Hydrodynamics of pulsating active liquids

TL;DR

This paper develops a hydrodynamic theory for pulsating active liquids inspired by biological tissues, capturing various dynamic states and their stability, and providing insights into wave phenomena and phase behavior.

Contribution

It introduces a novel hydrodynamic model linking mechanochemical feedback with phase and density, explaining complex pulsating behaviors in active liquids.

Findings

Identification of three main states: cycling, arrested, and wave propagating.

Demonstration that waves are secondary instabilities.

Predictions of phase boundaries via linear stability analysis.

Abstract

Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that the mechanochemical feedback between the local phase, which describes how cells deform due to autonomous driving, and the local density can be described in terms of a free energy. We demonstrate that such a feedback is compatible with the coarse-graining of a broad class of microscopic models. Our hydrodynamics captures the three main states emerging in its particle-based counterparts: a globally cycling state, a homogeneous arrested state with constant phase, and a state with propagating radial waves. Remarkably, we show that the competition between these states can be rationalized intuitively in terms of an effective landscape, and argue that waves can be regarded as secondary instabilities. Linear stability analysis of the arrested and cycling states, including the role of fluctuations, leads to predictions for the phase boundaries. Overall, our results demonstrate that our minimal, yet non-trivial model provides a relevant platform to study the rich phenomenology of pulsating liquids.