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Milk | Physical and Physico-Chemical Properties of Milk
Physical and Physico-Chemical Properties of Milk O J McCarthy, Massey University, Palmerston North, New Zealand ª 2002 Elsevier Ltd. All rights reserved. This article is reproduced from the previous edition, Volume 3, pp 1812–1821, ª 2002, Elsevier Ltd.
Introduction Milk is a complex colloidal dispersion of fat globules, casein micelles, and whey proteins in an aqueous solution of lactose, minerals, and a number of minor compounds. Its physical and physico-chemical properties depend on intrinsic compositional and structural factors, extrinsic factors such as temperature, and postmilking treatment. There is no clear dividing line between physical properties and physico-chemical properties. However, physical properties may be thought of as measures of the bulk behavior of milk and of how milk interacts with energy, while physico-chemical properties are measures of how bulk behavior and energy interactions depend on milk’s constituent colloidal particles, molecules, atoms, and ions. Knowledge of physical properties is of importance particularly in the technological and engineering design and control of milk processes and processing equipment. Knowledge of physico-chemical properties provides a basis for the design of modern methods of milk analysis, determination of milk microstructures, and elucidation of the complex chemical reactions that occur in milk. In this article, recognizably physical properties, such as rheological properties, density, and thermal properties, are discussed first. Then, properties that fall within the realms of both physics and physical chemistry are described: surface tension, acoustic properties, electrical and dielectric properties, and optical properties. Finally, recognizably physico-chemical properties – the colligative properties, and acid–base and oxidation–reduction equilibria – are discussed.
Rheological Properties The rheological behavior of milk is in accord with that of emulsions and suspensions in general. Milk may exhibit Newtonian or non-Newtonian behavior depending on composition, prior treatment, and measurement conditions (especially shear rate and temperature). At moderate to high shear rates, Newtonian behavior is exhibited by skim milk, by whole milk at temperatures >40 C (milk fat completely molten, no cold agglutination), and by whole milk at temperatures <40 C when cold agglutination is absent.
Non-Newtonian behavior manifests itself in raw whole milk under conditions that favor cold agglutination (temperatures <40 C) and at low shear rates. Shear thinning is the predominant rheological behavior. Skim milk shows shear-thinning behavior at low shear rates and at temperatures <30 C. As milk is concentrated by heat evaporation or by membrane processes, viscosity increases, shear thinning becomes more pronounced, and deviation from Newtonian behavior persists to higher shear rates. Thixotropy (time-dependent shear thinning) appears at a sufficiently high concentration, or after a sufficiently long storage time (at concentrations and temperatures above certain minima), during which structure development occurs. Such structure development, and the consequent steady viscosity increase, is known as age thickening. Viscosity of milk is greatly influenced by the concentration and state of the fat and casein, and thus on factors that affect these. Such factors include temperature, and technological treatments such as homogenization, heat treatment, renneting, and acidification. A full discussion of the rheological properties of milk may be found in the article Rheology of Liquid and Semi-Solid Milk Products.
Density and Specific Gravity (Relative Density) The density (kg m3) of milk is identified for a given measurement temperature as, for example, 20, where the superscript is the temperature in C. Specific gravity (SG), defined as milk/water, is identified in a similar way, 20 for example, SG20 20 or SG4 , where the superscript is the temperature at which the milk density was measured, and the subscript the temperature at which the density of water was determined. Density and specific gravity (more properly called ‘relative density’) are related by the equation 1 1 ¼ SG12 water
ð1Þ
where is the temperature ( C) and, usually, 1 ¼ 2. 20 of whole milk is about 1030 kg m3 and usually ranges from 1027 to 1033 kg m3 depending mainly on fat content. SG15:5 15:5 ranges from 1.030 to 1.035 for mixed-herd milk, and a commonly quoted average
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468 Milk | Physical and Physico-Chemical Properties of Milk
value is 1.032. Inter-breed variations in density and specific gravity are small. The density and specific gravity of milk depend on composition, temperature, and, in the melting point range of the milk triglycerides (–40 to þ40 C), thermal history; thermal history determines the ratio of liquid fat (lower density) to solid fat (higher density). Other factors, such as the stage of lactation and nutritional status of the cow, are important only insofar as they affect composition. Density data are needed for converting mass to volume and vice versa, and for calculating the values of physical properties such as kinematic viscosity and thermal diffusivity. The density of milk may be predicted, if the milk’s proximate composition is known, by using the equation 1 ¼
Xxi
ð2Þ
i
where xi and i are the mass fraction and density, respectively, of the ith component; (xi) ¼ 1 for the non-gaseous components. One of the non-gaseous components will be ice if the temperature is below the (initial) freezing point of the milk. The value of 20 of milk can be calculated using the values of component densities given in Table 1. The value of 918 kg m3 for milk fat given in the table assumes that the fat is a supercooled liquid, but allows for the higher density of the milk fat globule membrane. If milk contains dispersed gas, such as air, the actual density will be lower than that predicted by eqn [2]: actual ¼ ð1 – "a Þ predicted
ð3Þ
where "a is the volume fraction occupied by dispersed gas, which is assumed to have zero mass. is the temperature of measurement or prediction. Dispersed gas considerably lowers density, which then becomes pressure dependent. There have been many attempts to develop empirical equations relating milk density to fat content and temperature, the two most important determining variables. One such equation is as follows: ¼ ð – 2:307 10 – 3 2 Þ – ð0:2655Þ þ 1040:51 – ½F ð – 4:78 10 – 5 2 þ 9:69 10 – 3 þ 0:967Þ kg m – 3
where is the temperature ( C) and F is the % fat (w/w). Equation [4] is valid for milk and cream with fat contents in the range 0–15% (w/w), at temperature in the range 65–140 C. The temperature dependence of milk’s specific gravity is very slight, which is the principal advantage of expressing density in this way. Processing operations such as homogenization, pasteurization, and sterilization have negligible effects on milk density.
Thermal Properties Specific Heat Capacity and Enthalpy The specific heat capacity of milk determines the quantity of thermal energy that has to be added to or removed from milk to effect a given temperature change according to the following equation: q ¼ h ¼
Z2
cðÞ d ðJkg – 1 Þ
ð5Þ
1
where q is the quantity of heat energy per kg (J kg1), h is the change in milk enthalpy (J kg1), is the temperature ( C), ð2 – 1 Þ is the temperature change (1 to 2 or 2 to 1 ), and c ðÞ is the specific heat capacity (J kg1 K1) expressed as some function of temperature. c ðÞ is the specific heat capacity at constant pressure, rather than at constant volume. As milk is a liquid, the two can be considered equal, except perhaps under the conditions used in high-pressure processing. The equality of q and h is valid under isobaric conditions and in the absence of phase transitions, chemical reactions, changes in composition, and forms of work other than displacement. Equation [5] is valid for temperatures >40 C, the upper end of the milk fat melting point range. At temperatures between the (initial) freezing point of milk and 40 C, sensible heat demands are confounded with the latent heat demands caused by phase changes in the milk fat, and eqn [5] must be written as
ð4Þ h ¼
Z2
capp ðÞd
ð6Þ
1
Table 1 Density of milk components at 20 C Milk component
r20 (kg m3)
Water Fat Protein Lactose Residual components
998.2 918 1400 1780 1850
From Walstra P and Jenness R (1984) Dairy Chemistry and Physics. New York: Wiley.
where capp() is the apparent specific heat capacity (J kg1) expressed as some function of temperature. capp() depends on fat content, triacylglycerol composition, and thermal history. There is a maximum (4000 J kg1 K1) in the temperature range 15–20 C and a minimum (3880 J kg1 K1) at about 40 C. At temperatures away from the maximum, specific heat capacity is inversely related to fat content. At temperatures above 40 C, where the milk fat is completely molten and there are no phase changes, specific heat
Milk | Physical and Physico-Chemical Properties of Milk
capacity increases gradually with temperature, reaching 3940 J kg1 K1 at 100 C and 4000 J kg1 K1 at 140 C. The specific heat capacity of skim milk, which includes no significant latent heat effects due to phase changes in milk fat, increases essentially linearly but slowly with temperature over a wide range. Representative values are 3899 and 3988 J kg1 K1 at 0 and 50 C, respectively. For skim milk, and for whole milk with 4% fat, specific heat capacity may be predicted as a function of temperature (at temperatures above the milk fat melting point range) by the following equations: Skim milk at 52 143
–1
–1
C : c ¼ 2:814 þ 3942 ðJ kg K Þ ð7Þ
Whole milk at 53 153 C : c ¼ 2:976 þ 3692 ðJ kg – 1 K – 1 Þ ð8Þ
The ability to predict the enthalpy change between two chosen temperatures is, from a technological or engineering point of view, more useful than the ability to predict specific heat capacity at specific temperatures. The following general expression is valid for any temperature range, any fat content, and any total solids content: h1 $ 2 ¼ hfat xfat þ hnonfat xnonfat
ð9Þ
1
where hfat is the enthalpy change (J kg ) in milk fat between 1 and 2, hnonfat is the enthalpy change in the non-fat portion of the product between 1 and 2, xfat is the fraction of milk fat in the product, and xnon-fat is the mass fraction of the nonfat portion. hfat must be found from a suitable set of published empirical data. hnon-fat can be predicted from hnonfat ¼ hmilk plasma ¼
Z2 X ðci xi Þ d ¼
1 X ðci xi Þð1 – 2 Þ
ð10Þ
where ci is the specific heat of the ith component, xi is the mass fraction of the ith component, and (cixi) is the specific heat of milk plasma. Suitable values of ci for water, lactose, protein, and ash are 4200, 1400, 1600, and 800 J kg1 K1, respectively. The slight temperature dependence of the specific heat capacity of these non-fat components may usually be ignored for practical purposes, as indicated by eqn [10]. When milk is heat-concentrated, the enthalpy demand is almost wholly the latent heat of evaporation of water (hfg) that must be supplied. This demand can be expressed as kilograms of water evaporated per kilogram of unconcentrated milk hfg (J kg1), where hfg is read from steam tables at the pressure at which evaporation occurs. (There is an additional, though
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relatively small, sensible heat demand, as milk boiling point increases during concentration, but this demand is moderated by a concomitant decrease in specific heat capacity.) In calculating enthalpy changes over a temperature range that straddles or lies below the initial freezing point of milk, it is necessary to account for latent heat effects due to phase change in the water substance (water or ice) as well as in the milk fat. There are ways of doing this, but milk is rarely frozen.
