《乳品生物化学》（英文版） 7 Water in milk and dairy products

7 ater in milk and dairy products 7.1 Introduction he water content of dairy products ranges from around 2.5 to 94%(w/w) Table 7. 1) and is the principal component by weight in most dairy roducts, including milk, cream, ice-cream, yogurt and most cheeses. the moisture content of foods(or more correctly their water activity, section 7.3), together with temperature and ph, are of great importance to food technology. As described in section 7.8, water plays an extremely important role even in relatively low-moisture products such as butter(c. 16% mois- ture)or dehydrated milk powders(c 2.5-4% moisture). Water is the most important diluent in foodstuffs and has an important influence on the physical, chemical and microbiological changes which occur in dairy prod ucts. Water is an important plasticizer of non-fat milk solids 7.2 General properties of water Some physical properties of water are shown in Table 7. 2. Water has higher melting and boiling temperatures, surface tension, dielectric constant, heat capacity, thermal conductivity and heats of phase transition than similar molecules (Table 7.3). Water has a lower density than would be expected from comparison with the above molecules and has the unusual property of expansion on solidification. The thermal conductivity of ice is approxi mately four times greater than that of water at the same temperature and is high compared with other non-metallic solids. Likewise, the thermal dif- fusivity of ice is about nine times greater than that of water The water molecule(HOH) is formed by covalent(o)bonds between two of the four sp bonding orbitals of oxygen(formed by the hybridization of the 2s, 2px, 2p, and 2p, orbitals) and two hydrogen atoms( Figure 7. 1a). The remaining two sp' orbitals of oxygen contain non-bonding electrons. The verall arrangement of the orbitals around the central oxygen atom is trahedral and this shape is almost perfectly retained in the water molecule. Due to electronegativity differences between oxygen and hydrogen, the o-H bond in water is polar(a vapour state dipole moment of 1.84 D). This results in a partial negative charge on the oxygen and a partial positive charge on each hydrogen( Figure 7. 1b). Hydrogen bonding can occur between the two lone electron pairs in the oxygen atom and the hydrogen atoms of other

7 Water in milk and dairy products 7.1 Introduction The water content of dairy products ranges from around 2.5 to 94% (w/w) (Table 7.1) and is the principal component by weight in most dairy products, including milk, cream, ice-cream, yogurt and most cheeses. The moisture content of foods (or more correctly their water activity, section 7.3), together with temperature and pH, are of great importance to food technology. As described in section 7.8, water plays an extremely important role even in relatively low-moisture products such as butter (c. 16% mois￾ture) or dehydrated milk powders (c. 2.54% moisture). Water is the most important diluent in foodstuffs and has an important influence on the physical, chemical and microbiological changes which occur in dairy prod￾ucts. Water is an important plasticizer of non-fat milk solids. 7.2 General properties of water Some physical properties of water are shown in Table 7.2. Water has higher melting and boiling temperatures, surface tension, dielectric constant, heat capacity, thermal conductivity and heats of phase transition than similar molecules (Table 7.3). Water has a lower density than would be expected from comparison with the above molecules and has the unusual property of expansion on solidification. The thermal conductivity of ice is approxi￾mately four times greater than that of water at the same temperature and is high compared with other non-metallic solids. Likewise, the thermal dif￾fusivity of ice is about nine times greater than that of water. The water molecule (HOH) is formed by covalent (6) bonds between two of the four sp3 bonding orbitals of oxygen (formed by the hybridization of the 2s, 2p,, 2py and 2p, orbitals) and two hydrogen atoms (Figure 7.la). The remaining two sp3 orbitals of oxygen contain non-bonding electrons. The overall arrangement of the orbitals around the central oxygen atom is tetrahedral and this shape is almost perfectly retained in the water molecule. Due to electronegativity differences between oxygen and hydrogen, the O-H bond in water is polar (a vapour state dipole moment of 1.84 D). This results in a partial negative charge on the oxygen and a partial positive charge on each hydrogen (Figure 7.lb). Hydrogen bonding can occur between the two lone electron pairs in the oxygen atom and the hydrogen atoms of other

m 7.1 Approximate water content of some dairy products ified from Holland et al, 1991) Product Water(g/100 g) average ified plus SMP d° Channel Island milk, whole, pasteurized mi-skimmed, UHT Dried skimmed milk Evaporated milk, whole 8666800θ8 Goats milk, pasteurized milk. colostrum mature Fresh cream, whipping Cheeses Cheddar-type, reduced fat Cheese spread, plain reduced fa 97865 anish blue mage frais, fruit ery low fat Fu fat soft cheese Medium-fat soft chees Parmesan White cheese, average Drink Ice-cream, dairy, vanilla non-dairy, vanilla The value for pasteurized milk is similar to that for unpas- teurized milk

