Stability of co-annular active and passive confined fluids

TL;DR

This paper investigates the stability of passive droplets in active nematic fluids under confinement, revealing how active, elastic, capillary, and viscous stresses interact to cause instabilities relevant to biological systems.

Contribution

It provides a linear stability analysis of passive droplets in active nematic fluids, incorporating active, elastic, and viscous stresses, and extends to active droplets in passive fluids.

Findings

Instabilities occur in both extensile and contractile active nematics.

Growth rates depend on ratios of active, elastic, capillary, and viscous stresses.

The results are relevant to biological systems like cellular compartments.

Abstract

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and cell nucleus.