Thermal Conductivity and Thermal Diffusivity The thermal conductivity of skim milk, whole milk, and cream increases slowly with increasing temperature. It decreases with increasing %TS or increasing fat content, the effects being generally greater at higher temperatures. The following semi-empirical relationship, although developed specifically for creams of fat content 20% (w/w), is accurate to within 10% for milk and cream with a fat content in the range 0.1–42% (w/w), and for the temperature range 5–75 C: l ¼ ð0:5279 þ 2:13 10 – 3 – 7:32 10 – 6 2 Þ ½1 – ð0:843 þ 1:9 10 – 3 Þ fat ðW m – 1 K – 1 Þ
ð11Þ
where l is the thermal conductivity (W m1 K1), fat is the fat volume fraction, and is the temperature ( C). Representative values of thermal conductivity at 20 C calculated using eqn [11] are compared with the thermal conductivity of water in Table 2. The thermal conductivity of whole milk heat concentrates may be predicted using the following equation: l ¼ ð0:59 þ 0:001 2Þ ð1 – 0:007 8TSÞ ðW m – 1 K – 1 Þ
ð12Þ
The equation is valid for the temperature range 40 < < 90 C and the %TS range 37 < TS < 72%; it is accurate to 0.88%. The thermal diffusivity of milk may be calculated using the equation: ¼
l c
ðm2 s – 1 Þ
ð13Þ
Table 2 Representative values of the thermal conductivity of fluid milk products compared with the thermal conductivity of water, at 20 C Fluid
Thermal conductivity (W m1 K1)
Water Skim milk (0.1% fat) Whole milk (3.9% fat) Cream (42% fat)
0.603 0.568 0.548 0.357
From Fernandez-Martin F and Montes F (1972) Milchwissenschaft 27: 772–776.
470 Milk | Physical and Physico-Chemical Properties of Milk
where is the thermal diffusivity (m2 s1), is the density (kg m3), and c is the specific heat capacity (J kg1 K1). l, , and c can be predicted as described above, and , then, can be calculated. For example, at 20 C, l 0.548 W m1 K1, 1030 kg m3, and c 3980 J kg1 K1, giving a value for of 1.34 107 m2 s1.
Surface Tension The surface tension of milk lies in the range 40–60 mN m1 (average: 52 mN m1) at 20 C. Comparable values for some milk fractions are 72.8 (water), 51–52 (rennet whey), 52–52.5 (skim milk), 42–45 (25% fat cream), and 39–40 (sweet-cream buttermilk). Surface tension decreases with increasing temperature. For whole milk, the relationship is ¼ 1:8 10 – 4 2 – 0:163 þ 55:6
ð14Þ
1
where is the surface tension (mN m ) and is the temperature ( C). Surface tension is influenced by fat content, homogenization, and temperature history. It decreases with increasing fat content up to 4%, but no further decrease occurs at higher fat contents. Homogenization of pasteurized milk increases surface tension. Homogenization of raw milk, however, can lead to a decrease in surface tension owing to the release of free fatty acids by lipase activity. The surface tension of milk held at 5 C and brought to 20 C is lower than that of milk cooled to 20 C when measured immediately. Heat treatment of milk at sterilization temperatures can cause a small increase in surface tension, probably the result of denaturation of whey proteins, a change that reduces their surface activity.
Acoustic Properties Acoustics is the science of sound (mechanical vibrations at frequencies in the range 1.6 102 to 20 kHz, which are detectable by the human ear), infrasound (frequencies of <1.6 102 kHz), and ultrasound (frequencies of >20 kHz). Only low-power ultrasound (which involves power levels <1 W cm2) is of significance in dairy science and technology. It is used principally as an analytical tool for indirectly measuring food characteristics and as an in-line method for measuring flow rate. The ultrasonic properties of a material most frequently measured are the ultrasonic velocity (m s1), the attenuation coefficient (Np m1), and the acoustic impedance
(kg m2 s1). These depend on other physical properties of the material. The ultrasonic velocity (the distance traveled by an ultrasonic wave in unit time) is related to the elastic modulus, E, and density, : k ¼ ! E
ð15Þ
Here, ! is the angular frequency (rad s1) and k is the complex wave number ¼ (!/c) þ i, where c is the ultra1 sonic velocity (m sp ), is the attenuation coefficient ffiffiffiffiffiffiffiffi 1 (Np m ), and i ¼ – 1: For low-attenuating materials (i.e., << !/c), eqn [15] can be written as 1 ¼ c2 E
ð16Þ
where is the density (kg m3) and E is the modulus of elasticity (Pa). In the case of milk, E is the bulk modulus, as liquids are normally subjected to a compressive (as opposed to a shearing) ultrasonic wave. The attenuation coefficient, , is a measure of the decrease in the amplitude of an ultrasound wave as it travels through the material. It is given by the equation A ¼ A0 e – x
ð17Þ
where A0 is the initial amplitude of the wave and A is the amplitude after the wave has traveled a distance x through the material. Attenuation results from absorption and scattering. The acoustic impedance is a measure of the fraction of an ultrasonic wave reflected from a material’s surface. The (complex) specific acoustic impedance, Z, is defined as Z ¼
! k
ð18Þ
where Z ¼ RZ þ iXZ, with RZ being the resistive (real) part of the complex impedance and XZ the reactive (imaginary) part of the complex impedance. For low-attenuating materials (i.e., << !/c), eqn [18] can be written as Z ¼ RZ ¼ c
ð19Þ
Values of the three ultrasonic properties of skim milk (at 1 mHz and 28 C) are as follows: velocity, c ¼ 1522 m s1, attenuation coefficient, ¼ 23 Np m1, and impedance, Z ¼ 1.5 106 kg m2 s1. Ultrasonic properties, which are frequency and temperature dependent, are most commonly measured using the pulse-echo technique. Enhanced information about the characteristics of the sample can be gained by carrying out measurements over a range of frequencies and also a range of temperatures.
Milk | Physical and Physico-Chemical Properties of Milk
The ultrasonic properties of milk are fundamental properties, but they are not of interest by themselves. Their measurement is useful only insofar as it is possible to establish relationships between them and other physico-chemical characteristics such as composition, structure, and state – characteristics that determine how ultrasound interacts with the sample. Such relationships can be developed empirically by means of calibration experiments, or theoretically. Ultrasound has been used to measure the composition of milk in terms of fat and solids-not-fat, the particle size distributions of milk fat globules and casein micelles, and the rate of coagulation of milk by chymosin. Ultrasonic imaging has been used to measure teat milk flow rate, and to non-invasively monitor the microbial spoilage of packaged UHT milk. The measurement of creaming profiles, the principle of which is the measurement of the ultrasound velocity and/or attenuation coefficient as a function of sample height and time, has obvious potential for milk and other liquid dairy products. Apart from being non-invasive and non-destructive, ultrasound can be used to analyze opaque as well as concentrated systems, and is inexpensive, rapid, and accurate.
Electrical and Dielectric Properties Electrical Conductivity Electrical conductivity (EC), , is a measure of a material’s ability to carry an electrical current. It ranges in value from 1018 to 107 S m1 (Siemen per meter), depending on the material. The EC of normal whole milk is about 0.460 S m1. EC is most easily measured by applying a known DC voltage across a pair of parallel electrodes immersed in the sample, measuring the current produced, and calculating the resistance of the specimen (the volume bounded by the electrodes): ¼
1l l ¼ G ðS m – 1 Þ RA A
ð20Þ
where R is the resistance ( ), G the conductance (S), l the distance between the electrodes (m), and A the electrode area (m2). Equation [20] shows that EC and electrical conductance (the reciprocal of resistance) are related via the dimensions of the specimen. EC is generally measured in practice by impedance (or, admittance) spectroscopy, in which an AC rather than a DC voltage is applied to the sample. Impedance and admittance (the reciprocal of impedance) are complex properties, the real parts of which are, respectively, resistance and conductance. Measurements are best carried out at frequencies >10 kHz; at and above this frequency the
471
measured value is a property of the bulk milk and not of the milk–electrode interface. The EC of milk is determined mainly by the charged species present, particularly the salts. There is very little contribution from lactose; casein, also, makes a much smaller contribution than do the milk salts. The main effect of milk proteins in general is to hinder the migration of ions and thus depress EC. However, the release of calcium ions from the casein micelles as a result of a decrease in pH, caused by either deliberate acidification or bacterial growth, results in an increase in EC. A drop in milk pH to about 5 causes all of the colloidal calcium phosphate to dissolve, and the equilibria of milk buffer systems to change, resulting in saturation of the EC to a constant maximum value. This phenomenon is the basis of the automatic monitoring of the growth of lactic acid bacteria by conductimetric methods. Mastitis in a quarter of a cow’s udder results in decreases in the concentrations of lactose and Kþ in the milk secreted, and corresponding increases in the concentrations of Naþ and Cl that preserve the milk’s isoosmolality with the cow’s blood. The net effect is an increase in the milk’s EC. This phenomenon has led to much research over the last 60 years aimed at finding a reliable way of using in-line EC measurement at milking to detect both subclinical and clinical mastitis in the quarters of individual cows. Although the EC of milk from individual quarters can be monitored easily and accurately, achieving this aim has been hampered by the fact that variation in EC depends not only on the level of infection, but also on numerous other factors such as breed, parity, estrus, lactation stage, presence of other diseases, milking interval, time of day, and milk composition. In 1998, an extensive analysis of published data carried out by the International Dairy Federation concluded that EC measurement could not identify mastitic quarters or mastitic cows, nor detect subclinical mastitis, with sufficient accuracy to be useful. Currently, most automatic milking systems and some manual systems incorporate sensors for measuring the EC of quarter milk and software for processing the data generated. The development of sophisticated statistical modeling of the data, which involves comparisons between the quarters of the individual cow over successive milkings, has led to an improvement in the sensitivity of detection of subclinical and clinical mastitis. In the case of automatic milking systems, the farmer is dependent on EC measurement for detecting mastitic cows. The EC of fresh milk and cream decreases with increasing fat content because the fat globules (themselves nonconducting) occupy volume that would otherwise be filled with the conducting aqueous phase of the product, thus impeding the mobility of the conducting ions and increasing the distance that migrating ions have to travel. For a fat content in the range
472 Milk | Physical and Physico-Chemical Properties of Milk
0.15–51% (w/w), the EC of milks and creams is related to the volume fraction of fat, fat, as follows: ¼ skim ð1 – fat Þ ð1 þ q 2fat Þ
ð21Þ
where ¼ 1.56 0.04, and q varies between 3.0 and 3.5, depending on the batch of milk. Measurement of the admittance of milk has the potential to allow estimation of milk fat content if milk water content is known, and vice versa. The latter utility of the measurement could provide a means of detecting adulteration of milk with water. The EC of stored whole milk reaches a higher saturation value than that of stored skim milk, because for whole milk the EC-depressing effect of the presence of fat is more than compensated for by the production of free fatty acids and the release of phosphate ions from the milk fat globule membrane. The EC of milk increases markedly with temperature, as illustrated by the following empirical relationship for buffalo milk, valid for the temperature range 5–70 C: ¼ 1:71 10 – 1 þ 6:32 10 – 3 þ 9:01 10 – 6 2 ðS m – 1 Þ ð22Þ
The EC and the viscosity of milk have been shown to be related. This relationship is thought to be due to the fact that the ion content of milk affects both the EC and the conformation of milk proteins, the latter influencing viscosity.
