Phase separation in a homogeneous shear flow: morphology, growth laws, and dynamic scaling

We numerically investigate the influence of a homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are clarified. Our numerical data show unambiguously that, in the shear flow, the domains have on average an elliptic shape. The time evolution of the three parameters describing this ellipse is obtained for a wide range of shear rates. For the lowest shear rates investigated, we find the growth laws for the two principal axis R perpendicular (t) approximately const, R parallel (t) approximately t, while the mean orientation of the domains with respect to the flow is inversely proportional to the strain. This implies that when hydrodynamics is neglected, a shear flow does not stop the domain growth process. We also investigate the possibility of dynamic scaling, and show that only a nontrivial form of scaling holds, as predicted by a recent analytical approach to the case of a nonconserved order parameter. We show that a simple physical argument may account for these results.