The segregation of sheared binary fluids in the Bray-Humayun model

TL;DR

This paper investigates the phase separation of sheared binary fluids using a Bray-Humayun model, revealing anisotropic domain growth, characteristic structure factors, and exponential tails in the context of shear flow.

Contribution

It applies the Bray-Humayun convection-diffusion model to analyze shear-induced phase separation, highlighting anisotropic growth laws and structure factor features.

Findings

Domains grow as t^{5/4} along flow direction

Domains grow as t^{1/4} perpendicular to flow

Structure factor exhibits four peaks and exponential tails

Abstract

The phase separation process which follows a sudden quench inside the coexistence region is considered for a binary fluid subjected to an applied shear flow. This issue is studied in the framework of the convection-diffusion equation based on a Ginzburg-Landau free energy functional in the approximation scheme introduced by Bray and Humayun [{\it Phys.Rev.Lett.} {\bf 68}, 1559, (1992)]. After an early stage where domains form and shear effects become effective the system enters a scaling regime where the typical domains sizes $L_\parallel $, $L_\perp$ along the flow and perpendicular to it grow as $t^{5/4}$ and $t^{1/4}$. The structure factor is characterized by the existence of four peaks, similarly to previous theoretical and experimental observations, and by exponential tails at large wavevectors.