Sheared phase-separating binary mixtures with surface diffusion

The phase-separation process of a binary mixture with order-parameter-dependent mobility under shear flow is numerically studied. The ordering is characterized by an alternate stretching and bursting of domains which produce oscillations in the physical observables. The amplitude of such modulations reduce in time when the mobility vanishes in the bulk phase, disfavoring the growth of bubbles coming from bursted domains. We propose two equations for the typical sizes $R_x$ and $R_y$ of domains finding the long-time behaviors $R_x \sim t^{5/4}$ and $R_y \sim t^{1/4}$ in the flow and shear directions, respectively, in the case of surface diffusion. A reduction of the excess viscosity with increasing shear rate is observed in simulations.