## Properties Of Curved Interfaces

The majority of surfaces or interfaces found in food emulsions are curved rather than planar. The curvature of an interface alters its characteristics in a number of ways. The interfacial tension tends to cause an emulsion droplet to shrink in size so as to reduce the unfavorable contact area between the oil and water phases (Hunter 1986, Everett 1988). As the droplet shrinks, there is an increase in its internal pressure because of the compression of the water molecules. Eventually, an equilibrium is reached where the inward stress due to the interfacial tension is balanced by the outward stress associated with compressing the bonds between the liquid molecules inside the droplet.* At equilibrium, the pressure within the droplet is larger than that outside and can be related to the interfacial tension and radius of the droplets using the Laplace equation (Atkins 1994):

This equation indicates that the pressure difference across the surface of an emulsion droplet increases as the interfacial tension increases or the size of the droplet decreases. The properties of a material depend on the pressure exerted on it, and so the properties of a

* The shrinkage of a droplet due to the interfacial tension is usually negligibly small, because liquids have a very low compressibility.

material within a droplet are different from those of the same material in bulk (Atkins 1994). This effect is usually negligible for liquids and solids which are contained within particles that have radii greater than a few micrometers, but it does become significant for smaller particles (Hunter 1986). For example, the water solubility of oil increases as the radius of an oil droplet decreases (Dickinson 1992, Atkins 1994):

where S is the water solubility of the oil in the droplet, S* is the water solubility of bulk oil, and v is the molar volume of the oil. For a typical food oil (v = 10-3 m3 mol-1, y = 10 mJ m-2), the value of S/S* is 2.24, 1.08, 1.01, and 1.0 for oil droplets with radii of 0.01, 0.1, 1, and 10 |im, respectively. Equation 5.5 has important implications for the stability of emulsion droplets, fat crystals, and ice crystals to Ostwald ripening (Chapter 7).

So far, we have assumed that the interfacial tension of a droplet is independent of its radius. Experimental work has indicated that this assumption is valid for oil droplets, even down to sizes where they only contain a few molecules, but that it is invalid for water droplets below a few nanometers because of the disruption of long-range hydrogen bonds (Israelachvili

Emulsifier molecules have a major influence on the properties of curved surfaces and interfaces. Each type of surfactant has an optimum curvature which is governed by its molecular geometry and interactions with its neighbors (Section 4.5.3). When the curvature of an interface is equal to the optimum curvature of a surfactant monolayer, the interfacial tension is extremely low because the interactions between the emulsifier molecules are optimized and shielding between the oil and water molecules is extremely efficient. On the other hand, when the curvature of the interface is not close to the optimum curvature of the surfactant monolayer, the interfacial tension increases because the interactions between the surfactant molecules are not optimum and the shielding between oil and water molecules is less efficient. The interfacial tension of an interface therefore depends on the molecular geometry of the surfactant used.

In food systems, we are often interested in the ability of a liquid to spread over or "wet" the surface of another material. In some situations, it is desirable for a liquid to spread over a surface (e.g., when coating a food with an edible film), while in other situations it is important that a liquid does not spread (e.g., when designing waterproof packaging). When a drop of liquid is placed on the surface of a material, it may behave in a number of ways, depending on the nature of the interactions between the various types of molecules present. The two extremes of behavior that are observed experimentally are outlined below (Figure 5.8):

1. Poor wetting. The liquid gathers up into a lens, rather than spreading across the surface of a material.

2. Good wetting. The liquid spreads over the surface of the material to form a thin film, which has a liquid-gas interface and a liquid-solid interface.

The situation that occurs in practice depends on the relative magnitude of the interactions between the various types of molecules involved (i.e., solid-liquid, solid-gas, and liquidgas). A system tends to organize itself so that it can maximize the number of favorable

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