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The behavior of a phase separating binary mixture in uniform shear flow isinvestigated by numerical simulations and in a renormalization group (RG)approach. Results show the simultaneous existence of domains of twocharacteristic scales. Stretching and cooperative ruptures of the networkproduce a rich interplay where the recurrent prevalence of thick and thindomains determines log-time periodic oscillations. A power law growth $ R(t)\sim t^{\alpha}$ of the average domain size, with $\alpha =4/3$ and $\alpha =1/3$ in the flow and shear direction respectively, is shown to be obeyed.Comment: 5 Revtex pages, 4 figure

Two-Scale Competition in Phase Separation with Shear