Dynamics of a membrane coupled to an active fluid

TL;DR

This paper presents a theoretical study of membrane dynamics coupled to an active fluid with rotational symmetry, revealing conditions for stability and instability depending on fluid viscosity and activity type.

Contribution

It introduces a model for membrane-active fluid interactions with rotational symmetry, predicting finite-wavelength instability for contractile fluids and long-wavelength instability for extensile fluids.

Findings

Contractile active fluid can slow membrane relaxation at high viscosity.

Finite-wavelength instability occurs in strong contractility limit.

Extensile active fluid causes long-wavelength instability.

Abstract

The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. On the other hand, a membrane coupled to an extensile active fluid is always unstable against long wavelength perturbations due to splay induced flows.