"9ð!Þ ¼ "91 þ "0ð!Þ ¼
"9S – "91 1 þ !2 2
ð"9S – "91 Þ ð!t Þ þ 1 þ !2 2 !"0
ð24Þ ð25Þ
where "91 is the real permittivity at very high frequencies, "9S is the real static (low frequency) permittivity, ¼ 1=2 fR , where fR is the relaxation frequency, the electrical conductivity, and "0 the permittivity of free space (¼ 8.854 1012 F m1). Modeling shows that the complex permittivity of milk is essentially that of water, with perturbations caused by the ionic and nonionic milk components. Analysis of the spectral data relating to permittivity ("9S , "91 , and ) and those relating to loss factor (ð"9S – "91 Þ, , and ) shows that the perturbations are sensitive to the presence of fat, carbohydrate, protein, and ionic species. For example, permittivity is depressed by the nonionic components fat, lactose, and casein. Measurement of dielectric property spectra could potentially be useful in monitoring the gross composition of large quantities of milk in real time.
Optical Properties
Dielectric Properties The dielectric properties of a material, the permittivity ("9) and the dielectric loss factor ("0), are the real and imaginary parts, respectively, of the complex permittivity ("): "ð!Þ ¼ "9 ð!Þ – j"0ð!Þ
increasing temperature, whereas the loss factor is almost temperature-independent. The dielectric property spectra of whole milks of varying total solids content can be modeled using the following theoretical equations:
ð23Þ
pffiffiffiffiffiffiffi where ! is the frequency (Hz) and j ¼ – 1. "9is a measure of the ability of the material to store electromagnetic energy. "0 is a measure of the material’s ability to dissipate electromagnetic energy as heat. The latter phenomenon is exploited in microwave and radio frequency heating. Permittivity and loss factor are frequency and temperature dependent. Representative values of "9 and "0 for whole milk (3.25% fat) at 20 C and 2.45 GHz (the frequency most commonly used for microwave heating) are 67.9 and 17.6, respectively, relative to the values for free space. Corresponding values for water are 80.2 and 13.4. The permittivity at 20 C of skim milk, low-fat milk, and whole milk decreases with increasing frequency in the range 1–20 GHz. The loss factor, on the other hand, exhibits a net increase with frequency over this range, but goes through a minimum near the lower end and a maximum near the higher end. At a given frequency, the permittivity of whole milk decreases slowly with
The term ‘optical properties’ comprises properties with respect to electromagnetic radiation not only in the visible region of the spectrum (380–760 nm), but also in the infrared (IR, 760 nm to 1 mm) and ultraviolet (UV, 5–380 nm) regions that lie on either side of it. Visible, IR, or UV light incident on milk is absorbed, absorbed and reemitted (producing fluorescence), scattered, or transmitted, depending on wavelength. Milk, as a complex colloidal dispersion of fat globules, casein micelles, and whey proteins in an aqueous solution containing a number of solutes, not only absorbs light at several wavelengths but also scatters light, as well as transmitting it. In the visible region, riboflavin in milk absorbs strongly near 470 nm (giving the yellow-green color of whey) and emits fluorescent radiation with a maximum at 530 nm. The -carotene in milk fat absorbs near 460 nm, which is responsible for the yellow color of the fat. In the UV region, aromatic amino acid residues of proteins (tyrosine and tryptophan) absorb strongly near 280 nm, and a part of the UV radiation is emitted as fluorescence at 340 nm. Measurement of the intensity of this fluorescence has been used to quantify the protein
Milk | Physical and Physico-Chemical Properties of Milk
content of milk. The double bonds of the milk fat absorb very strongly near 220 nm. In the IR region, absorption is primarily by the amide (II) groups (CONH) of proteins at 6465 nm, the hydroxyl groups (OH) of lactose at 9610 nm, and the ester carbonyl groups (C¼O) of lipids at 5723 nm. This is the basis for the instrumental compositional analysis of milk using infrared analyzers. Milk samples are first homogenized to reduce the size of fat globules to <1 mm, to prevent their presence interfering with the measurement. Both fat globules and casein micelles scatter light. It is possible to measure the intensities of both the scattered light and the light transmitted by the sample. Both measurements form the basis of the determination of the fat content of milk and of the size distributions of fat globules and casein micelles. Instruments for fat determination are based on measurement of turbidity, that is, the attenuation of the incident beam, usually expressed as optical density or absorbance. The surface light scattering (diffuse reflection) and absorption properties of milk strongly affect the visual appearance of milk. The creamy color of whole milk is due to the -carotene in the fat. Casein micelles scatter blue light (shorter wavelength) more effectively than they scatter red (longer wavelength), giving skim milk its bluish color. Homogenization of whole milk makes milk whiter by increasing the diffuse reflection (e.g., by some 19% at 550 nm). Heating has the same effect initially, but severe heating causes nonenzymic browning. The penetration of light into milk can be important with respect to light-induced reactions. At 580 nm, light incident on whole milk loses 90 and 99% of its intensity at penetration depths of 8 and 24 mm, respectively. The refractive index of milk varies with temperature and wavelength. The value for bovine milk at 589.3 nm (the D line of the sodium spectrum) at 20 C, n20 D , lies in the range 1.344 0–1.348 5. This may be compared with the value of 1.333 0 for water. The difference (n) between the values of n20 D for milk and water reflects the presence of dissolved substances (lactose, minerals, etc.) and colloidal substances (casein micelles and whey proteins): n ¼ ðmr Þ
ð26Þ
where is the density of the aqueous part of milk (kg m3), and m and r are, respectively, the mass fractions and specific refractive increments (m3 kg1) of the individual substances. Values of r for the main determinants of n are 2.07 104 (casein micelles; m3 kg1 of dry casein), 1.87 104 (whey proteins), 1.40 104 (lactose), and 1.70 104 (other dissolved substances). Fat globules and air bubbles do not contribute to the refractive index of milk.
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Colligative Properties: Freezing Point, Boiling Point, and Osmotic Pressure The part of milk comprising water and low molecular weight solutes obeys Raoult’s law approximately. This law in one form states that the relative lowering of the solvent vapor pressure resulting from the presence of a solute is equal to the mole fraction of the solute in the solution. Consequences of the lowering of vapor pressure (the equilibrium relative humidity of milk at ambient temperature is 99.3%) are a depression of freezing point (f ) and an elevation of boiling point (b ). In addition, the presence of the solute gives rise to an osmotic pressure. For very dilute solutions f ¼ Kf M
ð27Þ
b ¼ Kb M
ð28Þ
and
where Kf and Kb are the cryoscopic constant and ebullioscopic constant, respectively, and M is the molality of the solution. The freezing point of milk is less than 0 C, and the boiling point higher than 100 C (at atmospheric pressure). Equations [27] and [28] can be used to roughly calculate the freezing point depression and boiling point elevation of milk as functions of the concentrations of water-soluble milk components. Lactose, chloride salts, and other components (calcium, potassium, magnesium, lactate, phosphate, citrate, etc.) contribute about 55, 25, and 20%, respectively, to the freezing point depression. The freezing point of the vast majority of individual milks lies in the range 0.512 to 0.550 C, and few fall outside the range 0.520 to 0.512 C. The constancy of the freezing point depression is a reflection of the constant osmolality of milk. Although the concentrations of individual water-soluble components can vary, the total molality of fully dissociated species remains fairly constant. As the milk secretion process dictates that the osmotic pressure of milk be kept equal to that of blood (687 kPa), a constant osmolality is maintained in milk by the passage of blood constituents into the mammary gland; any change in the concentration of lactose in milk is compensated for by changes in the concentrations of sodium and chloride. Milk with a freezing point of 0.53 C has an osmolality of 0.285 osmol kg1 water. The determination of freezing point is extensively used to assess whether or not milk has been adulterated by the addition of water, and to quantify the amount added. Milk with a freezing point 0.525 C is usually assumed to be unadulterated.
474 Milk | Physical and Physico-Chemical Properties of Milk
Acid–Base Equilibria pH of Milk The pH of bovine milk at 25 C usually lies in the range 6.5–6.7, with 6.6 being the most common value. The pH decreases with increasing temperature. This implies temperature-induced changes in milk’s complex buffering system rather than an increase in milk’s acidity. At a given temperature, differences in pH and buffering capacity between individual lots of fresh milk reflect compositional variation. The pH of colostrum can be as low as 6.0 and that of mastitic and endof-lactation milks as high as 7.5. High pH can be due to increases in [Naþ] and [Cl] (and possibly in the concentrations of other ions), a reduction in the lactose content, and a reduction in the concentration of soluble inorganic P – changes that alter buffering capacity in this pH range.
dB ¼ dpH ðvolume of acidor basesolution addedÞ ðnormality of solutionÞ ðaveragevolume of sampleÞ ðpH change producedÞ ð29Þ
The resulting value of dB/dpH is assigned to the pH at the mid-point of the pH change that has occurred. Buffering action is due to the presence in milk of acid buffers (weak acid–conjugate base pairs) and base buffers (weak base–conjugate acid pairs). Milk contains many acidic and alkaline groups that result in buffering action over a wide pH range. The main groups are listed in Table 3. The principal buffer components in milk are soluble phosphate, colloidal calcium phosphate (CCP), citrate, bicarbonate, and casein. The relationship between pH and pKa (the negative logarithm of the acidity constant Ka) for the titration of a weak acid against a strong base is given by the Henderson–Hasselbalch equation: pH pKa þ log
Buffering Constitutents of Milk Milk, because of its buffering system, resists change in pH when it is titrated against a strong acid or a strong base. The extent of resistance, that is, the buffering action, at a given pH is called the ‘buffering index’. The buffering index, dB/dpH, is the derivative (slope) of the titration curve (the plot of moles of strong acid or strong base added to milk vs. pH). It is calculated as follows:
½A – ½HA
ð30Þ
Maximum buffering occurs at pH ¼ pKa. In the case of a weak base–conjugate acid buffer, maximum buffering action likewise exists when pH ¼ pKa (¼ 14 pKb). Kb is the basicity constant and pKb is its negative logarithm. In some cases several values are given for pKa in Table 3; values for many milk constituents are uncertain because of the complexity of the overall system.
Table 3 Principal buffering groups in milk Group
Approximate concentration (mmol l1)
Expected pKa
pKa (in milk)
Salts Inorganic phosphate Citrate Organic phosphate esters Carbonate Lactic acid Formic acid Acetic acid Various amines
21.0 9.0–9.2 2.5–3.5 2.0 <0.4 0.2–1.8 0.05–0.8 1.5
2.1, 7.2, 12.3 3.1, 4.7, 5.4 1.4, 6.6 6.4, 10.1 3.9 3.6 4.7 7.6
3, 5.8, 6.6 3, 4.1, 4.8 1.7, 5.9 6.4, 10.1 3.9 3.6 4.8 7.6
Protein-bound residues Aspartic acid Glutamic acid Histidine Tyrosine Lysine Phosphoserine N-Acetylneuraminic acid Terminal carboxyl Terminal amino
Titratable group -COOH -COOH Imidazole Phenol -NHþ 3 Phosphate COOH -COOH -NHþ 3
Expected pKa 4.6 4.6 6.1 9.7 10.4 1.5, 6.5 2.6 3.6 7.9
pKa (in milk) 4.1 4.6 6.5 10.5 2, 6 5.0 3.7 7.9
From McCarthy OJ and Singh H (2009) Physico-chemical properties of milk. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 691–758. New York: Springer.
