  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.