Table 7.1 Approximate water content of some dairy products (modified from Holland et a/., 1991) Product Water (g/lOO g) Skimmed milk, average pasteurized fortified plus SMP UHT, fortified Whole milk, average pasteurized” summer winter sterilized summer winter semi-skimmed, UHT Dried skimmed milk with vegetable fat Evaporated milk, whole Flavoured milk Goats’ milk, pasteurized Human milk, colostrum Sheep’s milk, raw Fresh cream, whipping Cheeses Brie Camembert Cheddar, average vegetarian Cheddar-type, reduced fat Cheese spread, plain Cottage cheese, plain Channel Island milk, whole, pasteurized mature with additions reduced fat Cream cheese Danish blue Edam Feta Fromage frais, fruit plain very low fat Full-fat soft cheese Gouda Hard cheese, average Lymeswold Medium-fat soft cheese Parmesan Processed cheese, plain Stilton, blue White cheese, average Whey Drinking yogurt Low-fat plain yogurt Whole-milk yogurt, plain Ice-cream, dairy, vanilla fruit non-dairy, vanilla 91 91 89 91 88 88 88 88 88 86 86 86 89 3.0 2.0 69 85 89 88 87 83 55 49 51 36 34 41 53 79 17 80 46 45 44 51 72 18 84 58 40 31 41 10 18 46 39 41 94 84 85 82 13 62 65 “The value for pasteurized milk is similar to that for unpas￾teurized milk

DAIRY CHEMISTRY AND BIOCHEMISTRY Table 7.2 Physical constants of water and ice( from Fennema, 1985) Molecular weight 801534 oVert Melting point at 101.3 kPa(1 atm) Boiling point at 101.3 k Pa(1 atm Critical pressu 224MPa(2186am) 0.0099cand6104kPa(4.579mmHg) Heat of fusion at0°C 6.012 kJ(1.436 kcal)mol Heat of vaporization at 100C 40.63 kJ (9.705 kcal)mol-1 50.91kJ(12.16 kcal)mol-1 Other properties at 20°C o'C (ice) 20°cice) 0999841 0.9168 09193 1787×10-3 Surface tension against 72. 75x 10-3 756×10-3 air(Nm essure(Pa) pecific heat(J kg K ) 4.1819 237×1036104×1026.104×102 1.034×10 Thermal conductivity 5983×102 5644×1022240×1022433×102 Thermal diffusivity(m's)1.4x 10-5 ~1.1×10-4~1,1×10 Dielectric constant, 8000 at3×10°H 80.5 (25C) (1.5C) Limiting value at low frequencies Parallel to c-axis of ice; values about 15% larger if perpendicular to c-axis. Table 7-3 Properties of water and other compounds (from Roos, 1997) Hydrofluoric Hydrogen Ammonia sulphide Methane Water Property (CH,) (H2O 17.0 33.35 10000 2.1374.15 Critical P(bar) 464221.5 olecules which, due to the above- mentioned differences in electronegatiy ity, have some of the characteristics of bare protons. Thus, each water molecule can form four hydrogen bonds arranged in a tetrahedral fashion around the oxygen( Figure 7. 1d ). The structure of water has been described as a continuous three-dimensional network of hydrogen-bonded molecules with a local preference for tetrahedral geometry but with a large number of strained or broken hydrogen bonds. This tetrahedral geometry is usually

