A model of a sessile droplet on an inclining substrate #

Chung-Hao Wang, Alexander Korobkin

11:50 Tuesday in 4Q08.

Part of the Thin films and contact lines session.

Abstract #

We investigate the quasi-static problem of a sessile droplet which is initially placed on a flat horizontal solid substrate. The substrate is then slowly inclined, leading to deformations of the droplet. The contact angle at the contact line is not constant. The contact line is assumed to be split into two parts, which are termed the pinned and unpinned parts. The contact line in the pinned part keeps its position during the inclination of the substrate. In contrast, the contact line in the unpinned part is displaced forward or backward in its normal direction in such a way the contact angle in this part is equal to its limiting value. The displacement of the contact line is assumed much smaller than the linear scale of the droplet in the horizontal direction. This is a mixed boundary value problem. The position of the contact line is unknown in advance and should be determined as part of the solution. The problem is studied using methods of asymptotic analysis. The leading order and first order solutions will be presented and discussed.