Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids

TL;DR

This paper analyzes how shear flow influences the stability of domains in two-dimensional phase-separating binary fluids, revealing that shear stabilizes certain instabilities and aligns with experimental observations.

Contribution

It provides an analytical linear stability analysis of phase-separated domains under shear flow using coupled Cahn-Hilliard and Stokes equations.

Findings

Unstable varicose mode leads to coarsening in quiescent fluids.

External shear flow stabilizes the varicose instability.

Results qualitatively match experimental observations.

Abstract

We perform a linear stability analysis of extended domains in phase-separating fluids of equal viscosity, in two dimensions. Using the coupled Cahn-Hilliard and Stokes equations, we derive analytically the stability eigenvalues for long wavelength fluctuations. In the quiescent state we find an unstable varicose mode which corresponds to an instability towards coarsening. This mode is stabilized when an external shear flow is imposed on the fluid. The effect of the shear is seen to be qualitatively similar to that found in experiments.