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- W2040809598 abstract "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 $ell$ increases according to the power law $ellsim t^{1/3}$, 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 $ellsim t$. 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 $ellsim t$. 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 ..." @default.
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- W2040809598 date "2011-01-01" @default.
- W2040809598 modified "2023-09-25" @default.
- W2040809598 title "Upper Bounds on Coarsening Rates in Demixing Binary Viscous Liquids" @default.
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- W2040809598 doi "https://doi.org/10.1137/090775142" @default.
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