296 DAIRY CHEMISTRY AND BIOCHEMISTRY Table 7.2 Physical constants of water and ice (from Fennema, 1985) Molecular weight Phase transition properties Melting point at 101.3 kPa (1 atm) Boiling point at 101.3 kPa (1 atm) Critical temperature Critical pressure Triple point Heat of fusion at 0°C Heat of vaporization at 100°C Heat of sublimation at 0°C 18.01 534 0.ooo"c 100.00"C 374.15"C 22.14 MPa (218.6 atm) 0.0099'C and 610.4 kPa (4.579 mmHg) 6.012kJ (1.436kcal)mol-' 40.63 kJ (9.705 kcal) mol- 50.91 kJ (12.16kcal) mol-' Other properties at 20°C 0°C 0°C (ice) - 20°C (ice) Density (kg I-') 0.9998203 Surface tension against 72.75 x Vapor pressure (Pa) 2.337 x lo3 Specific heat (J kg-' K-I) 4.1819 Thermal conductivity 5.983 x 10' Thermal diffusivity (m2 s-I) Dielectric constant, Viscosity (Pa s) 1.002 x 10-3 air (N m-I) (J m-'s-' K-' 1 1.4 x static" 80.36 at 3 x lo9 Hz 76.7 (25'C) 0.999841 1.787 x 75.6 x 10-3 6.104 x 10' 4.2177 5.644 x 10' 1.3 10-5 80.00 80.5 (1 .5"C) 0.9168 - - 6.104 x 10' 2.1009 22.40 x lo2 - 1.1 x 10-4 91b - (- 12°C) 0.9193 - - 1.034 x 10' 1.9544 24.33 x 10' - 1.1 x 10-4 98b 3.2 - "Limiting value at low frequencies. bParallel to c-axis of ice; values about 15% larger if perpendicular to c-axis. Table 7.3 Properties of water and other compounds (from Roos, 1997) Hydrofluoric Hydrogen A m m o n i a acid sulphide Methane Water Property (NH,) (HF) W2.T (CHJ (HZO) Molecular weight 17.03 20.02 34.08 16.04 18.015 Melting point ('C) - 77.7 -83.1 - 85.5 - 182.6 0.00 Boiling point ("C) - 33.35 19.54 - 60.7 -161.4 100.00 Critical T ("C) 132.5 188.0 100.4 -82.1 374.15 Critical P (bar) 114.0 64.8 90.1 46.4 221.5 molecules which, due to the above-mentioned differences in electronegativ￾ity, have some of the characteristics of bare protons. Thus, each water molecule can form four hydrogen bonds arranged in a tetrahedral fashion around the oxygen (Figure 7.ld). The structure of water has been described as a continuous three-dimensional network of hydrogen-bonded molecules, with a local preference for tetrahedral geometry but with a large number of strained or broken hydrogen bonds. This tetrahedral geometry is usually

VATER IN MILK AND DAIRY PR( 297 104,5 (a) Figure 7.1 Schematic representations(a-c)of a water molecule and hydrogen bonding betwee maintained only over short distances. The structure is dynamic; molecules can rapidly exchange one hydrogen bonding partner for another and there may be some unbonded water molecules Water crystallizes to form ice. Each water molecule associates with four others in a tetrahedral fashion as is apparent from the unit cell of an ice crystal(Figure 7. 2). The combination of a number of unit cells, when viewed from the top, results in a hexagonal symmetry(Figure 7.3). Because of the tetrahedral arrangement around each molecule, the three-dimensional struc- ture of ice(Figure 7. 4)consists of two parallel planes of molecules lying close to each other (basal planes"). Basal planes of ice move as a unit under pressure. The extended structure of ice is formed by stacking of several basal planes. This is the only crystalline form of ice that is stable at a pressure of 1 atm at 0C, although ice can exist in a number of other crystalline forms, as well as in an amorphous state. The above description of ice is somewhat simplified; in practice the system is not perfect due to the presence of ionized

WATER IN MILK AND DAIRY PRODUCTS 297 Figure 7.1 Schematic representations (a-c) of a water molecule and hydrogen bonding between water molecules (d). maintained only over short distances. The structure is dynamic; molecules can rapidly exchange one hydrogen bonding partner for another and there may be some unbonded water molecules. Water crystallizes to form ice. Each water molecule associates with four others in a tetrahedral fashion as is apparent from the unit cell of an ice crystal (Figure 7.2). The combination of a number of unit cells, when viewed from the top, results in a hexagonal symmetry (Figure 7.3). Because of the tetrahedral arrangement around each molecule, the three-dimensional struc￾ture of ice (Figure 7.4) consists of two parallel planes of molecules lying close to each other ('basal planes'). Basal planes of ice move as a unit under pressure. The extended structure of ice is formed by stacking of several basal planes. This is the only crystalline form of ice that is stable at a pressure of 1 atm at O'C, although ice can exist in a number of other crystalline forms, as well as in an amorphous state. The above description of ice is somewhat simplified; in practice the system is not perfect due to the presence of ionized

