Foods as Dispersed Systems

The subjects discussed in this chapter are rather different from most of the material in this book, in the sense that true chemistry, that is, reactions involving electron transfer, is hardly involved. Nevertheless, many aspects of dispersed systems are important to an understanding of the properties of most foods and the manufacture of “fabricated foods.” 3.1.1 Foods as Dispersed Systems Most foods are dispersed systems. A few are homogeneous solutions, like cooking oil and some drinks, but even beer—as consumed—has a foam layer. The properties of a dispersed system cannot be fully derived from its chemical composition, since they also depend on physical structure. The structure can be very intricate, as is the case with foods derived from animal or vegetable tissues; these are discussed in Chapters 15 and 16. Manufactured foods, as well as some natural foods, may have a somewhat simpler structure: Beer foam is a solution containing gas bubbles; milk is a solution containing fat droplets and protein aggregates (casein micelles); plastic fats consist of an oil containing aggregated triacylglycerol crystals; a salad dressing may be just an emulsion; several gels consist of a network of polysaccharide molecules that immobilize a solution. But other manufactured foods are structurally complicated in that they contain several different structural elements of widely varying size and state of aggregation: filled gels, gelled foams, materials obtained by extrusion or spinning, powders, margarine, doughs, bread, and so forth. The existence of a dispersed state has some important consequences: 1. Since different components are in different compartments, there is no thermodynamic equilibrium. To be sure, even a homogeneous food may not be in equilibrium, but for dispersed systems this is a much more important aspect. It may have significant consequences for chemical reactions, as is briefly discussed in Section 3.1.3. 2. Flavor components may be in separate compartments, which may slow down their release during eating. Probably more important, compartmentalization of flavor components may lead to fluctuations in flavor release during eating, thereby enhancing flavor, because it offsets to some extent adaptation of the senses to flavor components. Thus, most “compartmentalized” foods taste quite different from the same food that has been homogenized before eating. Pag e 97 3. If, as is often the case, attractive forces act between structural elements, the system has a certain consistency, which is defined as its resistance against permanent deformation. This may be an important functional property as it is related to attributes such as stand-up, spreadability, or ease of cutting. Moreover, consistency affects mouth feel, as does any physical inhomogeneity of the food; food scientists often lump these properties under the word texture. 4. If the product has significant consistency, any solvent present—in most foods, water—will be immobilized against bulk flow. Transport of mass (and mostly of heat also) then has to occur by diffusion rather than convection. This may have a considerable effect on reaction rates. 5. The visual appearance of the system may be greatly affected. This is due to the scattering of light by structural elements, provided they are larger than about 50 nm. Large inhomogeneities are visible as such and give rise to what is the dictionary meaning of texture. 6. Since the system is physically inhomogeneous, at least at a microscopic scale, it may be physically unstable. Several kinds of change may occur during storage, which may be perceived as the development of macroscopic inhomogeneity, such as separation into layers. Moreover, during processing or usage, changes in the dispersed state may occur, which may be desirable—as in the whipping of cream—or undesirable—as in overwhipping of cream, where butter granules are formed. In this chapter, some of the foregoing aspects will be discussed. Large-scale mechanical properties will be largely left out, and so will aspects of hydrodynamics and process engineering. Of course, most foods show highly specific behavior, but treating them all would take too much space and provide little understanding. Therefore, some general aspects of fairly simple model dispersions will be emphasized. 3.1.2 Characterization of Dispersions A dispersion is a system of discrete particles in a continuous fluid phase. Various types exist and these are given in Table 1. Foods never exist as fog, and aerosols and powders will not be discussed. In addition to the dispersions listed in the table, solid foams, emulsions, or suspensions may exist: After the liquid systems have been made, the continuous phase may in some way solidify. In a foam omelette, the continuous protein solution has gelled; in margarine, the continuous oil phase now contains a continuous network of aggregated crystals; in chocolate much the same has happened and it thus contains solid particles (sugar, cacao) in a largely crystallized fat matrix. There are two types of food emulsions, oil-in-water (o/w) and water-in-oil (w/o). For emulsions, as well as for other dispersions, the nature of the continuous phase determines some TABLE 1 Various Types of Dispersions Dispersed phase Continuous phase Dispersion type Gas Liquid Foam Liquid Gas Fog , aerosol Liquid Liquid Emulsion Solid Gas Smoke, powder Solid Liquid Suspension, sol Pag e 98 FIGURE 1 Approximate size of some structural elements in foods. important properties of the dispersion, for instance, the type of liquid (aqueous or apolar) that can mix with the dispersion. In principle, there may be more than one continuous phase. The prime example is a wet sponge, where matrix and water both are continuous. Several foods are bicontinuous; for instance, in bread both the gas and solid phases are continuous. If not, the bread would lose most of its volume after baking, since the gas cells would shrink considerably on cooling, the more so as they partly consist of water vapor. The term phase needs some clarification. A phase is commonly defined as a domain bounded by a closed surface, at which surface at least some properties (e.g., pressure, refractive index, density, heat capacity, chemical composition) change abruptly. The surface contains free energy and it thus resists enlargement; in other words, it requires energy to make the surface (or interface). Since changes in properties mostly occur over a distance of a few molecular diameters, the criterion of abruptness implies that the dimensions of structural elements constituting a phase must be far larger than a single molecule in any direction. For instance, protein aggregates that float in a solution do not constitute a phase, since the aggregates are small and contain solvent. The particles may even sediment (certainly in a centrifuge) and form separate layers, but even these layers are not phases, since there is no phase boundary. The constituents water and polysaccharide that form a gel do not constitute phases: The polysaccharide strands in the gel are only about 1 nm in thickness. This brings us to the term colloid. A colloid is usually defined as a dispersion containing particles that are clearly larger than small molecules (say, solvent molecules), yet too small to be visible. This would imply a size range from about 10 nm to almost 1 mm. Two types of colloids are usually distinguished: reversible (or lyophilic) and irreversible (or lyophobic). The latter type consists of two (or more) phases of the types shown in Table 1 and these do not form spontaneously. A reversible colloid forms by “dissolving” a material in a suitable solvent. The main examples are macromolecules (polysaccharides, proteins, etc.) and association colloids. The latter are formed from amphiphilic molecules, like soaps. These have a fairly long hydrophobic “tail” and a smaller, very polar (i.e., hydrophilic) “head.” In an aqueous environment, the molecules tend to associate in such a way that the tails are close to each other and the heads are in contact with water. In this way, micelles or liquid crystalline structures are formed. Pag e 99 Micelles will be briefly discussed in Section 3.2.2; liquid crystalline phases [33] are not very prominent in foods. In foods, the difference between reversible and irreversible colloids is not always clear. For instance, an oil-in-water emulsion is certainly irreversible in the sense that it will never form spontaneously. But if the oil droplets are covered by a protein layer, the interactions between droplets may be like that of protein particles in solution, that is, like a reversible colloid. This means that for some properties of the emulsion macroscopic considerations are appropriate, whereas for other properties molecular considerations may be more suitable. The size scale of structural elements in foods can vary widely, spanning a range of six decades (Fig. 1). A water molecule has a diameter of about 0.3 nm. Also the shape of the particles is important, as is their volume fraction j (i.e., the proportion of the volume of the system that is taken up by the particles). All these variables affect product properties. Some effects of size or scale are: 1. Visual appearance. An o/w emulsion, for example, will be almost transparent if the droplets have a diameter of 0.03 mm; blueish white if 0.3 mm; white if 3 mm; and the color of the oil (usually yellow) will be discernable for 30-mm droplets. 2. Surface area. For a collection of spheres each with a diameter d (in m), the specific surface area is given by A = 6j/d (1) in square meters per cubic meter. The area can thus be large. For an emulsion of j=0.1 and d=0.3 mm, A=2m2 per ml emulsion; if 5 mg protein is adsorbed per square meter of oil surface, the quantity of adsorbed protein would amount to 1% of the emulsion. 3. Pore size. Between particles, regions of continuous phase exist and their size is proportional to particle size and smaller for a larger j. If the dispersed phase forms a continuous network, pores in this network follow the same rules. The permeability, that is, the ease with which solvent can flow through the pores, is inversely proportional to pore size squared. This is why a polymer gel is far less permeable than a gel made of fairly large particles (Sec. 3.5.2). 