Thickness and Stability of Liquid Films on Nonplanar Surfaces

7 THICKNESS AND STABILITY OF LIQUID FILMS ON NONPLANAR SURFACES 

In this section, conditions are determined about the stability of liquid films on cylindrical and spherical solid substrates. We shall see that stability is determined by an effective disjoining pressure isotherm, which differs from the 

When a liquid film covers a planar solid surface, its equilibrium with the vapor is determined by Equation 2.23 (see Section 2.2), which takes into account the simultaneous action of both the capillary pressure and the disjoining pressure in these liquid layers. 

In the following text, we consider thin liquid layers on curved surfaces, for example, the inner and outer surfaces of cylinders. Let a be the inner or outer radius of the cyUnder. If the film thickness, h, is much smaller than the cylinder radius, (h a), we can use, as a first approximation, the isotherm of the disjoining pressure, II(A), of a planar layer. However, in the general case, the 

Let us first examine equilibrium films on the convex surface of a cylinder with a radius, a. The conditions of the equilibrium have the form given by Equation 2.249 and Equation 2.251 (see Section 2.12 for the derivation), where the effective isotherm of disjoining pressure is given by Equation 2.245, which is rewritten as 

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