Nonlocal diffuse interface theory of thin films and the moving contact line

Abstract

A nonlocal diffuse interface model is explored using the "lubrication approximation" applicable to thin films. We show the inconsistency of the expansion leading to a nonlinear diffusion model, and solve an untruncated integro-differential mean field equation to compute the equilibrium density profile across the fluid-vapor interface. The disjoining potential and effect of interfacial curvature are computed using approximations compatible with the lubrication approximation. We explore the thick film asymptotics, and find it coinciding with the sharp interface limit. These results are further used for computation of the static contact angle and derivation of an evolution equation for flowing films of dynamic menisci in the lubrication approximation. The structure of the evolution equation is identical to that of the sharp interface theory, but it is free from troublesome divergences near the three-phase contact line.