4. Time scales involved. (Note: Time scale is defined as the characteristic time needed for an event to occur—for instance, for two molecules to react, for a particle to rotate, for a bread to be baked.) The larger the particles, the longer are the time scales involved. For example, the root mean square value of the diffusion distance (z) of a particle of diameter d as a function of time t is. (t/d)0.5 (2) In water, a particle of 10 nm diameter will diffuse over a distance equal to its diameter in 1 ms; a particle of 1 mm in 1 sec; and one of 0.1 mm in 12 days. Considering diffusion of a material into a structural element, the relation between diffusion coefficient D, distance l, and time t0.5 needed to halve a difference in concentration (or temperature) is l 2 = Dt0.5 (3) The D of small molecules in water is approximately 10-9 m2 .sec-1 and in most cases (larger molecules, more viscous solution) it is smaller; D for evening out a temperature difference (by heat conduction) equals approximately 10-7 m2 .sec-1 . Taking, for instance, D=10-10, we find a halving time of about 0.01 sec for a distance of 1 mm, and of 3 hr for a distance of 1 mm. Pag e 100 5. Physical stability. Most interaction forces between particles are roughly proportional to their diameter, and sedimentation rate to diameter squared. This implies that almost all dispersions become inhomogeneous more readily if the particles are larger. 6. Effect of external forces. Most external forces acting on particles are proportional to diameter squared, and most internal forces within or between particles are proportional to diameter. This implies that small particles are virtually impervious to external influences, like shearing forces or gravity. Large particles often can be deformed or even be disrupted by external forces. 7. Ease of separation. Some of the points raised earlier imply that it is much more difficult to separate small particles from a liquid than large ones. Particles rarely are all of the same size. The subject of size distributions is a complicated one [2,58] and it will not be discussed here. Suffice it to say that mostly a size range may be used to characterize the size distribution and that the volume/surface average diameter dvs or d32 is often a suitable estimate of the center of the distribution. However, different properties may need different types of averages. The wider the size distribution—width being defined as standard deviation divided by average—the greater the differences between average types (an order of magnitude is not exceptional). It is often very difficult to accurately determine a size distribution [2]. Difficulties in determination and interpretation increase with particles that are more anisometric or otherwise different in properties. 3.1.3 Effects on Reaction Rates As already mentioned, components in a dispersed food may be compartmentalized, and this can greatly affect reaction rates. In a system containing an aqueous (a) and an oil phase (b), a component often is soluble in both. Nernst’s distribution or partitioning law then states that the ratio of concentrations (c) in both phases is constant: ca/cb = constant (4) The constant will depend on temperature and possibly other conditions. For instance, pH has a strong effect on the partitioning of carboxylic acids, since these acids are oil soluble only when they are in a neutralized state. At high pH, where acids are fully ionized, almost all acid will be in the aqueous phase, whereas at low pH the concentration in the oil phase may be considerable. Note that the quantity of a reactant in a phase also depends on the phase volume fraction. When a reaction occurs in one of the phases present, it is not the overall concentration of a reactant but its concentration in that phase that affects the reaction rate [87]. This concentration may be higher or lower than the overall concentration, depending on the magnitude of the partitioning constant (Eq. 4). Since many reactions in foods actually are cascades of several different reactions, the overall reaction pattern, and thereby the mix of components formed, may also depend on partitioning. Chemical reactions will often involve transport between compartments and will then depend on distances and molecular mobility. Applying Equation 3, it follows that diffusion times for transport into or out of fairly small structural elements, say emulsion droplets, would mostly be very short. However, if the solvent is immobilized in a network of structural elements, this may greatly slow down reactions, especially if reactants, say O2, have to diffuse in from outside. Moreover, reactions may have to take place at the boundary between phases. An example is fat autoxidation, where the oxidizable material (unsaturated oil) is in oil droplets, and a catalyst, say Cu ions, is in the aqueous phase. Another example is that of an enzyme present in one structural element and the component on which it acts in another one. In such cases, the specific surface area may be rate-determining. Pag e 101 Adsorption of reactive substances onto interfaces between structural elements may diminish their effective concentration and thereby reactivity. On the other hand, if two substances that may react with each other are both adsorbed, their effective concentrations in the adsorption layer may be much greater, thereby enhancing reaction rate. Thus, rates of chemical reactions and the mix of reaction products may be quite different in a dispersed system than in a homogeneous one. Examples in vegetable and animal tissues are well known, but other cases have not been studied in great detail, except for the activity of some additives [87] and, of course, for enzymatic lipolysis. 3.2 Surface Phenomena As mentioned earlier, most foods have a large phase boundary or interfacial area. Often, substances adsorb onto interfaces, and this has a considerable effect on static and dynamic properties of the system. In this section basic aspects are discussed; applications are discussed later [see Refs. 1 and 51 for general literature]. 3.2.1 Interfacial Tension and Adsorption An excess of free energy is present at a phase boundary and the amount is conveniently expressed in joules per square meter. The interface can be solid or fluid; the latter is the case if both phases are fluid. A fluid interface is deformable and the interfacial free energy then becomes manifest as a two-dimensional interfacial tension, expressed in newtons per meter; it is usually denoted g. Note that g numerically equals the interfacial free energy (1 J=1 N). In foods, we may have air (A), aqueous (W), oil (O), or solid (S) phases; if one of the phases is air, g (e.g., gAW) is commonly called surface tension. The interfacial tension acts in the direction of the interface and resists enlargement of the interface. This provides a method to measure g. For example, one may measure the force to pull a plate out of the interface and divide the force by the contour length of the interface-plate contact (Fig. 2). Substances that lower g adsorb onto the interface because this leads to a lower total free energy. Such substances are called surfactants. Reference 36 gives a detailed treatment of adsorption to fluid interfaces and the consequences thereof. The amount adsorbed is expressed as the surface excess G (mol.m-2 or mg.m-2), loosely called surface load. According to Gibbs, for one adsorbing solute in one of the phases and at equilibrium conditions dg = -RT G d(ln a) (5) where R and T have their usual meaning and a is the activity of the solute. The latter is not equal to the total concentration of the solute because (a) part of the solute is adsorbed and a refers only to the surfactant in solution (usually called “the bulk”), and (b) the activity may be smaller than the bulk concentration, especially above the critical micelle concentration (see later). Whether adsorption does occur and g is thus lowered depends on the properties of the solute (Sec. 3.2.2). The lowering is expressed in the surface pressure , which can be envisaged as a two-dimensional pressure exerted by the adsorbed molecules onto any boundary that confines a certain interfacial area (Fig. 2). Interfacial tensions of some systems are given in Table 2. The Gibbs equation shows that g will be lower for a larger bulk concentration of an adsorbing solute, but it does not give the relation between g or P and G, nor the relation between G and bulk concentration. The former relation, a surface equation of state, will not be discussed here. The latter relation may be seen as an adsorption isotherm, if equilibrium is attained. Examples are shown later, in Fig. 5. Usually a plateau value of G is reached, at which the Pag e 102 FIGURE 2 Surface (interfacial) tension measurements. (a) General principle: The surface tension pulls the W ilhelmy plate downward. (b) Surfactant molecules in the surface exert a two-dimensional pressure P = g 0 – g on the movable barriers confining the surfactant-containing surface. interface is more or less fully packed with surfactant molecules. For most surfactants, the plateau value is a few milligrams per square meter. Adsorption naturally takes time, since adsorbing molecules have to be transported, often by diffusion, to the interface. If the bulk concentration of surfactant is c, the layer of solution needed to provide the surfactant is given by G/c. Using Equation 3, the time needed for adsorption would be approximately (6) This means that the time needed for adsorption would typically be <1 sec for a surfactant concentration of 0.1%. TABLE 2 Some Interfacial Tensions, Approximate Values (mN -1) at Room Temperature Material Ag ainst air Ag ainst water W ater 72 0 Saturated NaCl solution 82 0 Ethanol 22 0 Paraffin oil 30 50a Triacylg lycerol oil 34 27a Mercury 484 415 aSome buffer solutions g ive a lower interfacial tension than does pure water. Pag e 103 3.2.2 Surfactants Surfactants come in two types, polymers and soap-like substances. The latter are fairly small amphiphilic molecules, the hydrophobic (lipophilic) part being typically an aliphatic chain. The hydrophilic part can vary widely; in the classical surfactant, common soap, it is an ionized carboxyl group. Most amphiphilic substances are not highly soluble either in water or oil, and they feel the least repulsive interaction from these solvents when they are partly in a hydrophilic environment (water, a hydrophilic substance) and partly in a hydrophobic one (oil, air, a hydrophobic substance), that is, at an interface. In solution, they tend to form micelles to lessen repulsive interaction with solvent. (Note on terminology: Some workers use the word surfactant for small-molecule surfactants only. Also, surfactants are often called emulsifiers, even when the surfactant is not involved in making an emulsion.) Some small-molecule surfactants of importance to the food scientist are listed in Table 3 [32,53]. They are categorized as nonionic, anionic, and cationic, according to the nature of the hydrophilic part. Also, distinction is made between natural surfactants (e.g., soaps, monoacylglycerols, phospholipids) and synthetic ones. The Tweens are somewhat different from the other ones