Gradient theory of wetting transitions

Abstract

The physics of fluids near solids is studied with the gradient theory of inhomogeneous fluids. The theory defines fluid structure in terms of the equation of state of homogeneous fluid, the fluid-solid interaction potential, and the influence parameters of inhomogeneous fluid, the latter being moments of intermolecular distributions. Density profiles predicted by the theory reveal a first-order transition from zero to nonzero contact angle, the apparent angle of intersection of a fluid interface with the solid surface. When the states of two fluid phases lie near a critical point, one of the near-critical fluids is prevented from contacting any third phase by a wetting film of the other near-critical fluid. Far enough from critical points, however, the apparent contact angle is nonzero. The surface phase transition persists to temperatures and compositions where wetting film can no longer exist as bulk phase. The surface transition terminates at a critical temperature T es , below the bulk critical temperature T c . The variation of contact angle with fluid-fluid interfacial tension, a Zisman plot, is investigated. Two simple limiting relationships are found: one valid when the wetting transition is very near critical, where Cahn's critical point scaling law holds, the other valid when the wetting transition is far from critical, where the Good-Girifalco correlation holds. Gradient theory predictions of fluid structure near solids are compared with Monte Carlo simulations of fluids near solids, and with the predictions of theories based on the approximate density functional integral equation.