Structure and rheology of binary mixtures in 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 large-N approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear. For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales $R_x$ and $R_{\perp }$ respectively in the flow direction and perpendicularly to it. In the scaling regime $R_{\perp }\sim t^{{\alpha }_{\perp }}$ and $R_x \sim \gamma t^{\alpha_x}$(withlogarithmiccorrections),$\gamma $ being the shear rate, with ${\alpha }_x=5\mathrm{/}4$ and ${\alpha }_{\perp }=1\mathrm{/}4$. The excess viscosity $\mathrm{\Delta }\eta$ after reaching a maximum relaxes to zero as ${\gamma }^{-2}{t}^{-3\mathrm{/}2}$. $\Delta \eta$ 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. In the case of an oscillating shear a cross-over phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents of the case without shear.