An analysis based on the energy conservation is presented for the self-propelled droplet during coalescence of two droplets of the same size over a superhydrophobic rough surface. The self-propelled behavior occurs only for the coalescence of droplets with a certain range of radius. An analytical relation is established among the coalescence-induced velocity, surface energy, viscous dissipation, and droplet size if gravity is negligible. The coalescence-induced velocity increases with increasing droplet size to a maximum and then decreases with the size, which is in good accord with the experimental observation reported in the literature.

This paper was published as:
Wang FC; Yang FQ; Zhao YP. Size effect on the coalescence-induced self-propelled droplet. APPLIED PHYSICS LETTERS, 98(5):053112(2011)