Swimmer dynamics in externally-driven fluid flows: The role of noise

TL;DR

This paper develops a theoretical framework to analyze how random fluctuations like diffusion and tumbling influence the ability of microswimmers to cross flow barriers, revealing noise's significant role in swimmer transport.

Contribution

It introduces an asymptotic semiclassical method to compute crossing probabilities and orientation distributions of swimmers in fluid flows, incorporating noise effects.

Findings

Noise increases crossing probability of flow barriers.

Semiclassical approximation matches Monte Carlo results.

Orientation distribution affected by rotational diffusion and tumbling.

Abstract

We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e. sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmer's Fokker-Planck equation. Using the semiclassical technique, we compute (i) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (ii) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.