in that the hydrophilic part contains three or four polyoxyethylene chains of about five monomers in length. Phospholipids come in a wide range of composition and properties. An important characteristic of a small-molecule surfactant is its HLB value, where HLB stands for hydrophile-lipophile balance. It is defined so that a value of 7 means that the substance has about equal solubility in water and oil. Lower values imply greater solubility in oil. Surfactants range in HLB value from about 1 to 40. The relation between HLB value and solubility is in itself useful, but it also relates to the suitability of the surfactant as an emulsifier: Surfactants with HLB > 7 are generally suitable for making o/w emulsions, and those with HLB <7 for w/o emulsions (see also Sec. 3.6.2 about Bancroft's rule). Surfactants suitable as cleaning agents (detergents) in aqueous solutions have a high HLB number. Several other relations with HLB values have been claimed, but most of these are questionable. In general, a longer aliphatic chain yields a lower HLB and a more polar (especially an TABLE 3 Some Small-Molecule Surfactants and Their Hydrophile-Lipophile Balance (HLB) Values Type Example of surfactant HLB value Nonionics Aliphatic alcohol Hexadecanol 1 Monoacylg lycerol Glycerol monostearate 3.8 Esters of monoacylg lycerols Lactoyl monopalmitate 8 Spans Sorbitan monostearate 4.7 Sorbitan monooleate 7 Sorbitan monolaurate 8.6 Tween 80 Polyoxyethylene sorbitan monooleate 16 Anionics Soap Na oleate 18 Lactic acid esters Na stearoyl-2-lactoyl lactate 21 Phospholipids Lecithin Fairly larg e Teepola Na lauryl sulfate 40 Cationics a Large aNot used in foods but as deterg ents. Pag e 104 ionized) or a larger polar group a higher HLB. For most surfactants, the HLB number decreases with increasing temperature. This implies that some surfactants exhibit a HLB temperature or phase inversion temperature (PIT), at which a value of 7 is reached. Above the PIT the surfactant tends to make a w/o emulsion, and below it an o/w emulsion. Near the PIT, gOW is generally very small. Figure 3 shows the effect of concentration of surfactant on surface tension. Breaks in the curves occur at the critical micelle concentration (CMC). Beyond that concentration the surfactant molecules form micelles and their activity barely increases; hence, g becomes essentially independent of concentration (see Eq. 5). At a concentration slightly below the CMC the surface load reaches a plateau value. In a homologous series of surfactants, a longer chain length results in a lower CMC and a lower concentration to obtain a given lowering of g. This means that larger surfactant molecules sare more surface active. Also, smaller surfactant molecules give a somewhat less steep slope near the CMC. This implies, according to Equation 5, that the plateau value of the surface load is somewhat smaller than it is for larger surfactant molecules. For ionic surfactants, the CMC markedly decreases and surface activity increases with increasing ionic strength. Both of these properties can also depend on pH. At the oil-water interface much the same pattern is observed, but since g 0 is lower and P is roughly the same, g is much smaller. The smallest value of g obtained at the air-water interface is about 35 mN-1, whereas at the triacylglycerol oil—water interface it varies from < 1 to about 5 mN-1 for most small-molecule surfactants. The mode of adsorption of various surfactants is depicted in Figure 4. It should be realized that commercially available surfactants generally are mixtures of several components, varying in chain length and possibly in other properties. These components may differ, for example, in the plateau value of g (Fig. 3). In these instances, Equation 5 is no longer applicable and plots of the type in Figure 3 have a different shape, often with a local minimum in g. Especially, some trace components may be present that give a lower g than the main components, and at equilibrium the surfactants yielding the smallest g will dominate in the interface. Because of their small concentration, it will, however, take a long time for them to reach the interface; see Equation 6. This implies that it will take a long time before an equilibrium composition, and thus a steady g, is reached. Another complication is that in actua dispersions the surface to volume ratio is very large, whereas this ratio is quite small in situations where g is commonly measured, that is, at a macroscopic interface between the phases. This means that the result of such measurements of g may not be representative for the actual values in a foam or emulsion. Finally, the CMC may not be clearly evident in mixtures of surfactants, especially for nonionics. Macromolecules can be very surface active. Several synthetic polymers are used as surfactants, and a mass of experimental evidence as well as theory is available [22]. Copolymers, where part of the segments are fairly hydrophobic and others hydrophilic, are especially suitable. They tend to adsorb with “trains,” “loops,” and “tails” (Fig. 4). Actually, at an oil-water interface, parts of the molecule can also protrude for some instances into the oil phase (not into air). There are few natural polymers that adsorb in this way. Surface activity of polysaccharides still is controversial. Most workers assume that surfaceactive polysaccharides contain a protein moiety that is responsible for this attribute, and this is clearly the case for gum arabic [15]. On the other hand, it is believed that at least some galactomannans adsorb as such onto the o/w interface [24]. Proteins often are the surfactants of choice, especially for foams and o/w emulsions (because of their water solubility they are not suitable for w/o emulsions) [16,44,85]. The mode of adsorption of proteins varies. There always is a change of conformation, often considerably so. For instance, most enzymes completely lose their activity after adsorption at an oil-water interface due to conformational change. Some enzymes retain part of their activity after adsorption at an air-water interface. Most globular proteins appear to retain an approximately globular conformation at interfaces (Fig. 4), though not the native one. Proteins with little secondary structure, like gelatin and caseins, tend to adsorb more like a linear polymer (Fig. 4). Forms intermediate between those mentioned also occur. At high bulk protein concentration, multilayer adsorption may occur, but the second and more remote layers are only weakly adsorbed. In Figure 5 adsorption of a protein and adsorption of a soap-like surfactant are compared. It is apparent that proteins (like synthetic high polymers) are much more surface active than soap-like surfactants. Even if the concentration scale in Figure 5 were in kilograms per cubic meter, the concentration needed for a certain adsorption to occur would differ by two decades. However, the “soap” yields a greater surface pressure (lower interfacial tension) than the protein at the plateau adsorption. For small-molecule surfactants, the Gibbs relation (Eq. 5) holds, but for most proteins (and most high polymers) this is not so. Desorption of adsorbed protein cannot Pag e 106 FIGURE 5 Surface pressure (P) and surface load ( G) as a function of the bulk concentration of a protein and a small-molecule surfactant (“soap”). CMC is critical micelle concentration. Typical examples. (After Ref. 85.) be or barely can be achieved by dilution or “washing,” at least over time scales of interest. The difficulty of desorption may be enhanced by cross-linking reactions between adsorbed protein molecules; this has been clearly shown for proteins containing a free thiol group, where cysteine-cystine interchange can occur [20]. As exemplified in Figure 5, small-molecule surfactants generally yield a greater surface pressure, that is, a lower interfacial tension, than proteins, if the former are present in sufficient FIGURE 6 Surface load (G) in an o/w emulsion and interfacial tension (g) at the o/w interface for b-casein in the presence of increasing concentration of Na lauryl sulfate (SDS); g is also g iven for SDS only. (From Ref. 85, after Ref. 13.) Pag e 107 concentration. This implies that they will displace proteins from the interface [13]. This is illustrated in Figure 6. Proteins may also adsorb on top of an adsorbed monolayer of a displacing surfactant, especially if the monolayer is phospholipid. These are important aspects in relation to foam and emulsion stability. Many foods naturally contain some surfactants (fatty acids, monoacylglycerols, phospholipids), and these can modify the properties of adsorbed protein layers. To some extent, proteins can also displace each other in a surface layer, depending on concentration, surface activity, molar mass, molecular flexibility, etc. Although protein adsorption is irreversible in the sense that it is mostly not possible to lower G by diluting the system, the occurrence of mutual displacement nevertheless implies that individual protein molecules in the interfacial layer may interchange with those in solution, albeit slowly. 3.2.3 Contact Angles When two fluids are in contact with a solid and with each other, there is a contact line between the three phases [1]. An example is given in Figure 7a for the system air-water-solid. There must be a balance between the surface forces acting in the plane of the solid surface and this leads to Equation 7, called the Young equation: gSA = gSW + gAW cos q (7) The contact angle q is conventionally taken in the densest fluid phase. It depends on the three interfacial tensions. However, gSA and gSW cannot be measured, but their difference can be derived from the contact angle. If (gSA-gSW)/gAW> 1, Equation 7 has no solution, q=0, and the solid is completely wetted by the liquid; an example is water on clean glass. If the quotient FIGURE 7 Contact ang les (q), shown as cross sections throug h three-phase systems. A=air, W =water, O=oil, S=solid. (a) W ater drop on a solid substrate; (b) solid particle located in an oil-water interface; (c) oil droplet in an air-water interface; (d) air pocket in a crevice in a solid submerg ed in water. See text. Pag e 108 mentioned is <-1, there is no wetting at all; an example is water on Teflon or other strongly hydrophobic materials. Figure 7b depicts, in fact, the same situation. In case b1 the contact angle is about 150 degrees, and this would be fairly typical for a triacylglycerol crystal in a triacylglycerol oil-water interface. The contact angle can in such a case be lowered by adding a suitable surfactant, such as Na lauryl sulfate, to the water phase. Addition of a large quantity of surfactant can even lead to q=0, and thus to complete wetting of the crystal by the aqueous phase. This is accomplished in some processes to separate fat crystals from oil. Adherence of crystals to the w/o interface and the associated contact angle may be of importance for emulsion stability (e.g., Section 3.6.5). In Figure 7c the more complicated situation of contact between three fluids is shown. Now there has to be a balance of surface forces in the horizontal as well as in the vertical plane, giving two contact angles. Equation 8 defines the spreading pressures: pS = gAW - (gAO + gOW) In Figure 7c, p S <0. If it is greater than zero, the sum of the surface free energies of the a/o and the o/w interfaces is smaller than that of the a/w interface alone, and the oil will spread over the water surface. Use of the values in Table 2 leads to the conclusion that for paraffin oil pS=-8 mN.m-1, implying that the droplet will not spread (but it does adhere to the a/w interface). For triacylglycerol oil, it follows that pS = 11 mN.m-1, and spreading does occur. These aspects are of importance for the interactions between emulsion droplets and foam bubbles. The spreading pressures can, of course, be altered by surfactants. However, most proteins lower gAW and gOW by roughly the same amount, and the spreading pressure then is not greatly altered. It should be noted that the action of gravity can alter the situations depicted in Figure 7. If the droplets are smaller than about 1 mm, the effect of gravity is small. 