Phase separation in an homogeneous shear flow: Morphology, growth laws and dynamic scaling

Abstract

We investigate numerically the influence of an 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 are obtained for a wide range of shear rates. For the lowest shear rates investigated, we find the growth laws for the two principal axis $R_{\perp }(t)\sim constant$, $R_{\parallel }(t)\sim t$, 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 investigate also the possibility of dynamic scaling, and show that only a non trivial form of scaling holds, as predicted by a recent analytical approach to the case of a non-conserved order parameter. We show that a simple physical argument may account for these results.

Version accepted for publication - Physical Review E

References in corpus (7)

• Phase Separation under Shear in Two-dimensional Binary Fluids
• Two-scale competition in phase separation with shear
• Dynamics of Phase Separation under Shear: A Soluble Model
• Structure and rheology of binary mixtures in shear flow
• Ohta-Jasnow-Kawasaki Approximation for Nonconserved Coarsening under Shear
• Coarsening Dynamics of a Nonconserved Field Advected by a Uniform Shear Flow
• The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit

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