Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag
The Mullins-Sekerka sharp-interface model for phase transitions interpolates between attachment-limited and diffusion-limited kinetics if kinetic drag is included in the Gibbs-Thomson interface condition. Heuristics suggest that the typical length-scale of patterns may exhibit a crossover in coarsen...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2010
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| Summary: | The Mullins-Sekerka sharp-interface model for phase transitions interpolates between attachment-limited and diffusion-limited kinetics if kinetic drag is included in the Gibbs-Thomson interface condition. Heuristics suggest that the typical length-scale of patterns may exhibit a crossover in coarsening rate from l(t) ∼ t 1/2 at short times to l(t) ∼ t 1/3 at long times. We establish rigorous, universal one-sided bounds on energy decay that partially justify this understanding in the monopole approximation and in the associated Lifshitz-Slyozov-Wagner mean-field model. Numerical simulations for the Lifshitz-Slyozov-Wagner model illustrate the crossover behaviour. The proofs are based on a method for estimating coarsening rates introduced by Kohn and Otto, and make use of a gradient-flow structure that the monopole approximation inherits from the Mullins-Sekerka model by restricting particle geometry to spheres. Copyright © Royal Society of Edinburgh 2010. |
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