# Stability of the interface of an isotropic active fluid

## TL;DR

This paper analyzes the linear stability of isotropic active fluids in various geometries, revealing how activity influences interface stability and mode propagation, with implications for understanding active matter behaviors.

## Contribution

It provides a comprehensive stability analysis of isotropic active fluids across different geometries using hydrodynamic theory, highlighting activity-induced instabilities and mode propagation.

## Key findings

- Passive cases are stable in film and spherical droplet geometries.
- Large activity induces instability in film and spherical droplet geometries.
- Activity causes propagating damped or growing modes in all geometries.

## Abstract

We study the linear stability of an isotropic active fluid in three different geometries: a film of active fluid on a rigid substrate, a cylindrical thread of fluid, and a spherical fluid droplet. The active fluid is modeled by the hydrodynamic theory of an active nematic liquid crystal in the isotropic phase. In each geometry, we calculate the growth rate of sinusoidal modes of deformation of the interface. There are two distinct branches of growth rates; at long wavelength, one corresponds to the deformation of the interface, and one corresponds to the evolution of the liquid crystalline degrees of freedom. The passive cases of the film and the spherical droplet are always stable. For these geometries, a sufficiently large activity leads to instability. Activity also leads to propagating damped or growing modes. The passive cylindrical thread is unstable for perturbations with wavelength longer than the circumference. A sufficiently large activity can make any wavelength unstable, and again leads to propagating damped or growing modes.