Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 15
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Oliva-Ramirez, M. Macías-Montero, M. Borras, A. and González-Elipe, A. R. 2016. Ripening and recrystallization of NaCl nanocrystals in humid conditions. RSC Adv., Vol. 6, Issue. 5, p. 3778.


    Prüss, Jan Simonett, Gieri and Wilke, Mathias 2016. On Thermodynamically Consistent Stefan Problems with Variable Surface Energy. Archive for Rational Mechanics and Analysis, Vol. 220, Issue. 2, p. 603.


    Diop, Daouda Keïta Simonot, Lionel Destouches, Nathalie Abadias, Grégory Pailloux, Frédéric Guérin, Philippe and Babonneau, David 2015. Magnetron Sputtering Deposition of Ag/TiO2Nanocomposite Thin Films for Repeatable and Multicolor Photochromic Applications on Flexible Substrates. Advanced Materials Interfaces, Vol. 2, Issue. 14, p. 1500134.


    Kim, Jinho O'Neill, John D. and Vunjak-Novakovic, Gordana 2015. Rapid retraction of microvolume aqueous plugs traveling in a wettable capillary. Applied Physics Letters, Vol. 107, Issue. 14, p. 144101.


    Asgari, M and Moosavi, A 2014. Interaction of 3D dewetting nanodroplets on homogeneous and chemically heterogeneous substrates. Journal of Physics: Condensed Matter, Vol. 26, Issue. 22, p. 225001.


    Garcia, Angel A and Druschel, Gregory K 2014. Elemental sulfur coarsening kinetics. Geochemical Transactions, Vol. 15, Issue. 1,


    KITAVTSEV, GEORGY 2014. Coarsening rates for the dynamics of slipping droplets. European Journal of Applied Mathematics, Vol. 25, Issue. 01, p. 83.


    Sui, Mao Li, Ming-Yu Kim, Eun-Soo and Lee, Jihoon 2014. Mini droplets to super droplets: evolution of self-assembled Au droplets on GaAs(111)B and (110). Journal of Applied Crystallography, Vol. 47, Issue. 2, p. 505.


    Asgari, M and Moosavi, A 2013. Coarsening dynamics of nanodroplets on topographically structured substrates. Journal of Physics: Condensed Matter, Vol. 25, Issue. 4, p. 045012.


    Constantinescu, Adi Golubović, Leonardo and Levandovsky, Artem 2013. Beyond the Young-Laplace model for cluster growth during dewetting of thin films: Effective coarsening exponents and the role of long range dewetting interactions. Physical Review E, Vol. 88, Issue. 3,


    Prüss, Jan Simonett, Gieri and Zacher, Rico 2013. Qualitative Behavior of Solutions for Thermodynamically Consistent Stefan Problems with Surface Tension. Archive for Rational Mechanics and Analysis, Vol. 207, Issue. 2, p. 611.


    Asgari, M. and Moosavi, A. 2012. Coarsening dynamics of dewetting nanodroplets on chemically patterned substrates. Physical Review E, Vol. 86, Issue. 1,


    Kitavtsev, Georgy Recke, Lutz and Wagner, Barbara 2012. Asymptotics for the Spectrum of a Thin Film Equation in a Singular Limit. SIAM Journal on Applied Dynamical Systems, Vol. 11, Issue. 4, p. 1425.


    Li, Ming-Yu Hirono, Yusuke Koukourinkova, Sabina D Sui, Mao Song, Sangmin Kim, Eun-Soo Lee, Jihoon and Salamo, Gregory J 2012. Formation of Ga droplets on patterned GaAs (100) by molecular beam epitaxy. Nanoscale Research Letters, Vol. 7, Issue. 1, p. 550.


    Kitavtsev, G Recke, L and Wagner, B 2011. Centre manifold reduction approach for the lubrication equation. Nonlinearity, Vol. 24, Issue. 8, p. 2347.


    ×
  • European Journal of Applied Mathematics, Volume 20, Issue 1
  • February 2009, pp. 1-67

Ostwald ripening of droplets: The role of migration

  • KARL GLASNER (a1), FELIX OTTO (a2), TOBIAS RUMP (a2) and DEJAN SLEPČEV (a3)
  • DOI: http://dx.doi.org/10.1017/S0956792508007559
  • Published online: 01 February 2009
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. 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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×