DAIRY CHEMISTRY AND BIOCHEMISTRY 4.52A Figure 7.2 Unit cell of an ice crystal at 0 C. Circles represent the oxygen of water les.-indicates hydrogen bonding(Modified from Fennema, ater(H3 O, OH ) isotopic variants, solutes and vibrations within the ter molecules With the exceptions of water vapour and ice, water in dairy products contains numerous solutes. Thus, the interactions of water with solutes is of great importance. Hydrophilic compounds interact strongly with water by ion-dipole or dipole-dipole interactions while hydrophobic substances interact poorly with water and prefer to interact with each other (hydro- phobic interaction). Water in food products can be described as being free or bound. The definition of what consitiutes ' bound water is far from clear(see Fennema 1985)but it can be considered as that part of the water in a food which does not freeze at -40.C and exists in the vicinity of solutes and other non-aqueous constituents, has reduced molecular mobility and other signifi cantly altered properties compared with the ' bulk water'of the same system (Fennema, 1985). The actual amount of bound water varies in different products and the amount measured is often a function of the assay technique. Bound water is not permanently immobilized since interchange of bound water molecules occurs frequently. There are a number of types of bound water. Constitutional water is the most strongly bound and is an integral part of another molecule(e. g. within the structure of a globular protein). Constitutional water represents only a

298 DAIRY CHEMISTRY AND BIOCHEMISTRY 4.52 A Figure 7.2 Unit cell of an ice crystal at 0°C. Circles represent the oxygen atoms of water molecules, - indicates hydrogen bonding. (Modified from Fennema, 1985.) water (H30f, OH -), isotopic variants, solutes and vibrations within the water molecules. With the exceptions of water vapour and ice, water in dairy products contains numerous solutes. Thus, the interactions of water with solutes is of great importance. Hydrophilic compounds interact strongly with water by ion-dipole or dipole-dipole interactions while hydrophobic substances interact poorly with water and prefer to interact with each other (‘hydro￾phobic interaction’). Water in food products can be described as being free or bound. The definition of what consitiutes ‘bound’ water is far from clear (see Fennema, 1985) but it can be considered as that part of the water in a food which does not freeze at -40°C and exists in the vicinity of solutes and other non-aqueous constituents, has reduced molecular mobility and other signifi￾cantly altered properties compared with the ‘bulk water’ of the same system (Fennema, 1985). The actual amount of bound water varies in different products and the amount measured is often a function of the assay technique. Bound water is not permanently immobilized since interchange of bound water molecules occurs frequently. There are a number of types of bound water. Constitutional water is the most strongly bound and is an integral part of another molecule (e.g. within the structure of a globular protein). Constitutional water represents only a

WATER IN MILK AND DAIRY PRODUCTS Figure 7.3 The"basal planeof ice(combinations of two planes of sligh viewed from above. The closed circles represent oxygen atoms of water m in the lowe lane and the open circles oxygen atoms in the upper plane. (a) seen from above and(b)from small fraction of the water in high-moisture foods ' Vicinal or monolayer water is bound to the first layer sites of the most hydrophilic groups Multilayer water occupies the remaining hydrophilic sites and forms a number of layers beyond the monolayer water. There is often no clear distinction between constitutional, monolayer and multilayer water since they differ only in the length of time a water molecule remains associated with the food The addition of dissociable solutes to water disrupts its normal tetra hedral structure. Many simple inorganic solutes do not possess hydrogen bond donors or acceptors and therefore can interact with water only by dipole interactions(e.g. Figure 7.5 for Nacl). Multilayer water exists in a structurally disrupted state while bulk-phase water has properties similar to

WATER IN MILK AND DAIRY PRODUCTS 299 (b) Figure 7.3 The ‘basal plane’ of ice (combinations of two planes of slightly different elevations) viewed from above. The closed circles represent oxygen atoms of water molecules in the lower plane and the open circles oxygen atoms in the upper plane, (a) seen from above and (b) from the side (from Fennema, 1985). small fraction of the water in high-moisture foods. ‘Vicinal’ or monolayer water is bound to the first layer sites of the most hydrophilic groups. Multilayer water occupies the remaining hydrophilic sites and forms a number of layers beyond the monolayer water. There is often no clear distinction between constitutional, monolayer and multilayer water since they differ only in the length of time a water molecule remains associated with the food. The addition of dissociable solutes to water disrupts its normal tetra￾hedral structure. Many simple inorganic solutes do not possess hydrogen bond donors or acceptors and therefore can interact with water only by dipole interactions (e.g. Figure 7.5 for NaCl). Multilayer water exists in a structurally disrupted state while bulk-phase water has properties similar to

