Liquid interfaces force-area curves

Jarvis, N.L. and Zisman, W.A. "Surface Activity of Fluorinated Organic Compounds at Organic-Liquid/Air Interfaces Part II. Surface Tension vs Concentration Curves, Adsorption Isotherms, and Force-Area Isotherms for Partially Fluorinated Carboxylic Esters," Naval Research Labs Report 5364, Surface Chemistry Branch, Chemistry Division, October 8, 1959. 

The fluid phase that fills the voids between particles can be multiphase, such as oil-and-water or water-and-air. Molecules at the interface between the two fluids experience asymmetric time-average van der Waals forces. This results in a curved interface that tends to decrease in surface area of the interface. The pressure difference between the two fluids A/j = v, — 11,2 depends on the curvature of the interface characterized by radii r and r-2, and the surface tension, If (Table 2). In fluid-air interfaces, the vapor pressure is affected by the curvature of the air-water interface as expressed in Kelvin s equation. Curvature affects solubility in liquid-liquid interfaces. Unique force equilibrium conditions also develop near the tripartite point where the interface between the two fluids approaches the solid surface of a particle. The resulting contact angle 0 captures this interaction. 

Since it is relatively easy to transfer molecules from bulk liquid to the surface (e.g. shake or break up a droplet of water), the work done in this process can be measured and hence we can obtain the value of the surface energy of the liquid. This is, however, obviously not the case for solids (see later section). The diverse methods for measuring surface and interfacial energies of liquids generally depend on measuring either the pressure difference across a curved interface or the equilibrium (reversible) force required to extend the area of a surface, as above. The former method uses a fundamental equation for the pressure generated across any curved interface, namely the Laplace equation, which is derived in the following section. 

Consider the molecules in a liquid. As shown in Figure 3.1, for a liquid exposed to a gas the attractive van der Waals forces between molecules are felt equally by all molecules except those in the interfacial region. This imbalance pulls the latter molecules towards the interior of the liquid. The contracting force at the surface is known as the surface tension. Since the surface has a tendency to contract spontaneously in order to minimize the surface area, droplets of liquid and bubbles of gas tend to adopt a spherical shape this reduces the total surface free energy. For two immiscible liquids a similar situation applies, except that it may not be so immediately obvious how the interface will tend to curve. There will still be an imbalance of intermolecular forces resulting in an interfacial tension and the interface will adopt a configuration that minimizes the interfacial free energy. 

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