The interplay between bulk flow and boundary conditions on the distribution of micro-swimmers in channel flow

TL;DR

This study investigates how boundary conditions influence the distribution and orientation of micro-swimmers in channel flow, emphasizing the importance of boundary effects on bulk flow behavior and swimmer accumulation patterns.

Contribution

It introduces mathematically justified boundary conditions for continuum models and explores the impact of swimmer shape, shear, and diffusion on their distribution in flow.

Findings

Boundary conditions significantly affect swimmer distribution and boundary layer formation.

Swimmer orientation depends on shape, shear, and rotational diffusion.

Preferred orientations vary from perpendicular to parallel to the surface based on conditions.

Abstract

While previous experimental and numerical studies of dilute micro-swimmer suspensions have focused on the behaviours of swimmers in the bulk flow and near boundaries, models typically do not account for the interplay between bulk flow and the choice of boundary conditions imposed in continuum models. In our work, we highlight the effect of boundary conditions on the bulk flow distributions, such as through the development of boundary layers or secondary peaks of cell accumulation in bulk-flow swimmer dynamics. For the case of a dilute swimmer suspension in Poiseuille flow, we compare the distribution (in physical and orientation space) obtained from individual based stochastic models with those from continuum models, and identify mathematically sensible continuum boundary conditions for different physical scenarios (i.e. specular reflection, uniform random reflection and absorbing boundaries). We identify that the spread of preferred cell orientations is dependent on the interplay between rotation driven by the shear flow (Jeffery orbits) and rotational diffusion. We find that in the absence of hydrodynamic wall-interactions, swimmers preferentially approach the walls perpendicular to the surface in the presence of high rotational diffusion, and that the preferential approach of swimmers to the walls is shape-dependent at low rotational diffusion (when suspensions tend towards a fully deterministic case). In the latter case, the preferred orientations are nearly parallel to the surface for elongated swimmers and nearly perpendicular to the surface for near-spherical swimmers. Furthermore, we highlight the effects of swimmer geometries and shear throughout the bulk-flow on swimmer trajectories and show how the full history of bulk-flow dynamics affects the orientation distributions of micro-swimmer wall incidence.