DAIRY CHEMISTRY AND BIOCHEMISTRY Figure 7.4 The extended structure of ice. Open and shaded circles represent oxygen atoms of Figure 7.5 Arrangement of water molecules in the vicinity of sodium and chloride ions (modified from Fennema, 1985). those of water in a dilute aqueous salt solution. Ions in solution impose structure on the water but disrupt its normal tetrahedral structure. Concen- trated solutions probably do not contain much bulk-phase water and structures caused by the ions predominate. The ability of an ion to influence the structure of water is influenced by its electric field. Some ions(princi- pally small and or multivalent) have strong electric fields and loss of the inherent structure of the water is more than pensated for by the new structure resulting from the presence of the ions. However, large, mono alent ions have weak electric fields and thus have a net disruptive effect on the structure of water

300 DAIRY CHEMISTRY AND BIOCHEMISTRY C 4 Figure 7.4 The extended structure of ice. Open and shaded circles represent oxygen atoms of water molecules in the upper and lower layers, respectively, of a basal plane (from Fennema, 1985). Figure 7.5 Arrangement of water molecules in the vicinity of sodium and chloride ions (modified from Fennema. 1985). those of water in a dilute aqueous salt solution. Ions in solution impose structure on the water but disrupt its normal tetrahedral structure. Concen￾trated solutions probably do not contain much bulk-phase water and structures caused by the ions predominate. The ability of an ion to influence the structure of water is influenced by its electric field. Some ions (princi￾pally small and/or multivalent) have strong electric fields and loss of the inherent structure of the water is more than compensated for by the new structure resulting from the presence of the ions. However, large, mono￾valent ions have weak electric fields and thus have a net disruptive effect on the structure of water

WATER IN MILK AND DAIRY PRODUCTS Figure 7.6 Schet representation of the interaction of water molecules with carboxylic acid (a), alcohol(b),-NH and carbonyl groups(c) and amide groups(d) In addition to hydrogen bonding with itself, water may also form such bonds with suitable donor or acceptor groups on other molecules. Water solute hydrogen bonds are normally weaker than water-water interactions By interacting through hydrogen bonds with polar groups of solutes, the mobility of water is reduced and, therefore, is classified as either constitu tional or monolayer. Some solutes which are capable of hydrogen bonding with water do so in a manner that is incompatible with the normal structure of water and therefore have a disruptive effect on this structure. For this reason, solutes depress the freezing point of water(Chapter 11). Water can potentially hydrogen bond with lactose or a number of groups on proteins (e.g. hydroxyl, amino, carboxylic acid, amide or imino; Figure 7.6)in dairy product: Milk contains a considerable amount of hydrophobic material, especially lipids and hydrophobic amino acid side chains. The interaction of water with such groups is thermodynamically unfavourable due to a decrease in entropy caused by increased water-water hydrogen bonding(and thus an increase in structure)adjacent to the non-polar groups 7.3 Water activity Water activity(aw)is defined as the ratio between the water vapour pressure exerted by the water in a food system()and that of pure water(po)at the

WATER IN MILK AND DAIRY PRODUCTS 301 0 II Figure 7.6 Schematic representation of the interaction of water molecules with carboxylic acid (a), alcohol (b), -NH and carbonyl groups (c) and amide groups (d). In addition to hydrogen bonding with itself, water may also form such bonds with suitable donor or acceptor groups on other molecules. Water￾solute hydrogen bonds are normally weaker than water-water interactions. By interacting through hydrogen bonds with polar groups of solutes, the mobility of water is reduced and, therefore, is classified as either constitu￾tional or monolayer. Some solutes which are capable of hydrogen bonding with water do so in a manner that is incompatible with the normal structure of water and therefore have a disruptive effect on this structure. For this reason, solutes depress the freezing point of water (Chapter 11). Water can potentially hydrogen bond with lactose or a number of groups on proteins (e.g. hydroxyl, amino, carboxylic acid, amide or imino; Figure 7.6) in dairy products. Milk contains a considerable amount of hydrophobic material, especially lipids and hydrophobic amino acid side chains. The interaction of water with such groups is thermodynamically unfavourable due to a decrease in entropy caused by increased water-water hydrogen bonding (and thus an increase in structure) adjacent to the non-polar groups. 7.3 Water activity Water activity (a,) is defined as the ratio between the water vapour pressure exerted by the water in a food system (p) and that of pure water (p,) at the

