Thermocapillary migration of an attached drop on a solid surface

Migration of a small drop of liquid, initially at rest on a level, solid surface, can be induced by means of thermocapillary forces. If a temperature gradient is imposed across the solid, it has the effect of diminishing the surface tension on the warmer side of the droplet. Consequently, migration manifests itself as the difference in surface tension preferentially draws the droplet toward the cooler region of the solid. The study describes the behavior of a droplet modeled as an infinitely long strip of finite width and arbitrary height profile, subject to a uniform temperature gradient imposed along the base. Lubrication theory is employed to determine the velocity and pressure fields within the drop, as well as the net migration velocity of the droplet as a whole. The role of the dynamic boundary condition in the vicinity of the contact lines (including the allowance for slip) on the migration velocity is highlighted.