Stokes' second problem and reduction of inertia in active fluids

Abstract

We study a generalized Navier-Stokes model describing the coherent thin-film flows in semiconcentrated suspensions of ATP-driven microtubules or swimming cells that are enclosed by a moving ring-shaped container. Considering Stokes' second problem, which concerns the motion of an oscillating boundary, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. In the case of a freely suspended fluid-container system that is isolated from external forces or torques, active-fluid stresses can induce large fluctuations in the container's angular momentum if the confinement radius matches certain multiples of the intrinsic vortex size of the active suspension. This effect could be utilized to transform collective microscopic swimmer activity into macroscopic motion in optimally tuned geometries.