Ostwald ripening of droplets: The role of migration

Karl Glasner, Felix Otto, Tobias Rump, Dejan Slepčev

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1-67
Number of pages67
JournalEuropean Journal of Applied Mathematics
Volume20
Issue number1
DOIs
StatePublished - Feb 1 2009

ASJC Scopus subject areas

  • Applied Mathematics

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