3.2.4 Curved Interfaces [1] The pressure at the concave side of a curved phase boundary (interface) always is greater than that at the convex side. The difference is called the Laplace pressure. For a spherical surface of radius r, the Laplace pressure rL is pL = 2g/r An important consequence is that drops and bubbles tend to be spherical and that it is difficult to deform them, the more so when they are smaller. If a drop is not spherical, the radius of curvature differs with location, which implies a pressure difference within the drop. This causes material in the drop to move from regions with a high pressure to those with a lower one, until a spherical shape is obtained. Only if an outside stress is applied can the drop (or bubble) be deformed from the spherical shape. Some examples may be enlightening. For an emulsion droplet of radius 0.5 mm and interfacial tension 0.001 N.m-1, the Laplace pressure would be 4 × 104 Pa and a considerable external pressure would be needed to cause substantial deformation. For an air bubble of 1 mm radius and g=0.05 N.m-1 , pL would be 100 Pa, allowing deformation to occur more easily. These aspects will be discussed further in Sections 3.6.2, 3.6.4, and 3.7.1. Another consequence of the Laplace pressure is capillary rise. If a vertical capillary contains a liquid that gives zero contact angle, such as water in a glass tube, a concave meniscus is formed, implying a pressure difference between the water just below the meniscus and that Pag e 109 outside the tube at the same height. The liquid in the tube will then rise, until the pressure due to gravity (g times density times difference in height) balances the capillary pressure. For example, pure water in a cylindrical capillary of 0.1 mm internal diameter would rise 29 cm. If the contact angle is larger, the rise will be less; if it is > 90°, capillary depression occurs. These aspects are relevant to the dispersion of powders in water. If a heap of powder is placed on water, capillary rise of the water through the pores (voids) between the powder particles must occur for wetting of the particles to occur, and this is prerequisite for dispersion. It requires a contact angle (between powder material, water, and air) <90°. The effective contact angle in the powder is quite a bit smaller than that at a smooth surface of the powder material, so the angle must be distinctly smaller than 90° [see further in Ref. 65]. A third consequence of Laplace pressure is that the solubility of the gas in a bubble in the liquid around it is enhanced. According to Laplace (Eq. 9), the pressure of a gas in a (small) bubble is enhanced and, according to Henry's law, the solubility of a gas is proportional to its pressure. The effect of curvature of a particle on the solubility of the material in the particle is not restricted to gas bubbles and is in general given by the Kelvin equation: (10) where s is solubility, solubility at a plane surface (i.e., “normal” solubility), and M and r are molar mass and mass density, respectively, of the material in the particle. Examples of calculations according to Equation 10 are in Table 4. It is seen that for most systems, particle radius has to be very small (e.g., <0.1 mm) for a significant effect. However, gas in bubbles of 1 mm has perceptibly enhanced solubility. If the surface is concave rather than convex, the solubility is, of course, decreased (Fig. 7d). The increased solubility gives rise to Ostwald ripening, that is, the growth of large particles in a dispersion at the expense of small ones, and thus the eventual disappearance of the smallest particles. However, this only occurs if the material of the particles is at least somewhat soluble in the continuous phase. It may thus occur in foams and in water-in-oil emulsions, but not in triacylglycerol oil-in-water emulsions. The rate of Ostwald ripening is governed by several factors (see, e.g., Sec. 3.7.2). Ostwald ripening will always occur with crystals in a saturated solution, albeit slowly if the crystals are large. Another effect is that it causes “rounding” of small crystals. At the edge of a crystal, the radius of curvature may be very small, say some nanometers, and this will lead to a greatly enhanced solubility (Table 4, fat crystal). The material near the edge will thus TABLE 4 Examples of the Increase in Solubility of the Material in a Particle Due to Curvature, Calculated According to Equation 10 for Some Arbitrary Particle Radii and Some Reasonable Values of the Interfacial Tension (Temperature 300 K) Variable W ater in oil Air in water Fat crystal in oil Sucrose crystal in saturated solution r (m) 10-6 10-4 10-8 10-8 g (N.m-1) 0.005 0.05 0.005 0.005 r (kg .m-3 990 1.2 1075 1580 M (kg .mol -1 0.018 0.029 0.70 0.342 1.000073 1.010 1.30 1.091 Pag e 110 dissolve and be deposited somewhere else. In some systems, this leads to sintering of aggregated crystals (Section 3.4.4). 3.2.5 Interfacial Rheology [37,85] If an interface contains surfactant, it has rheological properties. Two kinds of surface rheology can be distinguished, in shear and in dilation (Fig. 8). When the interface is sheared (leaving both area and amount of surfactant in the interface constant), one can measure the force in the plane of the interface needed to do this. Often this is done as a function of the shear rate, and a surface shear viscosity hss (units N.sec.m-1) is obtained. For most surfactants hss is negligibly small, but not for several macromolecular surfactants. For most systems, shear rate thinning occurs and the observed viscosity is an apparent viscosity. If the interfacial area is enlarged, leaving its shape unaltered, one measures an increase of interfacial tension, because now G becomes smaller. This is usually expressed in the surface dilational modulus, defined as (11) where A is the interfacial area. Esd is finite for all surfactants, although it will be very small if surfactant activity is high and the rate of surface enlargement is small. In such a case surfactant rapidly diffuses to the enlarged surface, thereby increasing G and thus lowering g. In other words, the Gibbs equilibrium (Eq. 5) will be rapidly restored. Esd therefore strongly decreases with decreasing rate of deformation. For proteins Esd may be large and less dependent on time scale, because proteins adsorb more or less irreversibly. Besides the interfacial concentration of protein, changes in its conformation can affect the modulus. Surface rheological properties in dilation and in shear are fundamentally different. Essentially, hss is due to the viscosity of the material in the interfacial layer, which implies that it is a bulk property, but of a layer of unknown thickness; hence it is expressed as a two-dimensional quantity. On the other hand, Esd is a real interfacial property, which appears in several equations relating to interfacial phenomena. A problem is, however, that measurement of Esd is difficult or even impossible, except at fairly long time scales and/or at small deformation. By and large, for globular proteins at the a/w interface, values of about 30–100 mN.m-1 have been observed and for b-casein about 10–20 m‘-1 [25,63]. Surface rheological parameters of protein layers naturally depend on pH, ionic strength, solvent quality, temperature, etc. Often moduli and viscosities are at maximum near the isoelectric pH. It should further be noted that one can also measure a surface dilational viscosity and a surface shear modulus. FIGURE8 lllustration of the g eometrical chang es broug ht about in an interfacial element when performing interfacial rheolog y in simple shear and in dilation. (From Ref. 85.) Pag e 111 3.2.6 Surface-Tension Gradients If a fluid interface contains a surfactant, surface-tension gradients can be created. This is illustrated for the case of an a/w interface in Figure 9. In Figure 9A a velocity gradient (G=dny/dc) sweeps surfactant molecules downstream (one may also say moves the surface), thereby producing a surface tension gradient; g will now be smaller downstream. This implies a stress Dg/Dx, which must be equal and opposite to the shearing stress hG (h = viscosity of the liquid). If there were no surfactant, the surface would move with the flowing liquid; in the case of an o/w interface, the flow velocity would be continuous across the interface. This has important consequences, especially for foams, as is seen by comparing Figure 9C with D. In the absence of surfactant, the liquid between two foam bubbles rapidly streams downward, like a falling drop. In the presence of surfactant, flow is very much slower. In other words, development FIGURE 9 Surface-tension g radients at the a/w interface. (A) Streaming of liquid along a surface causes a surface-tension g radient. (B) A surface-tension g radient causes streaming of the adjacent liquid: Marang oni effect. (C) Drainag e of liquid from a vertical film in the absence or (D) presence of surfactant. (E) Gibbs mechanism of film stability. (From Ref. 79.) Pag e 112 of surface-tension gradients is essential to formation of a foam. It also means that an air bubble or emulsion droplet moving through the surrounding liquid in virtually all cases has an immobile surface; that is, it behaves like a rigid particle. Figure 9B illustrates that liquid adjacent to an interface will move with the interface when the latter exhibits (for some reason, say local adsorption of surfactant) an interfacial tension gradient. This is called the Marangoni effect. It is seen in a glass of wine, where wine drops above the liquid level tend to move upward; here evaporation of ethanol produces the g gradient. An important consequence is the mechanism for stability of a thin film, illustrated in Figure 9E. If the film somehow acquires a thin spot, the surface area of the film is locally increased; hence G is lowered, g is increased, and a g gradient is established. The Marangoni effect ensues, causing liquid to flow to the thin spot, thereby restoring film thicknesses. This Gibbs mechanism provides the basis for the stability of films, as in a foam. Another consequence is the Gibbs-Marangoni effect, which allows formation of emulsions (see Section 3.6.2). In all these situations, the effects depend on film or Gibbs elasticity, which is defined as twice the surface dilational modulus (twice because a film has two surfaces). Thin films typically have a large elasticity, because of the scarcity of dissolved surfactant. In a thick film containing a fairly high concentration of surfactant, surfactant molecules can rapidly diffuse toward a spot with a low surface load and restore the original surface tension. This cannot occur or occurs only very slowly, in a thin film, implying a large elasticity, except at very long time scale. 