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Two-scale competition in phase separation with shear

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) 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) \sim t^α$ of the average domain size, with $α=4/3$ and $α= 1/3$ in the flow and shear direction respectively, is shown to be obeyed.