On slippage induced by surface diffusion

The mechanism of surface diffusion is taken at the basis of the phenomenon of slippage of the contact line of a liquid film. With the aid of the condition of continuity of the traction vectors at the solid-liquid interface, we obtained an evolution equation for the velocity of the fluid particles at the wall which shows a marked resemblance with Millikan's equation for the slippage coefficient of gases and reduces, in the limit of small surface diffusivity, to the classical Stokes-Einstein model. The influence of surface roughness is explicitely taken into account and, among other results, cases of absence of slip caused by the attachment of the liquid film to the solid surface and of slippage solely induced by surface roughness are found. Finally, the effect of the surface deformation upon the surface velocity of the fluid particles is examined in some detail.