Linear stability of an active fluid interface

TL;DR

This paper analyzes the stability of actively driven fluid interfaces in a Hele-Shaw cell, revealing conditions under which fingering instabilities occur, with implications for biological processes like wound healing and cell crawling.

Contribution

It introduces a linear stability framework for active fluid interfaces considering active agents, surface tension, and sources, highlighting new instability regimes.

Findings

Active interfaces are prone to fingering instability regardless of viscosity contrast.

Two key dimensionless parameters govern the stability of the interface.

Stability regimes are mapped in a parameter space relevant to biological systems.

Abstract

Motivated by studies suggesting that the patterns exhibited by the collectively expanding fronts of thin cells during the closing of a wound [Mark et al., Biophys. J., 98:361-370, 2010] and the shapes of single cells crawling on surfaces [Callan-Jones et al., Phys. Rev. Lett., 100:258106, 2008] are due to fingering instabilities, we investigate the stability of actively driven interfaces under Hele-Shaw confinement. An initially radial interface between a pair of viscous fluids is driven by active agents. Surface tension and bending rigidity resist deformation of the interface. A point source at the origin and a distributed source are also included to model the effects of injection or suction, and growth or depletion, respectively. Linear stability analysis reveals that for any given initial radius of the interface, there are two key dimensionless driving rates that determine interfacial stability. We discuss stability regimes in a state space of these parameters and their implications for biological systems. An interesting finding is that an actively mobile interface is susceptible to fingering instability irrespective of viscosity contrast.