Hydrodynamic interactions between a sedimenting squirmer and a planar wall

TL;DR

This paper provides exact solutions and numerical analysis of the hydrodynamic interactions between a sedimenting microswimmer, modeled as a squirmer, and a planar wall, revealing complex gravity-induced swimming behaviors and bifurcation structures.

Contribution

It offers the first exact solutions for a squirmer near a wall facing gravity and validates a boundary integral method to explore detailed swimming dynamics and bifurcations.

Findings

Squirmer can transverse along the wall.

Existence of fixed points at specific heights and orientations.

Oscillatory and limit cycle behaviors near the wall.

Abstract

The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provides a platform for designing artificial microswimmers that can generate directed propulsion through their translation-rotation coupling near a wall. In this work we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1% of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may transverse along the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion.