Stability of cylindrical domains in phase-separating binary fluids in shear flow

TL;DR

This paper analyzes how shear flow influences the stability of cylindrical domains in phase-separating binary fluids, revealing that shear can suppress instabilities and stabilize the domains, aligning with experimental observations.

Contribution

It provides an analytical stability analysis of cylindrical domains under shear flow using coupled Cahn-Hilliard and Stokes equations, considering arbitrary viscosity contrasts.

Findings

Shear flow suppresses Rayleigh and thermodynamic instabilities.

Shear can stabilize cylinders against varicose perturbations.

Results align with observed 'string phase' in experiments.

Abstract

The stability of a long cylindrical domain in a phase-separating binary fluid in an external shear flow is investigated by linear stability analysis. Using the coupled Cahn-Hilliard and Stokes equations, the stability eigenvalues are derived analytically for long wavelength perturbations, for arbitrary viscosity contrast between the two phases. The shear flow is found to suppress and sometimes completely stabilize both the hydrodynamic Rayleigh instability and the thermodynamic instability of the cylinder against varicose perturbations, by mixing with nonaxisymmetric perturbations. The results are consistent with recent observations of a ``string phase'' in phase-separating fluids in shear.