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Ostwald ripening: The screening length revisited

  • Barbara Niethammer
  • Felix Otto
Original article

Abstract.

We are interested in the coarsening of a spatial distribution of two phases, driven by the reduction of interfacial energy and limited by diffusion, as described by the Mullins–Sekerka model. We address the regime where one phase covers only a small fraction of the total volume and consists of many disconnected components (“particles”). In this situation, the energetically more advantageous large particles grow at the expense of the small ones, a phenomenon called Ostwald ripening. Lifshitz, Slyozov and Wagner formally derived an evolution for the distribution of particle radii. We extend their derivation by taking into account that only particles within a certain distance, the screening length, communicate. Our arguments are rigorous and are based on a homogenization within a gradient flow structure.

Mathematics Subject Classification (1991): 35B27, 35Q72, 58E50, 82C26 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Barbara Niethammer
    • 1
  • Felix Otto
    • 1
  1. 1.Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6 und 10, 53115 Bonn, Germany DE

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