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Spinodal decomposition of a binary mixture in an uniform shear flow

Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The one-loop approximation is used to study the evolution of the model. We show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales $R_x$ and $R_y$ respectively in the flow and in the shear directions. In the scaling regime $R_y \sim t^{α_y}$ and $R_x \sim t^{α_x}$, with $α_x=5/4$ and $α_y =1/4$. The excess viscosity $Δη$ after reaching a maximum relaxes to zero as $γ^{-2}t^{-3/2}$, $γ$ being the shear rate. $Δη$ and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and break-up of domains cyclically occur.