Spinodal decomposition of a binary mixture in an uniform shear flow

TL;DR

This paper investigates the phase separation dynamics of a binary mixture under uniform shear flow using the time-dependent Ginzburg-Landau model, revealing anisotropic domain growth, oscillatory behavior, and specific scaling laws.

Contribution

It introduces a detailed analysis of spinodal decomposition under shear, highlighting anisotropic growth exponents and oscillatory phenomena not previously characterized.

Findings

Domains grow with different lengthscales in flow and shear directions.

The structure factor obeys generalized dynamical scaling.

Excess viscosity relaxes as a power law with oscillations.

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.