# Edge instability in incompressible planar active fluids

## TL;DR

This paper performs a linear stability analysis of a 2D incompressible active fluid model to understand interfacial instability, revealing that density variation is crucial for fingering instability in tissue regeneration.

## Contribution

It improves upon previous models by analyzing the stability of an active fluid with an open interface, emphasizing the role of density variation in instability.

## Key findings

- Fingering stability is absent in the minimal model for relevant parameters.
- Density variation is key to fingering instability in tissue regeneration.
- The model categorizes the stability of active fluid interfaces.

## Abstract

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used in J. Zimmermann, M. Basan and H. Levine, Euro. Phys. J.: Special Topics 223, 1259 (2014), we perform a linear stability analysis on a two dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorise the stability of the model and find that for experimentally relevant parameters, fingering stability is always absent in this minimal model. Our results point to the crucial importance of density variation in the fingering instability in tissue regeneration.