3.2.7 Functions of Surfactants Surfactants in a food, whether small-molecule amphiphiles or proteins, can produce several effects, and these are briefly summarized next. 1. Due to the lowering of g, the Laplace pressure is lowered and the interface can be more easily deformed. This is important for emulsion and foam formation (Sec. 3.6.2) and for the avoidance of coalescence (Sec. 3.6.4). 2. Contact angles are affected, which is important for wetting and dispersion events. The contact angle determines whether a particle can adsorb on a fluid interface and to what extent it then sticks out in either fluid phase. These aspects have an important bearing on stability of some emulsions (Sec. 3.6.5) and foams (Sec. 3.7.2). 3. A decrease in interfacial free energy will proportionally slow Ostwald ripening. The rate of Ostwald ripening may also be affected by the surface dilational modulus (Sec. 3.7.2). 4. The presence of surfactants allows the creation of surface-tension gradients and this may be their most important function. It is essential for formation and stability of emulsions and foams (Secs. 3.6.2, 3.6.4, 3.7.1, and 3.7.2). 5. Adsorption of surfactants onto particles may greatly modify (colloidal) interparticle forces, mostly enhancing repulsion and thereby stability. This is discussed in Section 3.3. 6. Small-molecule surfactants may undergo specific interactions with macromolecules. They often associate with proteins, thereby materially altering protein properties. Another example is the interaction of some polar lipids with amylose. 3.3 Colloidal Interactions In Section 3.1.2 colloids were defined and classified. Generally, between particles forces act that originate from material properties of the particles and the interstitial fluid. These colloidal Pag e 113 interaction forces act in a direction perpendicular to the particle surface, contrary to the surface forces discussed in Section 3.2, which act in the direction of the surface. Colloidal interaction has important consequences: 1. It determines whether particles will aggregate (Sec. 3.4.3), which, in turn, may determine further physical instability, for instance, sedimentation rate. (Note on terminology: The terms flocculation and coagulation are also used, often with a more specific connotation; the former would, for instance refer to reversible aggregation, and the latter to irreversible.) 2. Aggregating particles may form a network (Sec. 3.5), and the rheological properties and the stability of systems containing networks strongly depend on colloidal interaction. 3. It may greatly affect susceptibility of emulsion droplets to (partial) coalescence (Secs. 3.6.4–5). Literature on colloid science can be found in textbooks mentioned in the Bibliography. 3.3.1 Van der Waals Attraction Van der Waals forces between molecules are ubiquitous, and they also act between larger entities such as colloidal particles. Since these forces are additive, it turns out that, within certain limits, the dependence of the interaction force on interparticle distance (as measured between the outer surfaces) is much weaker between particles than between molecules. For two identical spherical particles the van der Waals interaction free energy is VA -Ar/12h h < ~10 nm (12) where r is particle radius, h is interparticle distance, and A is the Hamaker constant. The last depends on the material of the particles and the fluid in between, and it increases in magnitude as the differences in the properties of the two materials increase. For most particles in water, A is between 1 and 1.5 times kT (4-–6 × 10-21 J). Tabulated values are available [27,72]. If both particles are of the same material and the fluid in between is different, A always is positive and the particles attract each other. If the two particles are of different materials, A may be negative and there would be van der Waals repulsion, but this is fairly uncommon. 3.3.2 Electric Double Layers Most particles in an aqueous solution exhibit an electric charge, because of adsorbed ions or ionic surfactants. In most foods, charges predominantly are negative. Since the system must be electroneutral, the particles are accompanied by a cloud of oppositely charged ions, called counterions. An example of the distribution of counterions and coions is given in Figure 10a. It is apparent that at a certain distance from the surface, the concentrations of positive and negative charges in the solution become equal. Beyond that distance, the charge on the particle is neutralized, due to an excess of counterions in the electric double layer. The latter is defined as the zone between the particle surface and the plane at which neutralization is achieved. The double layer should not be envisaged as being immobilized, because solvent molecules and ions diffuse in and out of the layer. The electrical effects are usually expressed in the electric potential y. Its value, as a function of the distance h, from the surface, is given by y = y0e -kh (13) Pag e 114 FIGURE 10 The electric double layer: (a) the distribution of counterions and coions as a function of the distance from the charg ed surface, and (b) the potential y as a function of distance for three values of the ionic streng th l; the broken lines indicate the Debye leng th. where y0 is the potential at the surface and the nominal thickness of the electric double layer or Debye length 1/k is given by (13a) for dilute aqueous solutions at room temperature. The ionic strength I is defined as (14) where m is molar concentration and z is valence of each of the ionic species present. Note that for a salt like NaCl, I equals molarity of the solution, but this is not so if ions of higher valence are present. For CaCl2, I is three times the molarity. Calculations of the potential as a function of distance are given in Figure 10b. Ionic strengths in aqueous foods vary from 1 mM (a typical tap water) to more than 1 M (pickled materials). The I of milk is about 0.075 M, and of blood about 0.14. Consequently, the thickness of the double layer is often only about 1 nm or less. This has important consequences when both negative and positive charges occur on one particle. If the distance between charged groups (or clusters of charged groups) on a surface (or on a macromolecule) is less than, say, 2/k, only the average potential is sensed from a distance. If, on the other hand, the distance between charges is greater than 2/k, the charges can be sensed separate from each other, enabling positive groups on one particle or macromolecule to react with negative groups on another one, forming salt bridges. This is, of course, relevant for proteins, which often are amphipolar. Electrical interactions depend on the surface potential, and this, in turn, is often influenced by pH. For most food systems, values of ¦y0¦ are below 30 mV. At a high concentration of counterions (especially if these are divalent), ion pairs can be formed between counterions and charged groups on the particle surface thereby lowering ¦y0¦. In a nonaqueous phase, the dielectric constant generally is much smaller than in water, and Equation 13a is no longer valid. Moreover, the ionic strength in this situation generally will be negligible. This means that even if there is a charged surface (as may be the case for aqueous droplets floating in oil), electrical interaction forces will usually be unimportant. Pag e 115 3.3.3 DLVO Theory If electrically charged particles having the same sign come very close to each other, their electric double layers overlap. This is sensed and the particles repulse each other. The repulsive electric interaction free energy VE can be calculated. For spheres of equal size it is (15) which would be valid for h <10 nm, ¦y0¦ <40 mV, kr> 1, in water at room temperature. The interaction energies VA (due to van der Waals attraction) and VE can be added, and this has led to the first useful theory for colloid stability, the DLVO (Deryagin-Landau, Verwey-Overbeek) theory. This theory enables calculation of the total free energy V needed to bring two particles from infinite distance to a distance h. Particle radius can be determined, several Hamaker constants are known, k is derived from the ionic strength and the electrokinetic (or zeta) potential, which often is assumed to be equal to y0, can be experimentally determined by electrophoresis. The total interaction energy is usually divided by kT, that is, the average free energy involved in an encounter between two particles by Brownian (heat) motion. Some plots of V/kT versus h are presented in Figure 11. If V is negative for all h, the particles will aggregate. If there is a maximum in the curve (as in Fig. 11a near x) that is much larger than kT, particles may never overcome this free energy barrier; if, on the other hand the maximum is somewhat lower, say 10kT, two particles may occasionally reach the “primary minimum” (as in Fig. 11a near y) and become irreversibly aggregated. If there is a sufficiently deep “secondary minimum” (Fig. 11a bear z), the particles readily become aggregated, but not fully irreversibly. It is seen that y0 (Fig. 11b) and ionic strength (Fig. 11c) have large effects on stability. Also the effect of particle radius seems to be large (Fig. 11d), but the DLVO theory appears to be incorrect in predicting the effect of size. Quite generally, the DLVO theory—though very successful for many inorganic systems—seems to be inadequate for predicting stability of biogenic systems. Milk fat globules, for example, are stable against aggregation at their isoelectric pH (3.8), where they have zero surface FIGURE 11 Examples of the colloidal interaction free energ y V (in units of k T) as a function of interparticle distance h according to the DLVO theory for spherical particles in water. Illustrated are effects of the mag nitude of (a) the Hamaker constant A(b) surface potential y 0; (c) ionic streng th l; and (d) particle radius r. Unless indicated otherwise, A=1.25 kT; y 0=15 mV; l=10 mM; r=1 mm. Pag e 116 potential, so that the DLVO theory would predict zero repulsion [84]. Consequently, interaction forces other than those considered in this theory must be important. 