e  ( 9.9·10
6
 2 1.1·10 7  3  5.9·10 10  4 )
with θ = T+3.4
where ρ0 is milk density at atmospheric pressure in kg·m-3 and T is temperature in ºC.
Coefficients were adjusted (Levenberg-Marquardt algorithm) using the software TableCurve2D version 5.0
(SPSS Inc., Chicago, IL, USA). Correlation coefficient was 0.998. This relation was necessary to calculate
the initial sample volume in the high pressure volumetric device before pressurization at the corresponding
temperature of measurement. The form of the equation was adapted from [4]. Compared to data from
literature, our values agree within the range of values for whole milk at 20 ºC, that is: 1027 to
1033 kg·m-3 [5]. Such a wide range of variation is due to variability in the composition of milk from different
origins (cow breed, geographic region, season and so on).
The density of raw whole milk is given from 0 to 60 ºC as a function of pressure up to 350 MPa in Table 1.
The standard deviation between the results of the three experiments was lower than ±1 MPa for pressure,
±0.1 ºC for temperature (except at 28.5 ºC where it was ±1.3 ºC) and ±0.9 kg·m-3 for density. The density of
milk varies between 1013.2 kg·m-3 at 59.6 ºC and 0.1 MPa, and 1153.7 kg·m-3 at 0 ºC and 349.1 MPa. As
expected, the density increases with pressure because of molecules rapprochement through compression.
Compared to water, the density of milk is about 2-3 % higher. Solutes like proteins and lactose (with a higher
density than water) contribute more than fats (with a lower density than water) to the milk density. The
behavior of milk density with pressure appears roughly similar to that of water since milk contains mainly
water. By contrast, the behavior of milk density with temperature is significantly different to that of water. A
selected representative set of density values at different pressure is presented all over the studied temperature
range in Figure 1. The corresponding values for water are also represented in that Figure. At atmospheric
pressure, an almost parallel variation of both substances is appreciated; the main difference is the absence of
a maximal density value for milk at low temperature (water has this maximum close to 4 ºC). At higher
pressures, a similar variation to water is still observed below 150 MPa. However, from 150 MPa, the
behavior of milk density with temperature becomes distorted. At 350 MPa, it shows an increase between 20
and 30 ºC followed by a decrease between 30 and 40 ºC. In this temperature region, a specific phenomenon is
taking part which is attributable to the milk solute components. Lactose is likely not affected by pressure
because its structure depends on covalent bounds (which are not disrupted by pressure); moreover,
caramelization and the browning reaction are inhibited under pressure at 60 ºC [6]. Then, it is not the cause of
the density rise around 30 ºC. Proteins like casein micelles or whey proteins undergo structural changes with
pressure. In this way, many authors have already observed that casein micelles size is reduced at high
pressure, especially between 150 and 300 MPa [7-8] but it is increased near 40 ºC by interactions with
denatured whey proteins. Other authors have reported denaturation of whey proteins above 100 MPa with βlactoglobulin being the most sensitive to pressure denaturation [9]. Also some interactions with the milk fat
globule membrane proteins can appear [10]. The effect of proteins conformation changes on density is not
obvious: it is unclear whether the casein micelles size reduction or increase, and the whey protein
denaturation, can produce such a density variation around 30 ºC. Nevertheless, the pressure – temperature
region where it occurs corresponds to the pressure - temperature levels where changes in caseins and whey
proteins structures were reported.
Table 1. Mean values and standard deviations of whole milk density from three experiments.
