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 combining 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.
Highlights
The interaction between self-propelled particles and fluid flows is central to many active matter systems, including swimming bacteria [1], Janus particles [2, 3], and microtubule-based active nematics [4]
We derived a reduced model using an averaging technique [24], which captures the slow motion of swimmers transverse to the deterministic orbits that is induced by weak diffusion
The steady-state phase-space densities predicted by the reduced model are in good agreement with those obtained from the original model, showing that the main cause of depletion is the noise-induced drift of swimmers in phase space
Summary
The interaction between self-propelled particles and fluid flows is central to many active matter systems, including swimming bacteria [1], Janus particles [2, 3], and microtubule-based active nematics [4]. The Fokker-Planck model provides an accurate quantitative description of the swimmer density in the channel flow, but it does not provide a clear mechanism for the transition from lowshear to high-shear depletion It obscures the link between the concentration profile and the swimmer trajectories one observes in the presence of both fluid flows and rotational noise. It leaves open the question of how nonuniform distributions in the swimmer’s phase space arise in the first place, given that typical models of swimmer motion in planar shear flows are conservative dynamical systems perturbed by noise [12–14].
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