3.3.4 Steric Repulsion As depicted in Figure 4, some adsorbed molecules (polymers, Tweens© , etc.) have flexible molecular chains (“hairs”) that protrude into the continuous phase. These may cause steric repulsion. Two mechanisms can be distinguished. First, if the surface of another particle comes close, the hairs are restricted in the conformations they can assume, which implies loss of entropy, that is, increase of free energy, and repulsion occurs. This volume-restriction effect can be very large, but it can be of importance only if the surfaces have a very low hair density (number of hairs per unit area). This is because the hairy layers start to overlap on approach of the particles and then a second mechanism will act before the first one comes into play. The overlap causes an increased concentration of protruding hairs and thereby an increased osmotic pressure; this would lead to water moving to the overlap region, which results in repulsion. However, this is true only if the continuous phase is a good solvent for the hairs; if it is not, attraction may result. For example, emulsion droplets covered by casein have protruding hairs, providing stability to the droplets. If ethanol is added to the emulsion, the solvent quality is strongly decreased and the droplets aggregate [16]. In some cases, steric repulsion free energy can be calculated with reasonable accuracy [22]. If these values are added to the van der Waals attraction, curves for total interaction versus interparticle distance are obtained. Schematic examples are shown in Figure 12. The solvent quality usually is of overriding importance and if it is good, repulsion can be very strong; see curve c versus d. Only for large particles (strong van der Waals attraction) and a fairly thin adsorbed layer (short hairs) will aggregation occur in a good solvent (curve a, which shows a minimum free energy of about -12 kT). FIGURE 12 Hypothetical examples of theeffects of particle size, thickness of the layer of protruding molecular chains, and the quality of the solvent for those chains on the colloidal interaction free energ y (V in units of k T) between identical spherical particles as a function of the interparticle distance h. The interaction is supposed to be due to van der W aals attraction and steric repulsion. Curves: (a) g ood solvent, thin layer, particle diameter 2.5 mm; (b) same, but diameter 0.5 mm; (c) relatively poor solvent, thick layer diameter 2.5 mm; (d) same, but g ood solvent. Pag e 117 In practical food systems calculation of steric repulsion usually is not possible because the situation can be complex. For example, the nature of the adsorbing molecules can vary greatly [18,22,81]. It should also be mentioned that adsorbing polymers may cause bridging aggregation, by becoming simultaneously adsorbed onto two particles [22,81]. This may happen if too little polymer is present to fully cover the particle surface area or with certain methods of processing. 3.3.5 Depletion Interaction Nonadsorbing polymers are depleted near an interface, because the center of a molecule cannot come closer to the interface than the effective radius of the (random coil) molecule. Close to the interface, there is thus a layer with a polymer concentration lower than in the bulk. This depletion layer has a thickness (d) that is about equal to the radius of the gyration (Rg) of the polymer molecules (Fig. 13). If the particles come close to each other, the depletion layers overlap, implying that the polymer concentration in the bulk becomes lower. This leads to a larger mixing entropy, that is, to a lower free energy and to a driving force for particle aggregation. An estimate of the depletion free energy can be obtained from (16) where Posm is the osmotic pressure caused by the dissolved polymer. It is, in first approximation, proportional to the molar concentration of the polymer, but it will be more concentration dependent in a good solvent. Thus polysaccharides at low concentrations can cause depletion aggregation in foods; for example, 0.03% xanthan may be sufficient [16]. Fairly high concentrations of polymer often lead to immobilization of the particles (Section 3.4.2), thereby causing the system to be fairly stable. Other Aspects It should now be clear that several kinds of colloidal interactions can occur in foods and that the kind and concentration of surfactants present strongly influence these interactions. Even in the simplest cases, several variables are important (Table 5). Several additional complications may be mentioned. The DLVO theory does not apply at very small distances. One cause may be surface roughness. Another may be solvation repulsion. If solvent molecules are attracted by the material on the outside of the particle, this may cause some repulsion at short distance [28]. This may affect the depth of the primary minimum (in plots of V vs. h) and thereby the irreversibility of aggregation. Hydrophobic interactions also may occur, and they generally cause attraction. The effect is the result of poor solvent quality (Sec. 3.3.4 and Chap. 2). This type of interaction has a strong temperature dependence, being very weak near 0°C and increasing with increasing temperature. Such hydrophobic interactions may, in principle, occur if a protein is the surfactant. However, repulsion is more likely in this case. Usually this is caused by a’combination of steric and electrostatic repulsion, but calculation of the interaction free energy generally is not possible. Another aspect is double adsorption, that is, adsorption of a substance onto a layer of surfactant. There are many examples of polysaccharides adsorbing onto particles that are already covered with small-molecule surfactants or proteins [3]. General rules cannot be given, but a kind of bridging aggregation occurs in many cases. It thus turns out that added polysaccharides can act in various ways. If they adsorb they can provide steric repulsion, but under other conditions they can cause bridging aggregation. If they do not adsorb they may cause depletion aggregation, but at high concentration they may stabilize the system. 3.4 Liquid Dispersions 3.4.1 Description Several types of liquid dispersions exist. The discussions here will be limited to suspensions (solid particles in a liquid) and to those aspects of emulsions that follow the same rules. Foods Pag e 119 that are suspensions include skim milk (casein micelles in serum); fat crystals in oil; many fruit and vegetable juices (cells, cell clusters, and cell fragments in an aqueous solution); and some fabricated foods, such as soups. During processing (food fabrication), suspensions are also encountered, such as starch granules in water, sugar crystals in a saturated solution, and protein aggregates in an aqueous phase. Dispersions are subject to several kinds of instability, and these are schematically illustrated in Figure 14. Changes in particle size and in their arrangement are distinguished. Formation of small aggregates of particles may be considered to belong to both categories. Dissolution and growth of particles depend on concentration of the material, on its solubility, and on diffusion. In a supersaturated solution nucleation must occur before particles can be formed. Dissolution, nucleation, and growth will not be discussed further. Ostwald ripening is discussed in Sections 3.2.4 and 3.7.2 and coalescence in Section 3.6.4. The other changes are discussed next. The various changes may affect each other, as is illustrated in Figure 14. Moreover, sedimentation is enhanced by any growth in particle size, and sedimentation will enhance the rate of aggregation if the particles tend to aggregate. Agitation of the liquid may enhance the rate of some changes, but it can also disturb sedimentation and disrupt large aggregates. 3.4.2 Sedimentation If there is a difference in density (r) between the dispersed phase (subscript D) and the continuous phase (subscript C), there is a buoyancy force acting on the particles. According to Archimedes, this is for spheres apd 3 (rD-rC)/6, where a is acceleration. The sphere now FIGURE 14 Illustration of the various chang es in dispersity. Hig hly schematic. Pag e 120 FIGURE 15 Schematic examples of non-Newtonian flow behavior of liquids: apparent viscosity h * as a function of shearing stress s. Curve 1 is typical for a polymer solution. Curve 2 is typical for a slig htly ag g reg ating dispersion of very small particles. Curve 3 is typical for a system exhibiting a yield stress. sediments at a linear velocity n and feels a friction force, which is, according to Stokes, 3pdhCn, where hC is the viscosity of the continuous phase. By putting both forces equal, the equilibrium or Stokes sedimentation velocity is obtained: nS = a(rD – rC)d 2 /18hC (17) If the particles show a size distribution, d 2 should be replaced by , where ni is the number of particles per unit volume in class i with diameter di. For gravity sedimentation a=g=9.81 m.sec-2, and for centrifugal sedimentation a=Rw 2 , where R is the effective radius of the centrifuge and w its rotation rate in radians per second. To give an example: If the sphere diameter is 1 mm, the density difference is 100 kg.m-3, and the viscosity of the continuous phase is 1 mPa.sec (i.e., water), the spheres would sediment under gravity at a rate of 55 nm.sec-1 or 4.7 mm per day. Sedimentation greatly depends on particle size, and spheres of 10 mm would move 47 cm in a day. Normally, viscosity decreases and sedimentation rate increases with increasing temperature. If the density difference in Equation 17 is negative, sedimentation is upward, and one commonly speaks of creaming. Equation 17 is very useful to predict trends, but it is almost never truly valid. Among the many factors causing deviation from Equation 17 [83], the following are the most important for foods: 1. The particles are not homogenous spheres. Any anisometric particle tends to sediment more slowly, because it orients itself during sedimentation in such a way as to maximize friction; that is, a plate-shaped particle will adopt a “horizontal” orientation. An aggregate of particles, even if spherical, sediments more slowly than a homogeneous sphere of the same size, since the interstitial liquid in the aggregate causes the effective density difference to be smaller. 