The approach to steady state in microemulsions under shear flow

TL;DR

This paper analytically investigates how microemulsions in a ternary mixture approach steady state under shear flow, using a time-dependent Ginzburg-Landau model and providing explicit correlation functions.

Contribution

It introduces an exact analytical solution for the dynamics of microemulsions under shear, extending understanding of their non-equilibrium behavior.

Findings

Derived an explicit expression for dynamic correlation functions.

Provided scattering function plots at various times and shear rates.

Validated the theoretical model with visual comparisons.

Abstract

We present an analitical study of the dynamical process of the approach to steady state for a driven diffusive system represented by the microemulsion phase of a ternary mixture. The external applied field is given by a plane Couette shear flow and the problem is studied within the framework of a time-dependent Ginzburg-Landau model. A Fokker-Planck equation for the probability distribution of the concentration fluctuations is developed in a self-consistent one-loop approximation and solved exactly, giving an analytical expression for the dynamic correlation functions of the system. For comparison to experimental work, we also show grey-scale plots of the scattering function at different times during the dynamical process for two different shear rates.