Milk | Physical and Physico-Chemical Properties of Milk
The shape of a titration curve, and consequently the relationship between buffering index and pH, depends on the experimental methodology used; titration and backtitration curves of milk do not coincide (Figures 1 and 2). When milk is acidified (Figure 1), maximum buffering (a maximum in dB/dpH) occurs at about pH 5.1, but when acidified milk is back-titrated with a base, a low extent of buffering exists at pH 5.1 and a maximum at pH 6.3. The acid part of the titration curve is important because milk is acidified in the manufacture of products such as yogurt. When milk is titrated to pH 11.0 (Figure 2), buffering action is relatively slight at pH 8–9 but increases at higher pH values. There is little difference between the curves for titration with alkali and back-titration with acid. On back-titration, a buffering peak is not observed at pH 6.3 (cf. Figure 1). Although there is a peak at about pH 5.1, it is weaker and less distinct than the peak obtained when normal milk is first acidified (Figure 1). The maximum at pH 5.1 on acidification is due to dissolution of CCP and the consequent formation of HPO24 – and H2 PO4– . On back-titration, buffering action is low at this pH because the CCP is already solubilized. The maximum at pH 6.3 is due to the formation of calcium phosphate, resulting in the release of Hþ (from HPO24 – and H2 PO4– ), which can combine with OH. The buffering action of milk at high pH values is probably due to lysine residues and carbonate. When milk is titrated to high pH, all of the calcium phosphate precipitates. The precipitate dissolves again on subsequent acidification, resulting in buffering action over a wide pH range. Colostrum has a much higher buffering capacity than that of normal milk over the pH range 6.6–3.0. The buffering peak at pH 5.1 for mastitic milk is slightly higher than that for normal milk.
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Figure 2 Buffering curves of milk titrated from the initial pH (6.6) to pH 11.0 with 0.5 M NaOH (&) and then back-titrated to pH 3.0 with 0.5 M HCl (). Data supplied by J. A. Lucey, Department of Food Science, University of Wisconsin–Madison.
Titratable Acidity of Milk The alkaline range of the titration curve is important because of the widespread use of titratable acidity to characterize milk. The titratable acidity is the buffering capacity of milk between its own pH (6.6) and pH 8.3 (the phenolphthalein end point). The measurement of titratable acidity (usually expressed, somewhat arbitrarily, as percentage lactic acid) is useful for determining the freshness of milk and for controlling the manufacture of fermented dairy products. The titratable acidity of fresh milk seldom falls outside the range 0.14–0.16%.
Effects of Milk Treatment on Acid–base Equilibria Heating
Heat treating milk (e.g., by holding at 100 C for 10 min) results in an increase in buffering action at pH 5.0 during acid titration. This is probably caused by an increase in the concentration of CCP owing to the formation of heat-precipitated calcium phosphate. More severe heat treatment causes a shift of the peak from pH 5.0 to pH 4.4, and the buffering action in the pH range 5.0–4.0 is much stronger than that of unheated or less severely heated milk. The shift in the pH of the peak may be due to a change in the structure and composition of CCP during the severe heat treatment.
Freezing Figure 1 Buffering curves of milk titrated from the initial pH (6.6) to pH 3.0 with 0.1 M HCl () and then back-titrated to pH 11.0 with 0.5 M NaOH (&). Data supplied by J. A. Lucey, Department of Food Science, University of Wisconsin–Madison.
The pH of milk decreases to as low as 5.8 during slow freezing, probably owing to the precipitation of calcium phosphate and the consequent release of Hþ in the unfrozen phase as this phase becomes increasingly concentrated.
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Little change occurs on rapid freezing, possibly owing to insufficient time available for precipitation to occur. Dilution and concentration
Concentration of milk lowers milk pH owing to precipitation of calcium phosphate; dilution has the opposite effect. During the ultrafiltration concentration of milk, the buffering capacity of the retentate increases steadily owing to the increasing concentrations of casein, whey proteins, and milk salts.
Oxidation–Reduction Equilibria Oxidation and reduction are, respectively, the loss and gain of electrons. The potential of a system to transfer electrons, that is, the oxidation–reduction or redox potential (Eh), is measured relative to the hydrogen electrode, and expressed in volts. For a simple binary oxidation– reduction system, Eh is related to the concentrations of the oxidized and reduced forms of the substance involved by the Nernst equation: Eh ¼ E0 þ
RT ½Ox ln nF ½Red
ð31Þ
where E0 is the standard redox potential (V) (i.e., the potential when both the oxidized and reduced forms are at unit activity); [Ox] and [Red] are the activities of the oxidized and reduced forms, respectively; n is the number of electrons transferred per molecule; R is the gas constant (8.314 J K1 mol1); T is the absolute temperature (K); and F is the Faraday constant (96.5 kJ V1 mol1). Systems with a positive value of Eh are oxidizing systems, whereas those with a negative value are reducing ones. At 25 C and for a one-electron transfer, eqn [23] becomes Eh ¼ E0 þ 0:059log
½Ox ½Red
ð32Þ
In many biological systems, Hþ are involved in the overall oxidation reaction. In this case, again, for a oneelectron transfer, Eh ¼ E0 þ 0:059log
information is available on the considerable poising capacity of milk, because of measurement difficulties. These difficulties are the result of sluggishness of some oxidation–reduction systems in milk in coming to equilibrium (redox potentials pertain to equilibrium conditions), incomplete reversibility of some systems, and back- diffusion of oxygen during measurement. O2, ascorbate, and riboflavin are the principal systems determining the Eh of milk. The thiol–disulfide system contributes to the Eh of heated milk. All the ascorbate in freshly drawn milk is in the reduced form, but reversible oxidation to dehydroascorbate occurs at a rate dependent on the concentrations of Cu2þ, Fe3þ, and O2; the Eh values of all three of these are higher than that of ascorbate. Preservation of ascorbate depends on deaeration and prevention of contamination by copper. Oxidation–reduction reactions in milk are influenced by heat treatment, bacterial activity, and exposure to light, as well as by O2 and the presence of metal ions. Heating lowers the Eh of milk, the more so if high temperature–short time conditions are used and prior deaeration carried out; the result is better retention of reducing substances such as ascorbic acid. Bacterial activity reduces the Eh by consumption of available oxygen in the milk. The decrease in potential can lead to the reduction and loss of color of certain added dyes, and is the basis of the methylene blue test for the bacterial status of fresh milk. The riboflavin in milk does not contribute significantly to Eh or to poising. However, the absorption of visible light by riboflavin (at 470 nm) results in excitation. Excited-state riboflavin can oxidize a number of compounds in milk, thereby itself becoming reduced. This is an example of photooxidation, and it results in the production of off-flavors in milk exposed to sufficiently intense visible light, for example, direct sunlight.
½Ox – 0:059pH ½Red
ð33Þ
An oxidation system exhibits poising capacity, analogous to buffering capacity, at values of [Ox]/[Red] close to unity, that is, at Eh values close to the E0 value. The redox potentials of individual milk samples in equilibrium with air fall in the range þ0.25 to þ0.35 V at 25 C at the normal milk pH. The redox potential is inversely related to pH, ranging from about þ0.20 at pH 10 to about þ0.395 at pH 3.5 for raw milk. Little
Conclusions Some of the physical and physico-chemical properties of milk, such as density, thermal properties, freezing point, acid–base equilibria, and oxidation–reduction equilibria, have been well studied and are well understood. Others, such as acoustic properties and dielectric properties, have been studied to a relatively limited extent. This is a reflection of the relative importance, historically, of the different properties with respect to production, analysis, handling, and processing of milk. Milk, a complex biological fluid, is by no means fully understood. There is no doubt that future advances in our understanding of its nature and attributes will depend to a significant extent on the use of measurement techniques whose development will be built upon and will extend
Milk | Physical and Physico-Chemical Properties of Milk
our current knowledge of physical and physico-chemical properties. See also: Analytical Methods: Differential Scanning Calorimetry; Infrared Spectroscopy in Dairy Analysis; Light Scattering Techniques; Physical Methods; Rheological Methods: Instrumentation; Principles and Significance in Assessing Rheological and Textural Properties; Spectroscopy, Overview; Ultrasonic Techniques. Mastitis Therapy and Control: Automated Online Detection of Abnormal Milk. Rheology of Liquid and Semi-Solid Milk Products.
Further Reading Adam M, Celba J, Havlı´cˇek Z, Jeschke J, Kubesˇova´ A, Neumannova´ J, Pokorny´ Z, Sˇesta´k J, and Sˇra´mek P (1994) Thermophysical and Rheological Properties of Foods. Milk, Milk Products and SemiProducts. Prague: Institute of Agricultural and Food Information. Anonymous (1996) Physical Properties of Dairy Products. Hamilton, New Zealand: MAF Quality Management. Fernandez-Martin F and Montes F (1972) Influence of temperature and composition on some physical properties of milk and milk concentrates. III. Thermal conductivity. Milchwissenschaft 27: 772–776. Figura LO and Teixeira AA (2007) Food Physics. Physical Properties – Measurement and Applications. New York: Springer.
477
Fox PF and McSweeney PLH (2006) Advanced Dairy Chemistry, 3rd edn. New York: Springer. Jowitt R (ed.) (1983) Physical Properties of Foods, 3rd edn. London: Applied Science. Jowitt R (ed.) (1987) Physical Properties of Foods 2: COST 90bis Final Proceedings. London: Elsevier Applied Science. Lucey JA and Horne DS (2009) Milk salts: Technological significance. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 351–389. New York: Springer. McCarthy OJ and Singh H (2009) Physico-chemical properties of milk. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 691–758. New York: Springer. Rahman S (1995) Food Properties Handbook. Boca Raton, FL: CRC Press. Rao MA, Rizvi SSH, and Datta AK (2005) Engineering Properties of Foods, 3rd edn. Boca Raton, FL: CRC Press. Riedel L (1955) Kalorimetrische Untersuchungen u¨ber das Schmelzverhalten von Fetten und O¨len [Calorimetric studies on melting of fats and oils]. Fette Seifen Anstrichmittel 57: 771–782. Sahin S and Sumnu SG (2006) Physical Properties of Foods. New York: Springer. Speiss WEL and Schubert H (eds.) (1990) Engineering and Food, Vol. 1: Physical Properties and Process Control. London: Elsevier Applied Science. Urbicain MJ and Lorenzo JE (1997) Thermal and rheological properties of foodstuffs. In: Valentas KJ, Rotstein E, and Singh RP (eds.) Handbook of Food Engineering Practice, pp. 425–486. Boca Raton, FL: CRC Press. Walstra P and Jenness R (1984) Dairy Chemistry and Physics. New York: Wiley.
