Two-Scale Competition in Phase Separation with Shear

Abstract

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power-law growth $R(t)\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$ of the average domain size, with $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4/3$ and $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$ in the flow and shear direction, respectively, is shown to be obeyed.