Thermocapillary migration of pendant droplets

Abstract

The study focuses on the numerical evolution of a droplet, which hangs from a horizontal plane and moves due to thermocapillary effects. It is assumed that the liquid completely wets the substrate, that the surface tension of the liquid decreases linearly with temperature, that the imposed thermal gradient on the substrate is uniform, and that heat transport within the droplet is such that the temperature of its surface replicates that of the substrate. These assumptions, along with the lubrication approximation, allow for obtaining a differential equation that governs the evolution of the droplet. By introducing appropriate scales, this equation has a single dimensionless parameter, which expresses the ratio of gravitational to thermocapillary forces. Numerical solutions show that at sufficiently large volumes or weak thermal gradients, the droplet moves while maintaining a steady, slightly decreasing its volume, and leaving behind a tail whose width is uniform. By contrast, if the droplet is small or the thermal gradient is strong, it advances and stretches in the direction of movement.