Chemo-mechanical instabilities in polarizable active layers

TL;DR

This paper develops a continuum model for polarizable active layers incorporating chemo-mechanical interactions, revealing long-wave and short-wave instabilities that lead to polarization and pattern formation.

Contribution

It introduces a novel continuum framework combining neo-Hookean elasticity with chemo-mechanical effects in active layers, analyzing instability mechanisms.

Findings

Long-wave instability causes coarsening and polarization.

Oscillatory short-wave instability occurs under compression.

Analytical and numerical methods elucidate instability regimes.

Abstract

We formulate and explore a generic continuum model of a polarizable active layer with neo-Hookean elasticity and chemo-mechanical interactions. Homogeneous solutions of the model equations exhibit a stationary long-wave instability when the medium is activated by expansion, and an oscillatory short-wave instability in the case of compressive activation. Both regimes are investigated analytically and numerically. The long-wave instability initiates a coarsening process, which provides a possible mechanism for the establishment of permanent polarization in spherical geometry.