Multilayer wetting phenomenon at a binary liquid-vapor interface. I. Theory

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Abstract
An analytic theory of the wetting phenomenon is presented which is an extension of the phenomenological theory of de Gennes and includes gravitational, van der Waals, and surface-tension contributions. The equation describing wetting is derived from the equality of chemical potentials where the derivatives with respect to both area and thickness appear—this ensures that capillary-wave fluctuations are not suppressed at the surface. The wetting equation can have multiple solutions for the wetting thickness; the equilibrium solution is that solution which is thermodynamically stable and has the lowest wetting surface tension. The conditions for wetting and adsorption are also clarified, and it is demonstrated that density, concentration, and capillary-wave fluctuations are included intrinsically within the surface-tension terms.