# Science at the triple point between mathematics, mechanics and materials science

## Publication 11

### Crossover of the Coarsening Rates in Demixing of Binary Viscous Liquids

##### Authors:

Felix Otto
Max Planck Institute for Mathematics in the Sciences (MIS) in Leipzig

Christian Seis
Department of Mathematics, University of Toronto Toronto, Canada

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

##### Abstract:
We consider a model for phase separation in binary viscous liquids that allows for material transport due to cross-diffusion of unlike particles and convection by the hydrodynamic bulk flow. Typically, during the evolution, the average size of domains of the pure phases increases with time --- a phenomenon called coarsening. Siggia predicts that at an initial stage, coarsening proceeds mainly by diffusion, which leads to the well-known evaporation-recondensation growth law $\ell \sim t^{1/3}$, when $\ell$ denotes the average domains size and $t$ denotes time. Furthermore, he argued that at a later stage, convection by the bulk flow becomes the dominant transport mechanism, leading to a crossover in the coarsening rates to $\ell \sim t$. Siggia's predictions have been confirmed by experiments and numerical simulations.
##### Get the paper in its entirety
12-CNA-006.pdf

Back to Publications