European Journal of Applied Mathematics

Papers

Ostwald ripening of droplets: The role of migration

KARL GLASNERa1, FELIX OTTOa2, TOBIAS RUMPa2 and DEJAN SLEPČEVa3

a1 University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721, U.S.A. email: kglasner@math.arizona.edu

a2 University of Bonn, Wegelerstraβe 10, D–53115 Bonn, Germany email: otto@iam.uni-bonn.de; rump@iam.uni-bonn.de

a3 Carnegie Mellon University, Pittsburgh, PA 15213-3890, U.S.A. email: slepcev@math.cmu.edu

Abstract

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)