The effect of a field-dependent mobility on the phase-ordering dynamics of a binary mixture subject to an uniform shear flow is investigated. The problem is addressed in the context of the time-dependent Ginzburg-Landau equation with an external velocity term, using a self-consistent approximation to study the evolution of the model. Assuming a scaling ansatz for the structure factor, we are able to predict the asymptotic behavior of the observables in the scaling regime. All the observables show log-time periodic oscillations which we interpret as due to a cyclical mechanism of stretching and break-up of domains. These oscillations are dumped as consequence of the vanishing of the mobility in the bulk phase.

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