Instabilities and nonlinear dynamics of concentrated active suspensions

Suspensions of active particles, such as motile microorganisms and artificial microswimmers, are known to undergo a transition to complex large-scale dynamics at high enough concentrations. While a number of models have demonstrated that hydrodynamic interactions can in some cases explain these dynamics, collective motion in experiments is typically observed at such high volume fractions that steric interactions between nearby swimmers are significant and cannot be neglected. This raises the question of the respective roles of steric vs hydrodynamic interactions in these dense systems, which we address in this paper using a continuum theory and numerical simulations. The model we propose is based on our previous kinetic theory for dilute suspensions, in which a conservation equation for the distribution function of particle configurations is coupled to the Stokes equations for the fluid motion [D. Saintillan and M. J. Shelley, "Instabilities, pattern formation, and mixing in active suspensions," Phys. Fluids20, 123304 (2008)]10.1063/1.3041776. At high volume fractions, steric interactions are captured by extending classic models for concentrated suspensions of rodlike polymers, in which contacts between nearby particles cause them to align locally. In the absence of hydrodynamic interactions, this local alignment results in a transition from an isotropic base state to a nematic base state when volume fraction is increased. Using a linear stability analysis, we first investigate the hydrodynamic stability of both states. Our analysis shows that suspensions of pushers, or rear-actuated swimmers, typically become unstable in the isotropic state before the transition occurs; suspensions of pullers, or head-actuated swimmers, can also become unstable, though the emergence of unsteady flows in this case occurs at a higher concentration, above the nematic transition. These results are also confirmed using fully nonlinear numerical simulations in a periodic cubic domain, where pusher and puller suspensions are indeed both found to exhibit instabilities at sufficiently high volume fractions; these instabilities lead to unsteady chaotic states characterized by large-scale correlated motions and strong density fluctuations. While the dynamics in suspensions of pushers are similar to those previously reported in the dilute regime, the instability of pullers is novel and typically characterized by slower dynamics and weaker hydrodynamic velocities and active input power than in pusher suspensions at the same volume fraction.