European Journal of Applied Mathematics


Ostwald ripening of droplets: The role of migration


a1 University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721, U.S.A. email:

a2 University of Bonn, Wegelerstraβe 10, D–53115 Bonn, Germany email:;

a3 Carnegie Mellon University, Pittsburgh, PA 15213-3890, U.S.A. email:


A configuration of near-equilibrium liquid droplets sitting on a precursor film which wets the entire substrate can coarsen in time by two different 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 film, is also known as Ostwald ripening. As was shown by K. B. Glasner and T. P. Witelski (‘Collision versus collapse of droplets in coarsening of dewetting thin films’, Phys. D 209 (1–4), 2005, 80–104) in case of a one-dimensional substrate, the migration of droplets may interfere with Ostwald ripening: The configuration can coarsen by collision rather than by collapse. We study the role of migration in a two-dimensional substrate for a whole range of mobilities. We characterize the velocity of a single droplet immersed into an environment with constant flux field far away. This allows us to describe the dynamics of a droplet configuration on a two-dimensional substrate by a system of ODEs. In particular, we find by heuristic arguments that collision can be a relevant coarsening mechanism.

(Received June 14 2007)

(Revised March 20 2008)

(Online publication June 02 2008)