EQUILIBRIUM THIN-FILMS ON ROUGH SURFACES .1. CAPILLARY AND DISJOINING EFFECTS

Equilibrium menisci of wetting films on rough solid surfaces are calculated as Galerkin/finite element solutions of the augmented Young-Laplace (AYL) equation. Solutions are obtained for films on one-dimensional and two-dimensional periodic surfaces. The numerical solutions of the AYL equation indicate that wetting fluid distributions are characterized by three regimes: a thin-film regime dominated by disjoining pressure effects, a transition regime in which both disjoining pressure and capillarity are important, and a bulk regime dominated by capillarity. The interplay of capillarity, disjoining pressure, and the length scale of surface roughness is cast in the form of two dimensionless parameters, the values of which determine the distribution of the wetting fluid on the solid. Moreover, the transition from the thin films to pendular structures is traced through sequences of solutions of the AYL equation. The contributions of thin films and pendular structures to the total inventory of the wetting phase are analyzed by comparing analytical solutions of the Young-Laplace and the disjoining pressure equations to the finite element solutions of the AYL equation.