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© 0 © FIGURE 3.10 Distribution of ions around electrically charged emulsion droplets.

length (Figure 3.10). When two similarly charged droplets approach each other, their counterion clouds overlap, and this gives rise to a repulsive interaction (Evans and Wennerstrom 1994). There are two major contributions to this electrostatic interaction: (1) an enthalpic contribution associated with the change in the strength of the attractive and repulsive electrostatic interactions between the various charged species involved and (2) an entropic contribution associated with the confinement of the counterions between the droplets to a smaller volume. The entropic contribution is strongly repulsive, whereas the enthalpic contribution is weakly attractive, and therefore the overall interaction is repulsive (Evans and Wennerstrom 1994). The fact that the major contribution to the electrostatic interaction is entropic means that it increases in strength with increasing temperature.

Theoretical equations based on the Poisson-Boltzmann theory have been derived to relate the electrostatic interdroplet pair potential to the physical characteristics of the emulsion droplets and the intervening electrolyte solution (Hiemenz 1986, Hunter 1986, Carnie et al. 1994, Okshima 1994, Sader et al. 1995). The full equations cannot be solved analytically, but they can be solved numerically on a computer (Carnie et al. 1994) or by making simplifying assumptions that lead to relatively simple equations that are applicable under certain conditions (Sader et al. 1995).

If it is assumed that there is a relatively low surface potential (¥s < 25 mV) and that the Debye screening length and surface-to-surface separation are much less than the droplet size (i.e., K-1 < r/10 and h < r/10), then fairly simple expressions for the electrostatic interdroplet pair potential between two similar droplets can be derived (Hunter 1986).

At constant surface potential:

At constant surface charge:

The smallest droplets in most food emulsions are about 0.1 |im in radius, which means that these equations are likely to be applicable at droplet separations less than about 10 nm and at electrolyte concentrations greater than about 1 mM. Whether the electrostatic interaction between two droplets takes place under conditions of constant surface potential or constant surface charge depends on the ability of the surface groups to regulate their charge (Israelachvili 1992).

© 0 © FIGURE 3.10 Distribution of ions around electrically charged emulsion droplets.

So far, it has been assumed that the charge on the droplets is evenly spread out over the whole of the surface. In practice, droplets may have surfaces which have some regions which are negatively charged, some regions which are positively charged, and some regions which are neutral. The heterogeneous distribution of the charges on a droplet may influence their electrostatic interactions (Holt and Chan 1997). Thus, two droplets (or molecules) which have no net charge may still be electrostatically attracted to each other if they have patches of positive and negative charge.

3.4.3.1. Charge Regulation

As two similarly charged emulsion droplets move closer together, the interaction between them becomes increasingly repulsive. Certain systems are capable of reducing the magnitude of this increase by undergoing structural rearrangements, which is referred to as charge regulation. For example, the surface charge may be regulated by adsorption-desorption of ionic emulsifiers (Yaminsky et al. 1996a,b) or by association-dissociation of charged groups (Hunter 1986, 1989). Depending on the physical characteristics of a system, it is possible to discern three different situations which may occur when two droplets approach each other (Reiner and Radke 1993):

1. Constant surface charge. As the droplets move closer together, the number of charges per unit surface area remains constant (i.e., no adsorption-desorption or association-dissociation of ions occurs). In this case, the electrostatic repulsion between the surfaces is at the maximum possible value because the surfaces are fully charged.

2. Constant surface potential. As the droplets move closer together, the number of charges per unit surface area decreases (e.g., by an adsorption-desorption or association-dissociation mechanism). In this case, the electrostatic repulsion between the surfaces is at the minimum possible value because the surface charge is reduced.

3. Charge regulation. In reality, the electrostatic repulsion usually falls somewhere between the two extremes mentioned above because of charge regulation. The number of charges per unit surface area depends on the characteristics of the adsorption-desorption or association-dissociation mechanisms (e.g., the surface activity of an ionic emulsifier or the surface pK value of an ionizable group). These processes take a finite time to occur, and therefore the surface charge density may also depend on the speed at which the droplets come together (Israelachvili 1992, Israelachvili and Berman 1995).

The variation of the interdroplet pair potential with separation is shown for two similarly charged droplets in Figure 3.11. There is a strong repulsive interaction between the droplets at close separations, which decreases as the droplets move farther apart. This repulsive interaction is often sufficiently strong and long range to prevent droplets from aggregating. At relatively large droplet separations, Equations 3.14 and 3.15 give approximately the same predictions for the electrostatic interaction, but at closer separations, the assumption of constant charge predicts a significantly higher repulsion than the assumption of constant potential (Figure 3.11). In practice, the interdroplet pair potential always lies somewhere between these two extremes and depends on the precise nature of the system.

The magnitude and range of the electrostatic repulsion between two droplets decrease as the ionic strength of the solution separating them increases because of electrostatic screening (i.e., the accumulation of counterions around the surfaces) (Figure 3.12). This has important

FIGURE 3.11 Comparison of electrostatic interaction between a pair of emulsion droplets under conditions of constant surface charge and constant surface potential.

consequences for the texture and stability of many food emulsions and explains the susceptibility of protein-stabilized emulsions to flocculation when the electrolyte concentration is increased above a critical level (Demetriades et al. 1997a).

3.4.3.2. Effect of Electrolyte on Surface Potential

When the electrostatic interaction between a charged surface and the counterions is relatively weak, the surface charge density is simply related to the surface potential: o = This equation indicates that the electrical properties of a surface are altered by the presence of electrolytes in the aqueous phase and has important consequences for the calculation of the

Emulsions Flocculation

FIGURE 3.12 Electrolyte reduces the magnitude and range of the electrostatic repulsion between emulsion droplets due to electrostatic screening.

FIGURE 3.12 Electrolyte reduces the magnitude and range of the electrostatic repulsion between emulsion droplets due to electrostatic screening.

electrostatic interdroplet pair potential. If the surface charge density remains constant when salt is added to the aqueous phase, then the surface potential decreases (because less energy is needed to bring a charge from infinity to the droplet surface through an electrolyte solution). Conversely, if the electrical potential remains constant as the salt concentration is increased, this means that the surface charge density must decrease. In practice, both o and tend to change simultaneously. In food emulsions, one can usually assume that the surface charge density is independent of ionic strength at low to moderate electrolyte concentrations, and so one must take into account the variation in with ionic strength when calculating the electrostatic repulsion.

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