Dynamics of Phase Separation under Shear: A Soluble Model

TL;DR

This paper provides an exact solution for the phase separation dynamics of a binary fluid under shear, revealing anisotropic growth of characteristic length scales and matching experimental structure factor patterns.

Contribution

It introduces a solvable large-n model for phase separation under shear, deriving explicit growth laws and structure factor features.

Findings

Parallel and perpendicular length scales grow as (t^5/ln t)^{1/4} and (t/ln t)^{1/4}

Structure factor shows two parallel ridges in shear-flow plane

Results match experimental observations of phase separation under shear

Abstract

The dynamics of phase separation for a binary fluid subjected to a uniform shear are solved exactly for a model in which the order parameter is generalized to an n-component vector and the large-n limit taken. Characteristic length scales in directions parallel and perpendicular to the flow increase as (t^5/\ln t)^{1/4} and (t/\ln t)^{1/4} respectively. The structure factor in the shear-flow plane exhibits two parallel ridges as observed in experiment.