Dejan: Ostwald Ripening of Droplets: The Role of Migration

Abstract. A conguration of near-equilibrium liquid droplets sitting on a precursor lm which wets the entire substrate can coarsen in time by two dierent mechanisms: collapse or collision of droplets. The collapse mechanism, i.e., a larger droplet grows at the expense of a smaller one by mass exchange through the precursor lm, is also known as Ostwald ripening. As was shown by Glasner and Witelski [6] in case of a one-dimensional substrate, the migration of droplets may interfere with Ostwald ripening: The conguration can coarsen by \accidental " collision rather than by collapse. We study the role of migration in case of a two-dimensional substrate for a whole range of mobilities. In this paper, we characterize the sign and the scaling of the velocity of a single droplet immersed into an environment with constant ux eld far away. These results allow us { at least for the physically relevant choices for the mobility { to describe the dynamics of a droplet conguration on a two-dimensional substrate by a system of ODEs. In particular, we nd by heuristic arguments that collision can be a relevant coarsening mechanism. 1