Weakly nonlinear analysis of pattern formation in active suspensions

TL;DR

This paper performs a weakly nonlinear analysis of active suspensions modeled by Saintillan--Shelley equations, identifying bifurcation types and stability loss mechanisms, with implications for understanding turbulence transitions in active matter.

Contribution

It provides an exact characterization of how isotropic suspensions of active particles lose stability and undergo bifurcations, enhancing understanding of pattern formation in active suspensions.

Findings

Identified subcritical and supercritical bifurcations in active suspensions.

Mapped stability regimes of isotropic steady states.

Predicted bifurcation behaviors that can be tested experimentally.

Abstract

We consider the Saintillan--Shelley kinetic model of active rodlike particles in Stokes flow (Saintillan & Shelley 2008a,b), for which the uniform, isotropic suspension of pusher particles is known to be unstable in certain settings. Through weakly nonlinear analysis accompanied by numerical simulations, we determine exactly how the isotropic steady state loses stability in different parameter regimes. We study each of the various types of bifurcations admitted by the system, including both subcritical and supercritical Hopf and pitchfork bifurcations. Elucidating this system's behavior near these bifurcations provides a theoretical means of comparing this model with other physical systems which transition to turbulence, and makes predictions about the nature of bifurcations in active suspensions that can be explored experimentally.