DAIRY CHEMISTRY AND BIOCHEMISTRY same temperature P Due to the presence of various solutes, the vapour pressure exerted by water in a food system is always less than that of pure water (unity). Water activity is a temperature-dependent property of water which may be used to characterize the equilibrium or steady state of water in a food system(roos, 1997) For a food system in equilibrium with a gaseous atmosphere (i.e. no net gain or loss of moisture to or from the system caused by differences in the apour pressure of water), the equilibrium relative humidity(ErH) is elated to aw by ERH(%)=aw×100 Thus, under ideal conditions, erh is the relative humidity of atmosphere in which a foodstuff may be stored without a net loss or gain of moisture. Water activity, together with temperature and ph, is one of the most important parameters which determine the rates of chemical, bio chemical and microbiological changes which occur in foods. However, since w presupposes equilibrium conditions, its usefulness is limited to foods in which these conditions exist Water activity is influenced by temperature and therefore the assay tem- perature must be specified. The temperature dependence of aw is described by the Clausius-Clapeyron equation in modified form dln(au)△H (7.3) here T is temperature(K), r is the universal gas constant and AH is the change in enthalpy. Thus, at a constant water content, there is a linear relationship between log aw and 1/T(Figure 7.7). This linear relationship is not obeyed at extremes of temperature or at the onset of ice formation The concept of aw can be extended to cover sub-freezing temperatures. In these cases, aw is defined(Fennema, 1985)relative to the vapour pressure supercooled water(porscw) rather than to that of ice Po(scw porsch where per is the vapour pressure of water in the partially frozen food and p that of pure ice. There is a linear relationship between log aw and 1/T at sub-freezing temperatures(Figure 7.8). The influence of temperature on aw is greater below the freezing point of the sample and there is normally a pronounced break at the freezing point. Unlike the situation above freezing

302 same temperature: DAIRY CHEMISTRY AND BIOCHEMISTRY P Po a =-. W Due to the presence of various solutes, the vapour pressure exerted by water in a food system is always less than that of pure water (unity). Water activity is a temperature-dependent property of water which may be used to characterize the equilibrium or steady state of water in a food system (Roos, 1997). For a food system in equilibrium with a gaseous atmosphere (i.e. no net gain or loss of moisture to or from the system caused by differences in the vapour pressure of water), the equilibrium relative humidity (ERH) is related to a, by: ERH(%) = a, x 100. (7.2) Thus, under ideal conditions, ERH is the % relative humidity of an atmosphere in which a foodstuff may be stored without a net loss or gain of moisture. Water activity, together with temperature and pH, is one of the most important parameters which determine the rates of chemical, bio￾chemical and microbiological changes which occur in foods. However, since a, presupposes equilibrium conditions, its usefulness is limited to foods in which these conditions exist. Water activity is influenced by temperature and therefore the assay tem￾perature must be specified. The temperature dependence of a, is described by the Clausius-Clapeyron equation in modified form: (7.3) where T is temperature (K), R is the universal gas constant and AH is the change in enthalpy. Thus, at a constant water content, there is a linear relationship between log a, and 1/T (Figure 7.7). This linear relationship is not obeyed at extremes of temperature or at the onset of ice formation. The concept of a, can be extended to cover sub-freezing temperatures. In these cases, a, is defined (Fennema, 1985) relative to the vapour pressure of supercooled water (poCscw,) rather than to that of ice: where pfr is the vapour pressure of water in the partially frozen food and pice that of pure ice. There is a linear relationship between loga, and 1/T at sub-freezing temperatures (Figure 7.8). The influence of temperature on a, is greater below the freezing point of the sample and there is normally a pronounced break at the freezing point. Unlike the situation above freezing

ATER IN MILK AND DAIRY PRODUCTS 303 a00 008 004 PARAMETER IS WATER CONTENT 1000K 1 Figure 7.7 Clausius-Clapeyron relationship between water activity and temperature for native potato starch. Numbers on curves indicate water content, in g per g dry starchfrom Fennema 1985) .0 Ice or ological matte containing ice 0.89 0372

WATER IN MILK AND DAIRY PRODUCTS PARAMETER IS WATER CONTENT 303 20 5 0 -2 -4 6 -8 .lo -12 -14 a-4 - 0 1 .., I 1 I I 1 I I I I I I I I I I I t--- ----___ - -0.01 - - - -0.02 - - - - % .0.03 - m - -I - - :: -0.04 - - -0.05 - - - - -0.06 - - I I I I I I I 3.40 9.60 3.65 3.70 3.75 3.80 3.85 3.90 0.2 "i 1.00 0.981 0.962 0.940 0.925 0.907 0.890 0.872 m3 0.10 o.08~ 0.06 I 0.02 "O4I