Stokes' second problem and reduction of inertia in active fluids

TL;DR

This paper investigates how active fluids, such as suspensions of microtubules or bacteria, alter the dynamics of a moving boundary, revealing increased oscillation frequencies and inertia reduction due to activity, with potential for macroscopic motion control.

Contribution

It introduces a generalized Navier-Stokes model for active fluids in thin films and demonstrates how activity reduces inertia and induces large fluctuations in container motion, revealing new physical effects.

Findings

Oscillating ring in active fluid oscillates at higher frequency.

Active stresses can induce large angular momentum fluctuations.

Inertia reduction is caused by activity in the fluid.

Abstract

We study a generalized Navier-Stokes model describing the thin-film flows in non-dilute suspensions of ATP-driven microtubules or swimming bacteria 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.