Noise-induced aggregation of swimmers in the Kolmogorov flow

TL;DR

This paper models the behavior of microswimmers in a laminar flow, revealing how noise and flow parameters influence their aggregation patterns and providing a reduced stochastic description to predict their steady-state distributions.

Contribution

It introduces a weak-noise averaging approach to explain swimmer aggregation transitions in Kolmogorov flow, linking phase-space dynamics with steady-state distributions.

Findings

Swimmers favor different drift modes depending on their shape and speed.

Aggregation shifts from low-shear to high-shear regions as parameters vary.

The averaging method accurately predicts steady-state distributions.

Abstract

We investigate a model for the dynamics of ellipsoidal microswimmers in an externally imposed, laminar Kolmogorov flow. Through a phase-space analysis of the dynamics without noise, we find that swimmers favor either cross-stream or rotational drift, depending on their swimming speed and aspect ratio. When including noise, i.e. rotational diffusion, we find that swimmers are driven into certain parts of phase space, leading to a nonuniform steady-state distribution. This distribution exhibits a transition from swimmer aggregation in low-shear regions of the flow to aggregation in high-shear regions as the swimmer's speed, aspect ratio, and rotational diffusivity are varied. To explain the nonuniform phase-space distribution of swimmers, we apply a weak-noise averaging principle that produces a reduced description of the stochastic swimmer dynamics. Using this technique, we find that certain swimmer trajectories are more favorable than others in the presence of weak rotational diffusion. By combing this information with the phase-space speed of swimmers along each trajectory, we predict the regions of phase space where swimmers tend to accumulate. The results of the averaging technique are in good agreement with direct calculations of the steady-state distributions of swimmers. In particular, our analysis explains the transition from low-shear to high-shear aggregation.