Pressure (MPa)
0.1
68.8
99.5
149.6
198.8
248.8
299.4
349.1
0.1
69.3
99.5
149.4
198.9
248.6
299.1
348.9
0.1
69.0
99.4
149.2
198.9
248.5
298.8
349.1
Density (kg·m-3)
T = 0.5 ±0.1 ºC
±0.0
1033.8
±0.9
1063.7
±0.1
1075.9
±0.1
1094.2
±0.8
1110.6
±0.5
1126.0
±0.7
1140.4
±0.6
1153.7
T = 28.5 ±1.3 ºC
±0.0
1026.6
±0.8
1055.2
±0.1
1066.8
±0.2
1084.7
±0.2
1101.2
±0.3
1116.6
±0.2
1131.1
±0.4
1144.7
T = 59.6 ±0.1 ºC
±0.0
1013.2
±0.9
1041.2
±0.3
1052.3
±1.0
1069.1
±0.5
1084.7
±0.1
1099.3
±0.5
1113.3
±1.0
1126.5
±0.0
±0.1
±0.4
±0.5
±0.7
±0.8
±0.7
±0.8
±0.4
±0.9
±0.6
±0.6
±0.7
±0.6
±0.8
±0.9
Pressure (MPa)
Density (kg·m-3)
T = 10.3 ±0.1 ºC
0.1
±0.0
1032.4 ±0.0
68.2
±0.1
1061.1 ±0.0
99.5
±0.1
1073.2 ±0.0
149.1
±0.7
1090.9 ±0.4
198.9
±0.5
1107.0 ±0.2
248.5
±0.3
1121.9 ±0.2
298.9
±0.8
1136.0 ±0.4
348.8
±0.3
1149.0 ±0.3
T = 39.9 ±0.1 ºC
0.1
±0.0
1022.0 ±0.0
68.6
±0.4
1049.4 ±0.3
99.3
±0.2
1060.7 ±0.1
148.6
±0.4
1077.6 ±0.3
199.0
±0.7
1093.8 ±0.3
249.4
±0.5
1108.7 ±0.3
299.3
±0.6
1122.5 ±0.1
348.7
±0.5
1135.2 ±0.3
Pressure (MPa)
Density (kg·m-3)
T = 20.2 ±0.1 ºC
0.1
±0.0
1029.6 ±0.0
68.8
±1.1
1058.4 ±0.5
99.4
±0.0
1070.2 ±0.3
149.8
±0.1
1088.0 ±0.4
198.6
±0.9
1103.9 ±0.6
249.1
±1.0
1119.2 ±0.3
298.8
±0.3
1133.2 ±0.6
349.2
±0.5
1146.5 ±0.8
T = 49.8 ±0.1 ºC
0.1
±0.0
1017.6 ±0.1
68.7
±0.9
1045.2 ±0.3
99.4
±0.1
1056.4 ±0.1
148.5
±0.4
1073.1 ±0.4
198.5
±0.3
1088.8 ±0.4
248.9
±0.3
1103.6 ±0.3
299.1
±0.2
1117.3 ±0.1
349.0
±0.6
1130.0 ±0.5
±0.0
±0.4
±0.1
±0.3
±0.5
±0.6
±0.8
±0.9
Regarding milkfat, its crystallization at atmospheric pressure is complex and occurs over a wide range of
temperatures from about -35 to 38 ºC. The crystallization phenomenon is usually described as a slow process
of hours. Melting of fats causes a decrease in density. Then, the density of whole milk depends on the solid
and liquid fat fractions which are determined both by the considered temperature and the temperature history
of the sample [11]. However, the behavior of milk density with temperature at atmospheric pressure is overall
dominated by that of water. At high pressure, water is as dense as the other milk components and any change
in their contributions to density, for instance a phase transition, could become significant. The effect of
pressure on fat crystallization temperature is represented by a shift toward higher temperatures by about
16 ºC per 100 MPa compared to the value at atmospheric pressure [12-13]. As pressure is increased, the solid
fat content should be higher and higher for a given temperature. By contrast, as temperature is increased,
melting is favored. The crystallization of fat components under pressure is difficult to predict because
pressure and temperature act with antagonist effects on the solidification phenomenon. Thus, it is not
discarded to say that the density rise at 30 ºC may be related to phase transitions of milkfat.
Figure 1. Specific volume of whole milk as a function of temperature at 0.1 (▲), 150 (○) and 350 (♦) MPa. Dotted lines
represent the corresponding trends for pure water. Uncertainty in density is smaller than the symbol size.
CONCLUSION
Density of whole milk was determined at pressures from 0.1 to 350 MPa, and at temperatures between 0 and
60 ºC. While the behaviour of milk density with pressure is quite similar to that of water density, differences
appear for milk density behaviour with temperature at pressures above 150 MPa. Around 30 ºC, the density is
higher than expected from the tendency marked by water behaviour. Milk components such as proteins and
fats are known to be modified by pressure and temperature. It seems that contributions from the protein and
fat fractions to density become significant over that of water at enough high pressure. This study needs to be
pursue to bring light on which phenomenon is responsible for the density rise observed between 20 and 40 ºC
under high pressure. For example, measurements with skim milk in the same conditions would help in
discriminating between protein and fat contributions.
ACKNOWLEDGEMENTS
This work has been supported by the “National Plan of Spanish I+D+I MEC” through the project CSD200700045 MALTA CONSOLIDER-INGENIO 2010 and to the Madrid Community through the project
QUIMAPRES S2009/PPQ-1551. B. Guignon has a contract from CSIC (JAE Program).
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