Weakly nonlinear analysis of pattern formation in active suspensions

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.

40 pages, many figures. To appear in Journal of Fluid Mechanics

References in corpus (6)

• The hydrodynamics of swimming microorganisms
• Spontaneous motion in hierarchically assembled active matter
• Fluid Flows Created by Swimming Bacteria Drive Self-Organization in Confined Suspensions
• Excitable Patterns in Active Nematics
• Tunable dynamics of microtubule based active isotropic gels
• Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

Cited by in corpus (2)

• Orientation mixing in active suspensions
• Stability and Spatial Autocorrelations of Suspensions of Microswimmers with Heterogeneous Spin