科研之友
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摘要
We consider the coarsening process of a binary viscous liquid after a temperature quench. In a first, diffusion-dominated coarsening regime ("evaporation-recondensation process"), the typical length scale l increases according to the power law l similar to t(1/3), where t is the time. Siggia [Phys. Rev. A, 20 (1979), pp. 595-605] argued that in a second regime, coarsening should be mediated by viscous flow of the mixture. This leads to a crossover in the coarsening rates to the power law l similar to t. We consider a simple sharp-interface model which just allows for flow-mediated coarsening. For this model, we prove rigorously that coarsening cannot proceed faster than l similar to t. The analysis follows closely a method proposed in [R. V. Kohn and F. Otto, Comm. Math. Phys., 229 (2002), pp. 375-395], which is based on the gradient flow structure of the evolution. The analysis makes use of a Monge-Kantorowicz-Rubinstein transportation distance with logarithmic cost function as a proxy for the intrinsic distance, which is not known explicitly.
- 出版日期2011