Introduction Milk is a complex colloidal dispersion of fat globules, casein micelles, and whey proteins in an aqueous solution of lactose, minerals, and a number of minor compounds. Its physical and physico-chemical properties depend on intrinsic compositional and structural factors, extrinsic factors such as temperature, and postmilking treatment. There is no clear dividing line between physical properties and physico-chemical properties. However, physical properties may be thought of as measures of the bulk behavior of milk and of how milk interacts with energy, while physico-chemical properties are measures of how bulk behavior and energy interactions depend on milk’s constituent colloidal particles, molecules, atoms, and ions. Knowledge of physical properties is of importance particularly in the technological and engineering design and control of milk processes and processing equipment. Knowledge of physico-chemical properties provides a basis for the design of modern methods of milk analysis, determination of milk microstructures, and elucidation of the complex chemical reactions that occur in milk. In this article, recognizably physical properties, such as rheological properties, density, and thermal properties, are discussed first. Then, properties that fall within the realms of both physics and physical chemistry are described: surface tension, acoustic properties, electrical and dielectric properties, and optical properties. Finally, recognizably physico-chemical properties – the colligative properties, and acid–base and oxidation–reduction equilibria – are discussed.
Rheological Properties The rheological behavior of milk is in accord with that of emulsions and suspensions in general. Milk may exhibit Newtonian or non-Newtonian behavior depending on composition, prior treatment, and measurement conditions (especially shear rate and temperature). At moderate to high shear rates, Newtonian behavior is exhibited by skim milk, by whole milk at temperatures >40 C (milk fat completely molten, no cold agglutination), and by whole milk at temperatures <40 C when cold agglutination is absent.
Non-Newtonian behavior manifests itself in raw whole milk under conditions that favor cold agglutination (temperatures <40 C) and at low shear rates. Shear thinning is the predominant rheological behavior. Skim milk shows shear-thinning behavior at low shear rates and at temperatures <30 C. As milk is concentrated by heat evaporation or by membrane processes, viscosity increases, shear thinning becomes more pronounced, and deviation from Newtonian behavior persists to higher shear rates. Thixotropy (time-dependent shear thinning) appears at a sufficiently high concentration, or after a sufficiently long storage time (at concentrations and temperatures above certain minima), during which structure development occurs. Such structure development, and the consequent steady viscosity increase, is known as age thickening. Viscosity of milk is greatly influenced by the concentration and state of the fat and casein, and thus on factors that affect these. Such factors include temperature, and technological treatments such as homogenization, heat treatment, renneting, and acidification. A full discussion of the rheological properties of milk may be found in the article Rheology of Liquid and Semi-Solid Milk Products.
Density and Specific Gravity (Relative Density) The density (kg m3) of milk is identified for a given measurement temperature as, for example, 20, where the superscript is the temperature in C. Specific gravity (SG), defined as milk/water, is identified in a similar way, 20 for example, SG20 20 or SG4 , where the superscript is the temperature at which the milk density was measured, and the subscript the temperature at which the density of water was determined. Density and specific gravity (more properly called ‘relative density’) are related by the equation 1 1 ¼ SG12 water
ð1Þ
where is the temperature ( C) and, usually, 1 ¼ 2. 20 of whole milk is about 1030 kg m3 and usually ranges from 1027 to 1033 kg m3 depending mainly on fat content. SG15:5 15:5 ranges from 1.030 to 1.035 for mixed-herd milk, and a commonly quoted average
467
468 Milk | Physical and Physico-Chemical Properties of Milk
value is 1.032. Inter-breed variations in density and specific gravity are small. The density and specific gravity of milk depend on composition, temperature, and, in the melting point range of the milk triglycerides (–40 to þ40 C), thermal history; thermal history determines the ratio of liquid fat (lower density) to solid fat (higher density). Other factors, such as the stage of lactation and nutritional status of the cow, are important only insofar as they affect composition. Density data are needed for converting mass to volume and vice versa, and for calculating the values of physical properties such as kinematic viscosity and thermal diffusivity. The density of milk may be predicted, if the milk’s proximate composition is known, by using the equation 1 ¼
Xxi
ð2Þ
i
where xi and i are the mass fraction and density, respectively, of the ith component; (xi) ¼ 1 for the non-gaseous components. One of the non-gaseous components will be ice if the temperature is below the (initial) freezing point of the milk. The value of 20 of milk can be calculated using the values of component densities given in Table 1. The value of 918 kg m3 for milk fat given in the table assumes that the fat is a supercooled liquid, but allows for the higher density of the milk fat globule membrane. If milk contains dispersed gas, such as air, the actual density will be lower than that predicted by eqn [2]: actual ¼ ð1 – "a Þ predicted
ð3Þ
where "a is the volume fraction occupied by dispersed gas, which is assumed to have zero mass. is the temperature of measurement or prediction. Dispersed gas considerably lowers density, which then becomes pressure dependent. There have been many attempts to develop empirical equations relating milk density to fat content and temperature, the two most important determining variables. One such equation is as follows: ¼ ð – 2:307 10 – 3 2 Þ – ð0:2655Þ þ 1040:51 – ½F ð – 4:78 10 – 5 2 þ 9:69 10 – 3 þ 0:967Þ kg m – 3
where is the temperature ( C) and F is the % fat (w/w). Equation [4] is valid for milk and cream with fat contents in the range 0–15% (w/w), at temperature in the range 65–140 C. The temperature dependence of milk’s specific gravity is very slight, which is the principal advantage of expressing density in this way. Processing operations such as homogenization, pasteurization, and sterilization have negligible effects on milk density.
Thermal Properties Specific Heat Capacity and Enthalpy The specific heat capacity of milk determines the quantity of thermal energy that has to be added to or removed from milk to effect a given temperature change according to the following equation: q ¼ h ¼
Z2
cðÞ d ðJkg – 1 Þ
ð5Þ
1
where q is the quantity of heat energy per kg (J kg1), h is the change in milk enthalpy (J kg1), is the temperature ( C), ð2 – 1 Þ is the temperature change (1 to 2 or 2 to 1 ), and c ðÞ is the specific heat capacity (J kg1 K1) expressed as some function of temperature. c ðÞ is the specific heat capacity at constant pressure, rather than at constant volume. As milk is a liquid, the two can be considered equal, except perhaps under the conditions used in high-pressure processing. The equality of q and h is valid under isobaric conditions and in the absence of phase transitions, chemical reactions, changes in composition, and forms of work other than displacement. Equation [5] is valid for temperatures >40 C, the upper end of the milk fat melting point range. At temperatures between the (initial) freezing point of milk and 40 C, sensible heat demands are confounded with the latent heat demands caused by phase changes in the milk fat, and eqn [5] must be written as
ð4Þ h ¼
Z2
capp ðÞd
ð6Þ
1
Table 1 Density of milk components at 20 C Milk component
r20 (kg m3)
Water Fat Protein Lactose Residual components
998.2 918 1400 1780 1850
From Walstra P and Jenness R (1984) Dairy Chemistry and Physics. New York: Wiley.
where capp() is the apparent specific heat capacity (J kg1) expressed as some function of temperature. capp() depends on fat content, triacylglycerol composition, and thermal history. There is a maximum (4000 J kg1 K1) in the temperature range 15–20 C and a minimum (3880 J kg1 K1) at about 40 C. At temperatures away from the maximum, specific heat capacity is inversely related to fat content. At temperatures above 40 C, where the milk fat is completely molten and there are no phase changes, specific heat
Milk | Physical and Physico-Chemical Properties of Milk
capacity increases gradually with temperature, reaching 3940 J kg1 K1 at 100 C and 4000 J kg1 K1 at 140 C. The specific heat capacity of skim milk, which includes no significant latent heat effects due to phase changes in milk fat, increases essentially linearly but slowly with temperature over a wide range. Representative values are 3899 and 3988 J kg1 K1 at 0 and 50 C, respectively. For skim milk, and for whole milk with 4% fat, specific heat capacity may be predicted as a function of temperature (at temperatures above the milk fat melting point range) by the following equations: Skim milk at 52 143
–1
–1
C : c ¼ 2:814 þ 3942 ðJ kg K Þ ð7Þ
Whole milk at 53 153 C : c ¼ 2:976 þ 3692 ðJ kg – 1 K – 1 Þ ð8Þ
The ability to predict the enthalpy change between two chosen temperatures is, from a technological or engineering point of view, more useful than the ability to predict specific heat capacity at specific temperatures. The following general expression is valid for any temperature range, any fat content, and any total solids content: h1 $ 2 ¼ hfat xfat þ hnonfat xnonfat
ð9Þ
1
where hfat is the enthalpy change (J kg ) in milk fat between 1 and 2, hnonfat is the enthalpy change in the non-fat portion of the product between 1 and 2, xfat is the fraction of milk fat in the product, and xnon-fat is the mass fraction of the nonfat portion. hfat must be found from a suitable set of published empirical data. hnon-fat can be predicted from hnonfat ¼ hmilk plasma ¼
Z2 X ðci xi Þ d ¼
1 X ðci xi Þð1 – 2 Þ
ð10Þ
where ci is the specific heat of the ith component, xi is the mass fraction of the ith component, and (cixi) is the specific heat of milk plasma. Suitable values of ci for water, lactose, protein, and ash are 4200, 1400, 1600, and 800 J kg1 K1, respectively. The slight temperature dependence of the specific heat capacity of these non-fat components may usually be ignored for practical purposes, as indicated by eqn [10]. When milk is heat-concentrated, the enthalpy demand is almost wholly the latent heat of evaporation of water (hfg) that must be supplied. This demand can be expressed as kilograms of water evaporated per kilogram of unconcentrated milk hfg (J kg1), where hfg is read from steam tables at the pressure at which evaporation occurs. (There is an additional, though
469
relatively small, sensible heat demand, as milk boiling point increases during concentration, but this demand is moderated by a concomitant decrease in specific heat capacity.) In calculating enthalpy changes over a temperature range that straddles or lies below the initial freezing point of milk, it is necessary to account for latent heat effects due to phase change in the water substance (water or ice) as well as in the milk fat. There are ways of doing this, but milk is rarely frozen.
