On the Wetting of a Surface by a Very Viscous Fluid

The movement of a small viscous droplet on a flat surface is considered in self-spreading, in roundup, and as a result of an adhesion gradient. Edge conditions based on the dynamic contact angle are discussed within the context of lubrication theory. Tangential slip at the contact line is shown to be small compared to the normal velocity. The shapes of the droplet and its contact line are calculated, and nonlinear and inertial effects assessed.