2. Convection currents in the dispersion, caused, for instance, by slight temperature fluctuations, may strongly disturb sedimentation of small particles (<~1 mm). Pag e 121 3. If the volume fraction of particles j is not very small, sedimentation is hindered. For j=0.1, the sedimentation rate is already reduced by about 60%. 4. If particles aggregate, sedimentation velocity increases: The increase in d 2 is always larger than the decrease in Dr. Moreover, as larger aggregates sediment faster they overtake smaller ones, and thus become ever larger, leading to an even greater acceleration of sedimentation rate. This may enhance sedimentation by orders of magnitude. A good example is rapid creaming in cold raw milk, where fat globules aggregate due to the presence of cryoglobulins [84]. 5. An assumption implicit in Equation 17 is that viscosity is Newtonian, that is, independent of shear rate (or shear stress), and this is not true for many liquid foods. Figure 15 gives some examples of the dependence of apparent viscosity on shear stress. The stress caused by a particle is given by the buoyancy force over the particle cross section, that is, 2/3g Drd for spheres under gravity. The stress is on the order of a millipascal for many particles. This then is the stress that the particles sense during sedimentation. Viscosity should be measured at that stress (or the corresponding shear rate, given by h* /s), whereas most viscometers apply stresses of well over 1 Pa. Figure 15 shows that the apparent viscosity can differ by orders of magnitude, according to the shear stress applied. Also shown in Figure 15 is an example of a liquid exhibiting a small yield stress. Below that stress the liquid will not flow. However, this is never noticed during handling, because the yield stress is so very small (a stress of 1 Pa corresponds to a water “column” of 0.1 mm height). Nevertheless, such a small stress often is sufficient to prevent sedimentation (or creaming), as well as aggregation. Among liquid foods exhibiting a yield stress are soya milk, many fruit juices, chocolate milk, and several dressings. These aspects are discussed further in Section 3.5.2 and in Ref. 71. 3.4.3 Aggregation Kinetics Particles in a liquid exhibit Brownian motion and thereby frequently encounter each other. Such encounters may lead to aggregation, defined as a state in which the particles stay close together for a much longer time than they would in the absence of attractive colloidal interaction. The rate of aggregation is usually calculated according to Smoluchowski's theory of perikinetic aggregation [54]. The initial aggregation rate in a dilute dispersion of spheres of equal size is -dN/dt = 4kTN2 /3hW (18) where N is the number of particles, that is, unaggregated particles plus aggregates, per unit volume. The stability factor W was assumed to equal unity by Smoluchowski. The time needed to halve the number of particles then is t0.5 = ph/8kTj (18a) where j is the particle volume fraction. This results in d 3 /10j seconds for particles in water at room temperature where d is in micrometers. For d=1 mm and j=0.1, this would be 1 sec, implying that aggregation is very rapid. In most practical situations, aggregation is much slower, because W often has a large value. If it is desired to increase the halving time from 1 sec to 4 months, this would need a W of 107 . The magnitude of the stability factor is primarily determined by the colloidal repulsion between the particles (Sec. 3.3). Direct use of Equation 18 to predict stability is rarely possible in food systems. There are numerous complications. Some of the more important ones are that (a) it is mostly impossible Pag e 122 to establish the value of W, (b) the stability factor may change with time, (c) there are other encounter mechanisms, due to streaming (agitation) or to sedimentation, and (d) aggregation may take various forms, leading to coalescence or to aggregates, which may be compact or tenuous. There are even more complications. Nevertheless, application of aggregation theory often is possible and useful, but it is far more intricate than can be discussed here [8,81,83]. 3.4.4 Reversibility of Aggregation According to the nature of the interaction forces between aggregated particles (Sec. 3.3), agents can be added to cause deaggregation. This can occur during processing, or can be done in the laboratory to establish the nature of the forces. It should be realized that often more than one type of force is acting. Diluting with water may cause deaggregation (a) due to lowering of osmotic pressure (if depletion interaction was the main cause of aggregation), (b) due to lowering ionic strength (which enhances electrostatic repulsion), or (c) due to enhancing solvent quality (which can increase steric repulsion). Electric forces can also be manipulated by altering pH. Bridging by divalent cations can often be undone by addition of a chelating agent, say ethylenediamine tetraacetic acid (EDTA). Bridging by adsorbed polymers or proteins can mostly be undone by addition of a suitable small-molecule surfactant (Sec. 3.2.2). Reversal of specific interactions, such as -S-S- bridges, requires specific reagents. Also, a change in temperature can affect aggregate stability, by altering solvent quality. If the forces between the particles in an aggregate are not very strong, deaggregation can be achieved by shear forces. These exert a stress hG, where G is the shear rate. In water, G=103 sec-1 would be needed to achieve a shear stress of 1 Pa, which does not seem very large. However, the shear force acting on an aggregate is proportional to aggregate diameter squared, and large aggregates often have weak spots, because of their inhomogeneity. This means that aggregates often are degraded to a certain size by a given shear rate. Another aspect is that bonds may strengthen after aggregation. It may be better to speak of junctions between particles, since any such junction may represent many (often hundreds of) separate bonds. The strengthening may occur by several mechanisms [81]. 3.5 Gels Many foods are “soft solids,” and these can often be said to be gels or gel-like. Some general aspects of idealized model systems will be discussed here, with principles being emphasized. Especially the mechanical (i.e., rheological and fracture) properties [e.g., 47] cannot be discussed in depth, because it would take far too much space and is outside the realm of this book. Nevertheless, some basic facts involving rheology are needed to understand gel properties. 3.5.1 Description From a rheological viewpoint a typical gel is a material that exhibits a yield stress, has viscoelastic properties and has a moderate modulus (say, <106 Pa). This is illustrated in Figure 16a. When a small stress acts on the material, it behaves elastically: It instantaneously deforms, keeps the shape obtained as long as the stress acts, and returns instantaneously to its original shape as soon as the stress is removed. For a greater stress, the material may show viscoelastic behavior: It first deforms elastically but then starts to flow; after removal of the stress it only partly regains its original shape. Figure 16b illustrates the differences between a liquid, a solid, and a viscoelastic material. Strain (e) means relative deformation, and strain rate is its change with time (de/dt) (the latter may be equal to the shear rate or to some other parameter, according to the type of deformation). Figure 16 also explains what yield stress Pag e 123 FIGURE 16 Characteristics of a visco-elastic material: (a) Example of the relation between deformation (strain) and time, when a visco-elastic material is suddenly broug ht under a certain stress, as well as after removal of the stress. The broken line is for a stress below the yield stress. (b) Strain rate as a function of stress for a Newtonian liquid, a viscoelastic material, and an elastic solid. (sy) means. The behavior of a viscoelastic material greatly depends on the time scale of the deformation. Rapid deformation—for instance, achieved by applying a fluctuating stress at high frequency—implies a short time scale. At very short time scales a gel is almost purely elastic, and at very long time scales almost purely viscous. Also the yield stress mostly is time dependent, being smaller at longer time scales. All these rheological parameters may vary greatly in magnitude among gels. For instance, yield stresses from 10-5 to 104 Pa have been observed. From a structural point of view, a gel has a continuous matrix of interconnected material with much interstitial solvent. Figure 17 illustrates three main types of gels occurring in food systems; moreover, intermediate and combined types occur. The various types have different properties; for instance, particle gels are much coarser than polymer gels, thus having a much greater permeability (Sec. 3.5.2). The mechanical properties of various gels differ greatly. To explain this, the behavior at large deformations should be considered [47,55,66,67]. Figure 18a gives a hypothetical stress-strain curve, ending at the point where fracture occurs. Fracture implies that the stressed specimen breaks, mostly into many pieces; if the material contains a large proportion of solvent, the space between the pieces may immediately become filled with solvent, rather than air. The modulus of the material (G), also called stiffness, is stress divided by strain, provided this quotient is constant. For most gels, proportionality of stress and strain is only observed at very small strains, and at larger strains the quotient may be called an apparent modulus. The strength of the material is the stress at fracture (sfr). Terms like firmness, hardness, and strength are often used rather indiscriminately; sensoric firmness or hardness often correlates with fracture stress. Modulus and fracture stress need not be closely correlated, as is clear in Figure 18b. These parameters also vary greatly with concentration of the gelling material. It is frequently observed that addition of inert particles (“fillers”) to a gelling material increases the modulus but decreases the fracture stress [38]. Part of the explanation of these divergencies is that a modulus is predominantly determined by number and strength of the bonds in the gel, whereas fracture properties