Spinodal Decomposition of Binary Mixtures in Uniform Shear Flow

Abstract

The spinodal decomposition of binary mixtures in uniform shear flow is studied in the context of the time-dependent Ginzburg-Landau equation, approximated at one-loop order. We show that the structure factor obeys a generalized dynamical scaling with different growth exponents ${\ensuremath{\alpha}}_{x}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5/4$ and ${\ensuremath{\alpha}}_{y}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/4$ in the flow and in the shear directions, respectively. The excess viscosity $\ensuremath{\Delta}\ensuremath{\eta}$ after reaching a maximum relaxes to zero as ${\ensuremath{\gamma}}^{\ensuremath{-}2}{t}^{\ensuremath{-}3/2}$, $\ensuremath{\gamma}$ being the shear rate. $\ensuremath{\Delta}\ensuremath{\eta}$ and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains cyclically occur.