Non-reciprocal mixtures in suspension: the role of hydrodynamic interactions

TL;DR

This paper investigates how hydrodynamic interactions influence the stability of emergent flocking waves in non-reciprocal scalar mixtures within suspensions, revealing that non-reciprocity can stabilize these waves despite linear instabilities.

Contribution

It introduces a coupled non-reciprocal Cahn-Hilliard model with fluid dynamics to study stability of flocking waves in active suspensions, highlighting the stabilizing role of non-reciprocity.

Findings

Non-reciprocal coupling leads to stable traveling waves in suspensions.

Linear instability occurs for certain active stress signs.

Numerical simulations show non-reciprocity stabilizes waves across phase space.

Abstract

The collective chasing dynamics of non-reciprocally coupled densities leads to stable travelling waves which can be mapped to a model for emergent flocking. In this work, we couple the non-reciprocal Cahn-Hilliard model (NRCH) to a fluid to minimally describe scalar active mixtures in a suspension, with the aim to explore the stability of the waves, i.e. the emergent flock in the presence of self-generated fluid flows. We show that the emergent polarity is linearly unstable to perturbations for a specific sign of the active stress recalling instabilities of orientational order in a fluid. Using numerical simulations, we find however that non-reciprocity stabilizes the waves against the linear instability in a large region of the phase space.