The Motion with Slip of a Thin Viscous Droplet over a Solid Surface

Source abstract

A thin droplet of a viscous liquid moves under the influence of surface tension across the contaminated surface of a solid. There is a slip velocity of the fluid along the surface proportional to the tangential stress. For small values of the constant of proportionality and for a significant distance from the contact line there is an asymptotic expansion for the droplet thickness. The speed of the contact line is found to depend nonlinearly on the normal derivative of the leading term.