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Ostwald ripening of droplets: The role of migration


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. D209 (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.

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[1]N. D. Alikakos , Peter W. Bates & Chen Xinfu (1994) Convergence of the Cahn–Hilliard equation to the Hele– Shaw model. Arch. Rational Mech. Anal. 128 (2), 165205.

[3]N. D. Alikakos , G. Fusco & G. Karali (2003) The effect of the geometry of the particle distribution in Ostwald ripening. Comm. Math. Phys. 238 (3), 481488.

[4]N. D. Alikakos , G. Fusco & G. Karali (2004) Ostwald ripening in two dimensions – the rigorous derivation of the equations from the Mullins–Sekerka dynamics. J. Differ. Eq. 205 (1), 149.

[5]P. Constantin , T. F. Dupont , R. E. Goldstein , L. P. Kadanoff , M. J. Shelley & S.-M. Zhou (June 1993) Droplet breakup in a model of the Hele–Shaw cell. Phys. Rev. E 47 (6), 41694181.

[6]C. M. Elliott & H. Garcke (1996) On the Cahn–Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27 (2), 404423.

[11]L. Onsager (1931) Reciprocal relations in irreversible processes, ii. Phys. Rev. 38, 2265.

[12]A. Oron , S. H. Davis & S. G. Bankof (1997) Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931980.

[13]F. Otto , T. Rump & D. Slepčev (2006) Coarsening rates for a droplet model: rigorous upper bounds. SIAM J. Math. Anal. 38 (2), 503529 (electronic).

[14]R. L. Pego (1989) Front migration in the nonlinear Cahn–Hilliard equation. Proc. R. Soc. Lond., Ser. A 422 (1863), 261278.

[15]L. M. Pismen & Y. Pomeau (2004) Mobility and interactions of weakly nonwetting droplets. Phys. Fluids 16 (7), 26042612.

[16]T. Podgorski , J.-M. Flesselles & L. Limat (2001) Corners, cusps, and pearls in running drops. Phys. Rev. Lett. 87, 036102.

[18]U. Thiele , K. Neuffer , M. Bestehorn , Y. Pomeau & M. Velarde (2001) Sliding drops in the diffuse interface model coupled to hydrodynamics. Phys. Rev. E. 64, 061601.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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