highly depend on large-scale inhomogeneities. The strain at fracture (efr) may be called longness, but this term is rarely used. The terms shortness and brittleness are used, and they are closely related to 1/efr. The strain at fracture may vary widely; for gelatin efr may be 3, and for some polysaccharide gels only 0.1. For gels as Pag e 124 FIGURE 17 Schematic illustrations of three main types of g el. The dots in frame (a) denote cross-links. Note the differences in approximate scale. depicted in Figure 17a and b, efr greatly depends on length and stiffness of the polymer chains between cross links. Another parameter is the toughness or work of fracture Efr. This is derived from the area under the curve in Figure 18a and expressed in joules per cubic meter. All these parameters depend on time scale or rate of deformation, but in various manners. Several gels do not fracture at all when deformed slowly, but do so when deformation is rapid. In some cases, it is even difficult to distinguish between yielding and fracture. For some gels, fracture itself takes a long time. Gels may be formed in various ways, according to the kind of gelling material. Polymer molecules in solution [e.g., 4] behave more or less as random coils, effectively immobilizing a large amount of solvent (water), thereby increasing viscosity considerably. If the polymer concentration is not very low, the individual molecules tend to interpenetrate and form entanglements. This gives the solution some elasticity, but no yield stress. Gelation is caused by formation of intermolecular cross-links. These can be covalent bonds, salt bridges, or microcrystalline regions. Covalent bonds are provoked by added reagents or by increased temperature. The latter can occur with some proteins, where -S—S- bridges form during heating. For polyelectrolytes, Pag e 125 FIGURE 18 (a) Hypothetical example of the relation between stress and strain when deforming a viscoelastic material until it fractures. The modulus equals tan a. See text. (b) Relation between modulus and fracture stress for g els of various materials (curdlan is a bacterial b-1,3-g lucan) at varying concentration. (After Ref. 31.) that is, charged polymers such as proteins, formation of salt bridges may induce gelation. Other polymers gel by forming microcrystalline regions that act as cross-links. These are commonly formed on cooling, because then a reversible transition occurs that involves stiffening and localized crystallization of polymer chains. Polymer gels are often discussed in terms of the so-called rubber theory, where it is assumed that the polymer chains between cross-links are very long and can assume a large number of conformations. Deforming the gel leads to a decrease in the possible number of conformations and thereby to a decrease in entropy. In such an ideal entropic gel, the elastic modulus is simply G = nkT (19) where n is the number of effective cross-links per unit volume. As will be seen later, only a few food polymer gels behave like this. Particle gels may form because of aggregation, induced by a change in pH, ionic strength, solvent quality, etc. (Section 3.3). In these gels, the entropy loss on deformation is negligible and they derive their elastic modulus from deformation of bonds, an enthalpic effect. Particle gels are often fractal in nature [86]. If attractive particles encounter each other at random they form aggregates, and as these aggregates encounter other aggregates, larger aggregates form. This is called cluster-cluster aggregation. The relation between the average number of particles in an aggregate Np and the radius of the aggregate R then is Np = (R/r)D (20) where r is the radius of the primary (component) particles and D is a constant < 3 and is called the fractal dimensionality. Because it is smaller than 3, aggregates become more tenuous (rarefied) when they increase in size. The average volume fraction of particles in an aggregate is given by Pag e 126 (21) where Nm is the number of primary particles that a sphere of the same radius can contain assuming close packing. It is apparent that jag decreases as R increases. When jag becomes equal to the volume fraction of primary particles in the system, j, the aggregates touch each other and a gel forms. This implies an unequivocal gel point. It also implies that a gel is formed for any j, however small, although the gel may be extremely weak. The critical radius of the aggregates at gelation is given by Rcr = rj1/(D-3) (22) The size of the largest holes in the gel network equals about Rcr. Often, it is found that D 2.2 and it then follows that for j = 0.01, Rcr/r=316. For j=0.1 the ratio is 18, and for j=0.4 it is about 3. Although particles gels may seem to be rather disordered structures, simple scaling laws hold. Such relations can be given for rheological properties and permeability (see later). Such simple relations do not exist for most polymer gels. 3.5.2 Functional Properties Food technologists make gels for a purpose, often to obtain a certain consistency or to provide physical stability. The properties desired and the means of achieving those are summarized in Tables 6 and 7. Consistency has already been briefly discussed, but the message of Table 6 is an important one: According to the purpose in mind, the rheological measurements must be of a relevant type and conducted at the relevant time scale or strain rate. This need not be difficult. For instance, to evaluate stand-up (i.e., the propensity of a piece of gel, say, a pudding, to keep its shape under its own weight), measurement of a modulus makes no sense. The proper experiment is simply watching the piece, and possibly measuring the height of a specimen that will just start yielding. To ensure stand-up, the yield stress must be greater than g×r×H, where H is specimen height. For a piece 10 cm tall, this would be about 10×103×0.1=103 Pa. It should be realized that yield stress often is smaller when time scale is longer. Very weak gels were briefly discussed in Section 3.4.2. In daily life, such a system appears to be liquid—that is, it will readily flow out of a bottle if its yield stress is <10 Pa or so; but it nevertheless has elastic properties at extremely small stresses. This small yield stress may be sufficient to prevent sedimentation. A good example is soya milk (Fig. 19). Soya milk contains small particles, consisting of cell fragments and organelles. These particles aggregate, forming TABLE 6 Consistency of Gels: Specification of the Mechanical Characteristics Desired of Gels Made for a Given Purpose Property desired Relevant parameters Relevant conditions “Stand-up” Yield stress Time scale Firmness Modulus or fracture stress or yield stress Time scale, strain Shaping Yield stress + restoration time Several Handling , slicing Fracture stress and work of fracture Strain rate Eating characteristics Yield or fracture properties, or both Strain rate Streng th (e.g ., of film) Fracture properties Stress, time scale Pag e 127 TABLE 7 Gel Properties Needed to Provide Physical Stability Prevent or impede Gel property needed Motion of particles Sedimentation Hig h viscosity; or sig nificant yield stress + short restoration time Ag g reg ation Hig h viscosity or sig nificant yield stress Local volume chang es Ostwald ripening Very hig h yield stress Coalescence Very hig h yield stress Motion of liquid Leakage Low permeability and sig nificant yield stress Convection Hig h viscosity or sig nificant yield stress Motion of solute Diffusion Small diffusivity a weak reversible gel. If processing conditions are appropriate, the yield stress is sufficient to prevent these particles, and even larger particles, from sedimenting. Also, some mixtures of polysaccharides, such as solutions of xanthan gum and locust bean gum, even if very dilute, can exhibit a small yield stress (Fig. 15, curve 3). This yield stress can prevent sedimentation of any particles present [39]. Sometimes it is desired to arrest the motion of liquid, in which a case permeability is an essential parameter. According to Darcy's law, the superficial velocity n of a liquid through a porous matrix, for instance a gel, is FIGURE 19 Flow curves (shear stress vs. shear rate) of soya milk. The yield stress is g iven by the y intercept of the lines. Curves 1 and 2 are for milk made from dehulled soya beans, about 6% dry matter; 3 and 4 from whole beans, about 7% dry matter. Curves 1 and 3, soaking of the beans overnig ht at room temperature; curves 2 and 4, soaking 4 h at 60°C. (From Ref. 45.) Pag e 128 (23) where Q is the volume flow rate (m3 .sec-1) through a cross-sectional area A and Dr is the pressure difference over distance x. The permeability B (m2 ) is a material constant that varies greatly among gels. A particle gel like renneted milk (built of paracasein micelles) has a permeability of the order of 10-12 m2 , whereas a polymer gel (e.g., gelatin) typically would have a B of 10-17. In the latter case, leakage of liquid from the gel would be negligibly slow. Swelling and syneresis are additional properties of gels. Syneresis refers to expulsion of liquid from the gel, and it is the opposite of swelling. There are no general rules governing their occurrence. In a polymer gel, lowering of solvent quality (e.g., by changing temperature), adding salt (in the case of polyelectrolytes), or increasing the number of cross-links or junctions may cause syneresis. However, because both the pressure difference in Equation 23 and B are usually very small, syneresis (or swelling) often is very slow. In particle gels, syneresis may occur much faster, due to the far greater permeability. It is well known that renneted milk is prone to syneresis, an essential step in cheese making. The combination of variables influencing syneresis is intricate [68]. Transport of a solute through the liquid in a gel has to occur by diffusion, because convection generally is not possible. The diffusion coefficient D is not greatly different from that in solution, at least for small molecules in a not very concentrated gel. The Stokes relation for diffusivity D=kT/6phr, where r is molecule radius, cannot be applied. The macroscopic viscosity of the system is irrelevant, since it concerns here the viscosity as sensed by the diffusing molecules, which would be the viscosity of the solvent. On the other hand, the solute has to diffuse around the strands of the gel matrix, and the hindrance will be greater for larger molecules and smaller pores between strands in the gel. These aspects are illustrated in Figure 20. FIGURE 20 Diffusion of solutes in polysaccharide g els. Hig hly schematic examples after results by Muhr and Blanshard [42]. Pag e 129 3.5.3 Some F

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