On the stabilizing effect of swimming in an active suspension

Abstract

We consider a kinetic model of an active suspension of rod-like microswimmers. In certain regimes, swimming has a stabilizing effect on the suspension. We quantify this effect near homogeneous isotropic equilibria ψ = const. Notably, in the absence of particle (translational and orientational) diffusion, swimming is the only stabilizing mechanism. On the torus, in the non-diffusive regime, we demonstrate linear Landau damping up to the stability threshold predicted in the applied literature. With small diffusion, we demonstrate nonlinear stability of arbitrary equilibrium values for pullers (rear-actuated swimmers) and enhanced dissipation for both pullers and pushers (front-actuated swimmers) at small concentrations. On the whole space, we prove nonlinear stability of the vacuum equilibrium due to generalized Taylor dispersion. Contents 1. Introduction 1 2. Landau damping 9 3. Taylor dispersion 15 4. Enhanced dissipation 23 Appendix A. Nondimensionalization 32 Appendix B. Strong solution theory 33 Appendix C. Proof of Lemma 4.3 36 References 37

Weakly nonlinear analysis of pattern formation in active suspensions

“…As noted in , 'the finiteness of the domain may act to stabilize the system'. Indeed, the stabilizing effects of mixing on T d (d = 2, 3) due to swimming are studied in Albritton & Ohm (2022) and play a role in the patterns observed here.…”

“…Our numerical tests indicate that the eigenvalues calculated in § 2.3 provide a fairly full picture of the stability boundaries, but it would be reassuring to verify this rigorously, particularly in the absence of translational or rotational diffusion. See forthcoming work (Albritton & Ohm 2022) where…”