Thermal Conductivity and Thermal Diffusivity The thermal conductivity of skim milk, whole milk, and cream increases slowly with increasing temperature. It decreases with increasing %TS or increasing fat content, the effects being generally greater at higher temperatures. The following semi-empirical relationship, although developed specifically for creams of fat content 20% (w/w), is accurate to within 10% for milk and cream with a fat content in the range 0.1–42% (w/w), and for the temperature range 5–75 C: l ¼ ð0:5279 þ 2:13 10 – 3 – 7:32 10 – 6 2 Þ ½1 – ð0:843 þ 1:9 10 – 3 Þ fat ðW m – 1 K – 1 Þ
ð11Þ
where l is the thermal conductivity (W m1 K1), fat is the fat volume fraction, and is the temperature ( C). Representative values of thermal conductivity at 20 C calculated using eqn [11] are compared with the thermal conductivity of water in Table 2. The thermal conductivity of whole milk heat concentrates may be predicted using the following equation: l ¼ ð0:59 þ 0:001 2Þ ð1 – 0:007 8TSÞ ðW m – 1 K – 1 Þ
ð12Þ
The equation is valid for the temperature range 40 < < 90 C and the %TS range 37 < TS < 72%; it is accurate to 0.88%. The thermal diffusivity of milk may be calculated using the equation: ¼
l c
ðm2 s – 1 Þ
ð13Þ
Table 2 Representative values of the thermal conductivity of fluid milk products compared with the thermal conductivity of water, at 20 C Fluid
Thermal conductivity (W m1 K1)
Water Skim milk (0.1% fat) Whole milk (3.9% fat) Cream (42% fat)
0.603 0.568 0.548 0.357
From Fernandez-Martin F and Montes F (1972) Milchwissenschaft 27: 772–776.
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where is the thermal diffusivity (m2 s1), is the density (kg m3), and c is the specific heat capacity (J kg1 K1). l, , and c can be predicted as described above, and , then, can be calculated. For example, at 20 C, l 0.548 W m1 K1, 1030 kg m3, and c 3980 J kg1 K1, giving a value for of 1.34 107 m2 s1.
Surface Tension The surface tension of milk lies in the range 40–60 mN m1 (average: 52 mN m1) at 20 C. Comparable values for some milk fractions are 72.8 (water), 51–52 (rennet whey), 52–52.5 (skim milk), 42–45 (25% fat cream), and 39–40 (sweet-cream buttermilk). Surface tension decreases with increasing temperature. For whole milk, the relationship is ¼ 1:8 10 – 4 2 – 0:163 þ 55:6
ð14Þ
1
where is the surface tension (mN m ) and is the temperature ( C). Surface tension is influenced by fat content, homogenization, and temperature history. It decreases with increasing fat content up to 4%, but no further decrease occurs at higher fat contents. Homogenization of pasteurized milk increases surface tension. Homogenization of raw milk, however, can lead to a decrease in surface tension owing to the release of free fatty acids by lipase activity. The surface tension of milk held at 5 C and brought to 20 C is lower than that of milk cooled to 20 C when measured immediately. Heat treatment of milk at sterilization temperatures can cause a small increase in surface tension, probably the result of denaturation of whey proteins, a change that reduces their surface activity.
Acoustic Properties Acoustics is the science of sound (mechanical vibrations at frequencies in the range 1.6 102 to 20 kHz, which are detectable by the human ear), infrasound (frequencies of <1.6 102 kHz), and ultrasound (frequencies of >20 kHz). Only low-power ultrasound (which involves power levels <1 W cm2) is of significance in dairy science and technology. It is used principally as an analytical tool for indirectly measuring food characteristics and as an in-line method for measuring flow rate. The ultrasonic properties of a material most frequently measured are the ultrasonic velocity (m s1), the attenuation coefficient (Np m1), and the acoustic impedance
(kg m2 s1). These depend on other physical properties of the material. The ultrasonic velocity (the distance traveled by an ultrasonic wave in unit time) is related to the elastic modulus, E, and density, : k ¼ ! E
ð15Þ
Here, ! is the angular frequency (rad s1) and k is the complex wave number ¼ (!/c) þ i, where c is the ultra1 sonic velocity (m sp ), is the attenuation coefficient ffiffiffiffiffiffiffiffi 1 (Np m ), and i ¼ – 1: For low-attenuating materials (i.e., << !/c), eqn [15] can be written as 1 ¼ c2 E
ð16Þ
where is the density (kg m3) and E is the modulus of elasticity (Pa). In the case of milk, E is the bulk modulus, as liquids are normally subjected to a compressive (as opposed to a shearing) ultrasonic wave. The attenuation coefficient, , is a measure of the decrease in the amplitude of an ultrasound wave as it travels through the material. It is given by the equation A ¼ A0 e – x
ð17Þ
where A0 is the initial amplitude of the wave and A is the amplitude after the wave has traveled a distance x through the material. Attenuation results from absorption and scattering. The acoustic impedance is a measure of the fraction of an ultrasonic wave reflected from a material’s surface. The (complex) specific acoustic impedance, Z, is defined as Z ¼
! k
ð18Þ
where Z ¼ RZ þ iXZ, with RZ being the resistive (real) part of the complex impedance and XZ the reactive (imaginary) part of the complex impedance. For low-attenuating materials (i.e., << !/c), eqn [18] can be written as Z ¼ RZ ¼ c
ð19Þ
Values of the three ultrasonic properties of skim milk (at 1 mHz and 28 C) are as follows: velocity, c ¼ 1522 m s1, attenuation coefficient, ¼ 23 Np m1, and impedance, Z ¼ 1.5 106 kg m2 s1. Ultrasonic properties, which are frequency and temperature dependent, are most commonly measured using the pulse-echo technique. Enhanced information about the characteristics of the sample can be gained by carrying out measurements over a range of frequencies and also a range of temperatures.
Milk | Physical and Physico-Chemical Properties of Milk
The ultrasonic properties of milk are fundamental properties, but they are not of interest by themselves. Their measurement is useful only insofar as it is possible to establish relationships between them and other physico-chemical characteristics such as composition, structure, and state – characteristics that determine how ultrasound interacts with the sample. Such relationships can be developed empirically by means of calibration experiments, or theoretically. Ultrasound has been used to measure the composition of milk in terms of fat and solids-not-fat, the particle size distributions of milk fat globules and casein micelles, and the rate of coagulation of milk by chymosin. Ultrasonic imaging has been used to measure teat milk flow rate, and to non-invasively monitor the microbial spoilage of packaged UHT milk. The measurement of creaming profiles, the principle of which is the measurement of the ultrasound velocity and/or attenuation coefficient as a function of sample height and time, has obvious potential for milk and other liquid dairy products. Apart from being non-invasive and non-destructive, ultrasound can be used to analyze opaque as well as concentrated systems, and is inexpensive, rapid, and accurate.
Electrical and Dielectric Properties Electrical Conductivity Electrical conductivity (EC), , is a measure of a material’s ability to carry an electrical current. It ranges in value from 1018 to 107 S m1 (Siemen per meter), depending on the material. The EC of normal whole milk is about 0.460 S m1. EC is most easily measured by applying a known DC voltage across a pair of parallel electrodes immersed in the sample, measuring the current produced, and calculating the resistance of the specimen (the volume bounded by the electrodes): ¼
1l l ¼ G ðS m – 1 Þ RA A
ð20Þ
where R is the resistance ( ), G the conductance (S), l the distance between the electrodes (m), and A the electrode area (m2). Equation [20] shows that EC and electrical conductance (the reciprocal of resistance) are related via the dimensions of the specimen. EC is generally measured in practice by impedance (or, admittance) spectroscopy, in which an AC rather than a DC voltage is applied to the sample. Impedance and admittance (the reciprocal of impedance) are complex properties, the real parts of which are, respectively, resistance and conductance. Measurements are best carried out at frequencies >10 kHz; at and above this frequency the
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measured value is a property of the bulk milk and not of the milk–electrode interface. The EC of milk is determined mainly by the charged species present, particularly the salts. There is very little contribution from lactose; casein, also, makes a much smaller contribution than do the milk salts. The main effect of milk proteins in general is to hinder the migration of ions and thus depress EC. However, the release of calcium ions from the casein micelles as a result of a decrease in pH, caused by either deliberate acidification or bacterial growth, results in an increase in EC. A drop in milk pH to about 5 causes all of the colloidal calcium phosphate to dissolve, and the equilibria of milk buffer systems to change, resulting in saturation of the EC to a constant maximum value. This phenomenon is the basis of the automatic monitoring of the growth of lactic acid bacteria by conductimetric methods. Mastitis in a quarter of a cow’s udder results in decreases in the concentrations of lactose and Kþ in the milk secreted, and corresponding increases in the concentrations of Naþ and Cl that preserve the milk’s isoosmolality with the cow’s blood. The net effect is an increase in the milk’s EC. This phenomenon has led to much research over the last 60 years aimed at finding a reliable way of using in-line EC measurement at milking to detect both subclinical and clinical mastitis in the quarters of individual cows. Although the EC of milk from individual quarters can be monitored easily and accurately, achieving this aim has been hampered by the fact that variation in EC depends not only on the level of infection, but also on numerous other factors such as breed, parity, estrus, lactation stage, presence of other diseases, milking interval, time of day, and milk composition. In 1998, an extensive analysis of published data carried out by the International Dairy Federation concluded that EC measurement could not identify mastitic quarters or mastitic cows, nor detect subclinical mastitis, with sufficient accuracy to be useful. Currently, most automatic milking systems and some manual systems incorporate sensors for measuring the EC of quarter milk and software for processing the data generated. The development of sophisticated statistical modeling of the data, which involves comparisons between the quarters of the individual cow over successive milkings, has led to an improvement in the sensitivity of detection of subclinical and clinical mastitis. In the case of automatic milking systems, the farmer is dependent on EC measurement for detecting mastitic cows. The EC of fresh milk and cream decreases with increasing fat content because the fat globules (themselves nonconducting) occupy volume that would otherwise be filled with the conducting aqueous phase of the product, thus impeding the mobility of the conducting ions and increasing the distance that migrating ions have to travel. For a fat content in the range
472 Milk | Physical and Physico-Chemical Properties of Milk
0.15–51% (w/w), the EC of milks and creams is related to the volume fraction of fat, fat, as follows: ¼ skim ð1 – fat Þ ð1 þ q 2fat Þ
ð21Þ
where ¼ 1.56 0.04, and q varies between 3.0 and 3.5, depending on the batch of milk. Measurement of the admittance of milk has the potential to allow estimation of milk fat content if milk water content is known, and vice versa. The latter utility of the measurement could provide a means of detecting adulteration of milk with water. The EC of stored whole milk reaches a higher saturation value than that of stored skim milk, because for whole milk the EC-depressing effect of the presence of fat is more than compensated for by the production of free fatty acids and the release of phosphate ions from the milk fat globule membrane. The EC of milk increases markedly with temperature, as illustrated by the following empirical relationship for buffalo milk, valid for the temperature range 5–70 C: ¼ 1:71 10 – 1 þ 6:32 10 – 3 þ 9:01 10 – 6 2 ðS m – 1 Þ ð22Þ
The EC and the viscosity of milk have been shown to be related. This relationship is thought to be due to the fact that the ion content of milk affects both the EC and the conformation of milk proteins, the latter influencing viscosity.
