Spinodal decomposition of a binary mixture in an uniform shear flow

Abstract

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 one-loop approximation is used to study the evolution of the model. We show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales $R_x$ and $R_y$ respectively in the flow and in the shear directions. In the scaling regime $R_y\sim t^{{\alpha }_y}$ and $R_x\sim t^{{\alpha }_x}$, with ${\alpha }_x=5/4$ and ${\alpha }_y=1/4$. The excess viscosity $\Delta \eta$ after reaching a maximum relaxes to zero as ${\gamma }^{-2}{t}^{-3/2}$, $\gamma$ being the shear rate. $\Delta \eta$ 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.

4 Revtex pages, 3 figures

References in corpus (2)

• Discrete scale invariance and complex dimensions
• Condensation vs. phase-ordering in the dynamics of first order transitions

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