Structure and rheology of binary mixtures in shear flow

Results are presented for the phase separation process of a binary mixture subject to a 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 length scales R-x and R-perpendicular to, respectively, in the flow direction and perpendicularly to it. In the scaling regime R(perpendicular to)similar to t(alpha perpendicular to) and R(x)similar to gamma(alpha x) (with logarithmic corrections), gamma being the shear rate, with alpha(x)=5/4 and alpha(perpendicular to)=1/4. The excess viscosity Delta eta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2). Delta eta and other observables exhibit logarithmic-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains occur cyclically. In the case of an oscillating shear a crossover 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 as in the case without shear.