"9ð!Þ ¼ "91 þ "0ð!Þ ¼
"9S – "91 1 þ !2 2
ð"9S – "91 Þ ð!t Þ þ 1 þ !2 2 !"0
ð24Þ ð25Þ
where "91 is the real permittivity at very high frequencies, "9S is the real static (low frequency) permittivity, ¼ 1=2 fR , where fR is the relaxation frequency, the electrical conductivity, and "0 the permittivity of free space (¼ 8.854 1012 F m1). Modeling shows that the complex permittivity of milk is essentially that of water, with perturbations caused by the ionic and nonionic milk components. Analysis of the spectral data relating to permittivity ("9S , "91 , and ) and those relating to loss factor (ð"9S – "91 Þ, , and ) shows that the perturbations are sensitive to the presence of fat, carbohydrate, protein, and ionic species. For example, permittivity is depressed by the nonionic components fat, lactose, and casein. Measurement of dielectric property spectra could potentially be useful in monitoring the gross composition of large quantities of milk in real time.
Optical Properties
Dielectric Properties The dielectric properties of a material, the permittivity ("9) and the dielectric loss factor ("0), are the real and imaginary parts, respectively, of the complex permittivity ("): "ð!Þ ¼ "9 ð!Þ – j"0ð!Þ
increasing temperature, whereas the loss factor is almost temperature-independent. The dielectric property spectra of whole milks of varying total solids content can be modeled using the following theoretical equations:
ð23Þ
pffiffiffiffiffiffiffi where ! is the frequency (Hz) and j ¼ – 1. "9is a measure of the ability of the material to store electromagnetic energy. "0 is a measure of the material’s ability to dissipate electromagnetic energy as heat. The latter phenomenon is exploited in microwave and radio frequency heating. Permittivity and loss factor are frequency and temperature dependent. Representative values of "9 and "0 for whole milk (3.25% fat) at 20 C and 2.45 GHz (the frequency most commonly used for microwave heating) are 67.9 and 17.6, respectively, relative to the values for free space. Corresponding values for water are 80.2 and 13.4. The permittivity at 20 C of skim milk, low-fat milk, and whole milk decreases with increasing frequency in the range 1–20 GHz. The loss factor, on the other hand, exhibits a net increase with frequency over this range, but goes through a minimum near the lower end and a maximum near the higher end. At a given frequency, the permittivity of whole milk decreases slowly with
The term ‘optical properties’ comprises properties with respect to electromagnetic radiation not only in the visible region of the spectrum (380–760 nm), but also in the infrared (IR, 760 nm to 1 mm) and ultraviolet (UV, 5–380 nm) regions that lie on either side of it. Visible, IR, or UV light incident on milk is absorbed, absorbed and reemitted (producing fluorescence), scattered, or transmitted, depending on wavelength. Milk, as a complex colloidal dispersion of fat globules, casein micelles, and whey proteins in an aqueous solution containing a number of solutes, not only absorbs light at several wavelengths but also scatters light, as well as transmitting it. In the visible region, riboflavin in milk absorbs strongly near 470 nm (giving the yellow-green color of whey) and emits fluorescent radiation with a maximum at 530 nm. The -carotene in milk fat absorbs near 460 nm, which is responsible for the yellow color of the fat. In the UV region, aromatic amino acid residues of proteins (tyrosine and tryptophan) absorb strongly near 280 nm, and a part of the UV radiation is emitted as fluorescence at 340 nm. Measurement of the intensity of this fluorescence has been used to quantify the protein
Milk | Physical and Physico-Chemical Properties of Milk
content of milk. The double bonds of the milk fat absorb very strongly near 220 nm. In the IR region, absorption is primarily by the amide (II) groups (CONH) of proteins at 6465 nm, the hydroxyl groups (OH) of lactose at 9610 nm, and the ester carbonyl groups (C¼O) of lipids at 5723 nm. This is the basis for the instrumental compositional analysis of milk using infrared analyzers. Milk samples are first homogenized to reduce the size of fat globules to <1 mm, to prevent their presence interfering with the measurement. Both fat globules and casein micelles scatter light. It is possible to measure the intensities of both the scattered light and the light transmitted by the sample. Both measurements form the basis of the determination of the fat content of milk and of the size distributions of fat globules and casein micelles. Instruments for fat determination are based on measurement of turbidity, that is, the attenuation of the incident beam, usually expressed as optical density or absorbance. The surface light scattering (diffuse reflection) and absorption properties of milk strongly affect the visual appearance of milk. The creamy color of whole milk is due to the -carotene in the fat. Casein micelles scatter blue light (shorter wavelength) more effectively than they scatter red (longer wavelength), giving skim milk its bluish color. Homogenization of whole milk makes milk whiter by increasing the diffuse reflection (e.g., by some 19% at 550 nm). Heating has the same effect initially, but severe heating causes nonenzymic browning. The penetration of light into milk can be important with respect to light-induced reactions. At 580 nm, light incident on whole milk loses 90 and 99% of its intensity at penetration depths of 8 and 24 mm, respectively. The refractive index of milk varies with temperature and wavelength. The value for bovine milk at 589.3 nm (the D line of the sodium spectrum) at 20 C, n20 D , lies in the range 1.344 0–1.348 5. This may be compared with the value of 1.333 0 for water. The difference (n) between the values of n20 D for milk and water reflects the presence of dissolved substances (lactose, minerals, etc.) and colloidal substances (casein micelles and whey proteins): n ¼ ðmr Þ
ð26Þ
where is the density of the aqueous part of milk (kg m3), and m and r are, respectively, the mass fractions and specific refractive increments (m3 kg1) of the individual substances. Values of r for the main determinants of n are 2.07 104 (casein micelles; m3 kg1 of dry casein), 1.87 104 (whey proteins), 1.40 104 (lactose), and 1.70 104 (other dissolved substances). Fat globules and air bubbles do not contribute to the refractive index of milk.
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Colligative Properties: Freezing Point, Boiling Point, and Osmotic Pressure The part of milk comprising water and low molecular weight solutes obeys Raoult’s law approximately. This law in one form states that the relative lowering of the solvent vapor pressure resulting from the presence of a solute is equal to the mole fraction of the solute in the solution. Consequences of the lowering of vapor pressure (the equilibrium relative humidity of milk at ambient temperature is 99.3%) are a depression of freezing point (f ) and an elevation of boiling point (b ). In addition, the presence of the solute gives rise to an osmotic pressure. For very dilute solutions f ¼ Kf M
ð27Þ
b ¼ Kb M
ð28Þ
and
where Kf and Kb are the cryoscopic constant and ebullioscopic constant, respectively, and M is the molality of the solution. The freezing point of milk is less than 0 C, and the boiling point higher than 100 C (at atmospheric pressure). Equations [27] and [28] can be used to roughly calculate the freezing point depression and boiling point elevation of milk as functions of the concentrations of water-soluble milk components. Lactose, chloride salts, and other components (calcium, potassium, magnesium, lactate, phosphate, citrate, etc.) contribute about 55, 25, and 20%, respectively, to the freezing point depression. The freezing point of the vast majority of individual milks lies in the range 0.512 to 0.550 C, and few fall outside the range 0.520 to 0.512 C. The constancy of the freezing point depression is a reflection of the constant osmolality of milk. Although the concentrations of individual water-soluble components can vary, the total molality of fully dissociated species remains fairly constant. As the milk secretion process dictates that the osmotic pressure of milk be kept equal to that of blood (687 kPa), a constant osmolality is maintained in milk by the passage of blood constituents into the mammary gland; any change in the concentration of lactose in milk is compensated for by changes in the concentrations of sodium and chloride. Milk with a freezing point of 0.53 C has an osmolality of 0.285 osmol kg1 water. The determination of freezing point is extensively used to assess whether or not milk has been adulterated by the addition of water, and to quantify the amount added. Milk with a freezing point 0.525 C is usually assumed to be unadulterated.
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Acid–Base Equilibria pH of Milk The pH of bovine milk at 25 C usually lies in the range 6.5–6.7, with 6.6 being the most common value. The pH decreases with increasing temperature. This implies temperature-induced changes in milk’s complex buffering system rather than an increase in milk’s acidity. At a given temperature, differences in pH and buffering capacity between individual lots of fresh milk reflect compositional variation. The pH of colostrum can be as low as 6.0 and that of mastitic and endof-lactation milks as high as 7.5. High pH can be due to increases in [Naþ] and [Cl] (and possibly in the concentrations of other ions), a reduction in the lactose content, and a reduction in the concentration of soluble inorganic P – changes that alter buffering capacity in this pH range.
dB ¼ dpH ðvolume of acidor basesolution addedÞ ðnormality of solutionÞ ðaveragevolume of sampleÞ ðpH change producedÞ ð29Þ
The resulting value of dB/dpH is assigned to the pH at the mid-point of the pH change that has occurred. Buffering action is due to the presence in milk of acid buffers (weak acid–conjugate base pairs) and base buffers (weak base–conjugate acid pairs). Milk contains many acidic and alkaline groups that result in buffering action over a wide pH range. The main groups are listed in Table 3. The principal buffer components in milk are soluble phosphate, colloidal calcium phosphate (CCP), citrate, bicarbonate, and casein. The relationship between pH and pKa (the negative logarithm of the acidity constant Ka) for the titration of a weak acid against a strong base is given by the Henderson–Hasselbalch equation: pH pKa þ log
Buffering Constitutents of Milk Milk, because of its buffering system, resists change in pH when it is titrated against a strong acid or a strong base. The extent of resistance, that is, the buffering action, at a given pH is called the ‘buffering index’. The buffering index, dB/dpH, is the derivative (slope) of the titration curve (the plot of moles of strong acid or strong base added to milk vs. pH). It is calculated as follows:
½A – ½HA
ð30Þ
Maximum buffering occurs at pH ¼ pKa. In the case of a weak base–conjugate acid buffer, maximum buffering action likewise exists when pH ¼ pKa (¼ 14 pKb). Kb is the basicity constant and pKb is its negative logarithm. In some cases several values are given for pKa in Table 3; values for many milk constituents are uncertain because of the complexity of the overall system.
Table 3 Principal buffering groups in milk Group
Approximate concentration (mmol l1)
Expected pKa
pKa (in milk)
Salts Inorganic phosphate Citrate Organic phosphate esters Carbonate Lactic acid Formic acid Acetic acid Various amines
21.0 9.0–9.2 2.5–3.5 2.0 <0.4 0.2–1.8 0.05–0.8 1.5
2.1, 7.2, 12.3 3.1, 4.7, 5.4 1.4, 6.6 6.4, 10.1 3.9 3.6 4.7 7.6
3, 5.8, 6.6 3, 4.1, 4.8 1.7, 5.9 6.4, 10.1 3.9 3.6 4.8 7.6
Protein-bound residues Aspartic acid Glutamic acid Histidine Tyrosine Lysine Phosphoserine N-Acetylneuraminic acid Terminal carboxyl Terminal amino
Titratable group -COOH -COOH Imidazole Phenol -NHþ 3 Phosphate COOH -COOH -NHþ 3
Expected pKa 4.6 4.6 6.1 9.7 10.4 1.5, 6.5 2.6 3.6 7.9
pKa (in milk) 4.1 4.6 6.5 10.5 2, 6 5.0 3.7 7.9
From McCarthy OJ and Singh H (2009) Physico-chemical properties of milk. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 691–758. New York: Springer.
