Nonlocal diffuse interface theory of thin films and the moving contact line - art. no. 021603

A nonlocal diffuse interface model is explored using the "lubrication appro ximation" applicable to thin films. We show the inconsistency of the expans ion leading to a nonlinear diffusion model, and solve an untruncated integr o-differential mean field equation to compute the equilibrium density profi le across the fluid-vapor interface. The disjoining potential and effect of interfacial curvature are computed using approximations compatible with th e lubrication approximation. We explore the thick film asymptotics, and fin d it coinciding with the sharp interface limit. These results are further u sed for computation of the static contact angle and derivation of an evolut ion equation for flowing films of dynamic menisci in the lubrication approx imation. The structure of the evolution equation is identical to that of th e sharp interface theory, but it is free from troublesome divergences near the three-phase contact line.