Milk | Physical and Physico-Chemical Properties of Milk
The shape of a titration curve, and consequently the relationship between buffering index and pH, depends on the experimental methodology used; titration and backtitration curves of milk do not coincide (Figures 1 and 2). When milk is acidified (Figure 1), maximum buffering (a maximum in dB/dpH) occurs at about pH 5.1, but when acidified milk is back-titrated with a base, a low extent of buffering exists at pH 5.1 and a maximum at pH 6.3. The acid part of the titration curve is important because milk is acidified in the manufacture of products such as yogurt. When milk is titrated to pH 11.0 (Figure 2), buffering action is relatively slight at pH 8–9 but increases at higher pH values. There is little difference between the curves for titration with alkali and back-titration with acid. On back-titration, a buffering peak is not observed at pH 6.3 (cf. Figure 1). Although there is a peak at about pH 5.1, it is weaker and less distinct than the peak obtained when normal milk is first acidified (Figure 1). The maximum at pH 5.1 on acidification is due to dissolution of CCP and the consequent formation of HPO24 – and H2 PO4– . On back-titration, buffering action is low at this pH because the CCP is already solubilized. The maximum at pH 6.3 is due to the formation of calcium phosphate, resulting in the release of Hþ (from HPO24 – and H2 PO4– ), which can combine with OH. The buffering action of milk at high pH values is probably due to lysine residues and carbonate. When milk is titrated to high pH, all of the calcium phosphate precipitates. The precipitate dissolves again on subsequent acidification, resulting in buffering action over a wide pH range. Colostrum has a much higher buffering capacity than that of normal milk over the pH range 6.6–3.0. The buffering peak at pH 5.1 for mastitic milk is slightly higher than that for normal milk.
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Figure 2 Buffering curves of milk titrated from the initial pH (6.6) to pH 11.0 with 0.5 M NaOH (&) and then back-titrated to pH 3.0 with 0.5 M HCl (). Data supplied by J. A. Lucey, Department of Food Science, University of Wisconsin–Madison.
Titratable Acidity of Milk The alkaline range of the titration curve is important because of the widespread use of titratable acidity to characterize milk. The titratable acidity is the buffering capacity of milk between its own pH (6.6) and pH 8.3 (the phenolphthalein end point). The measurement of titratable acidity (usually expressed, somewhat arbitrarily, as percentage lactic acid) is useful for determining the freshness of milk and for controlling the manufacture of fermented dairy products. The titratable acidity of fresh milk seldom falls outside the range 0.14–0.16%.
Effects of Milk Treatment on Acid–base Equilibria Heating
Heat treating milk (e.g., by holding at 100 C for 10 min) results in an increase in buffering action at pH 5.0 during acid titration. This is probably caused by an increase in the concentration of CCP owing to the formation of heat-precipitated calcium phosphate. More severe heat treatment causes a shift of the peak from pH 5.0 to pH 4.4, and the buffering action in the pH range 5.0–4.0 is much stronger than that of unheated or less severely heated milk. The shift in the pH of the peak may be due to a change in the structure and composition of CCP during the severe heat treatment.
Freezing Figure 1 Buffering curves of milk titrated from the initial pH (6.6) to pH 3.0 with 0.1 M HCl () and then back-titrated to pH 11.0 with 0.5 M NaOH (&). Data supplied by J. A. Lucey, Department of Food Science, University of Wisconsin–Madison.
The pH of milk decreases to as low as 5.8 during slow freezing, probably owing to the precipitation of calcium phosphate and the consequent release of Hþ in the unfrozen phase as this phase becomes increasingly concentrated.
476 Milk | Physical and Physico-Chemical Properties of Milk
Little change occurs on rapid freezing, possibly owing to insufficient time available for precipitation to occur. Dilution and concentration
Concentration of milk lowers milk pH owing to precipitation of calcium phosphate; dilution has the opposite effect. During the ultrafiltration concentration of milk, the buffering capacity of the retentate increases steadily owing to the increasing concentrations of casein, whey proteins, and milk salts.
Oxidation–Reduction Equilibria Oxidation and reduction are, respectively, the loss and gain of electrons. The potential of a system to transfer electrons, that is, the oxidation–reduction or redox potential (Eh), is measured relative to the hydrogen electrode, and expressed in volts. For a simple binary oxidation– reduction system, Eh is related to the concentrations of the oxidized and reduced forms of the substance involved by the Nernst equation: Eh ¼ E0 þ
RT ½Ox ln nF ½Red
ð31Þ
where E0 is the standard redox potential (V) (i.e., the potential when both the oxidized and reduced forms are at unit activity); [Ox] and [Red] are the activities of the oxidized and reduced forms, respectively; n is the number of electrons transferred per molecule; R is the gas constant (8.314 J K1 mol1); T is the absolute temperature (K); and F is the Faraday constant (96.5 kJ V1 mol1). Systems with a positive value of Eh are oxidizing systems, whereas those with a negative value are reducing ones. At 25 C and for a one-electron transfer, eqn [23] becomes Eh ¼ E0 þ 0:059log
½Ox ½Red
ð32Þ
In many biological systems, Hþ are involved in the overall oxidation reaction. In this case, again, for a oneelectron transfer, Eh ¼ E0 þ 0:059log
information is available on the considerable poising capacity of milk, because of measurement difficulties. These difficulties are the result of sluggishness of some oxidation–reduction systems in milk in coming to equilibrium (redox potentials pertain to equilibrium conditions), incomplete reversibility of some systems, and back- diffusion of oxygen during measurement. O2, ascorbate, and riboflavin are the principal systems determining the Eh of milk. The thiol–disulfide system contributes to the Eh of heated milk. All the ascorbate in freshly drawn milk is in the reduced form, but reversible oxidation to dehydroascorbate occurs at a rate dependent on the concentrations of Cu2þ, Fe3þ, and O2; the Eh values of all three of these are higher than that of ascorbate. Preservation of ascorbate depends on deaeration and prevention of contamination by copper. Oxidation–reduction reactions in milk are influenced by heat treatment, bacterial activity, and exposure to light, as well as by O2 and the presence of metal ions. Heating lowers the Eh of milk, the more so if high temperature–short time conditions are used and prior deaeration carried out; the result is better retention of reducing substances such as ascorbic acid. Bacterial activity reduces the Eh by consumption of available oxygen in the milk. The decrease in potential can lead to the reduction and loss of color of certain added dyes, and is the basis of the methylene blue test for the bacterial status of fresh milk. The riboflavin in milk does not contribute significantly to Eh or to poising. However, the absorption of visible light by riboflavin (at 470 nm) results in excitation. Excited-state riboflavin can oxidize a number of compounds in milk, thereby itself becoming reduced. This is an example of photooxidation, and it results in the production of off-flavors in milk exposed to sufficiently intense visible light, for example, direct sunlight.
½Ox – 0:059pH ½Red
ð33Þ
An oxidation system exhibits poising capacity, analogous to buffering capacity, at values of [Ox]/[Red] close to unity, that is, at Eh values close to the E0 value. The redox potentials of individual milk samples in equilibrium with air fall in the range þ0.25 to þ0.35 V at 25 C at the normal milk pH. The redox potential is inversely related to pH, ranging from about þ0.20 at pH 10 to about þ0.395 at pH 3.5 for raw milk. Little
Conclusions Some of the physical and physico-chemical properties of milk, such as density, thermal properties, freezing point, acid–base equilibria, and oxidation–reduction equilibria, have been well studied and are well understood. Others, such as acoustic properties and dielectric properties, have been studied to a relatively limited extent. This is a reflection of the relative importance, historically, of the different properties with respect to production, analysis, handling, and processing of milk. Milk, a complex biological fluid, is by no means fully understood. There is no doubt that future advances in our understanding of its nature and attributes will depend to a significant extent on the use of measurement techniques whose development will be built upon and will extend
Milk | Physical and Physico-Chemical Properties of Milk
our current knowledge of physical and physico-chemical properties. See also: Analytical Methods: Differential Scanning Calorimetry; Infrared Spectroscopy in Dairy Analysis; Light Scattering Techniques; Physical Methods; Rheological Methods: Instrumentation; Principles and Significance in Assessing Rheological and Textural Properties; Spectroscopy, Overview; Ultrasonic Techniques. Mastitis Therapy and Control: Automated Online Detection of Abnormal Milk. Rheology of Liquid and Semi-Solid Milk Products.
Further Reading Adam M, Celba J, Havlı´cˇek Z, Jeschke J, Kubesˇova´ A, Neumannova´ J, Pokorny´ Z, Sˇesta´k J, and Sˇra´mek P (1994) Thermophysical and Rheological Properties of Foods. Milk, Milk Products and SemiProducts. Prague: Institute of Agricultural and Food Information. Anonymous (1996) Physical Properties of Dairy Products. Hamilton, New Zealand: MAF Quality Management. Fernandez-Martin F and Montes F (1972) Influence of temperature and composition on some physical properties of milk and milk concentrates. III. Thermal conductivity. Milchwissenschaft 27: 772–776. Figura LO and Teixeira AA (2007) Food Physics. Physical Properties – Measurement and Applications. New York: Springer.
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Fox PF and McSweeney PLH (2006) Advanced Dairy Chemistry, 3rd edn. New York: Springer. Jowitt R (ed.) (1983) Physical Properties of Foods, 3rd edn. London: Applied Science. Jowitt R (ed.) (1987) Physical Properties of Foods 2: COST 90bis Final Proceedings. London: Elsevier Applied Science. Lucey JA and Horne DS (2009) Milk salts: Technological significance. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 351–389. New York: Springer. McCarthy OJ and Singh H (2009) Physico-chemical properties of milk. In: McSweeney PLH and Fox PF (eds.) Advanced Dairy Chemistry, Vol. 3: Lactose, Water Salts and Minor Constituents, 3rd edn., pp. 691–758. New York: Springer. Rahman S (1995) Food Properties Handbook. Boca Raton, FL: CRC Press. Rao MA, Rizvi SSH, and Datta AK (2005) Engineering Properties of Foods, 3rd edn. Boca Raton, FL: CRC Press. Riedel L (1955) Kalorimetrische Untersuchungen u¨ber das Schmelzverhalten von Fetten und O¨len [Calorimetric studies on melting of fats and oils]. Fette Seifen Anstrichmittel 57: 771–782. Sahin S and Sumnu SG (2006) Physical Properties of Foods. New York: Springer. Speiss WEL and Schubert H (eds.) (1990) Engineering and Food, Vol. 1: Physical Properties and Process Control. London: Elsevier Applied Science. Urbicain MJ and Lorenzo JE (1997) Thermal and rheological properties of foodstuffs. In: Valentas KJ, Rotstein E, and Singh RP (eds.) Handbook of Food Engineering Practice, pp. 425–486. Boca Raton, FL: CRC Press. Walstra P and Jenness R (1984) Dairy Chemistry and Physics. New York: Wiley.