Dynamics of spherical squirmers under gravity near a no-slip planar wall

The hydrodynamic interactions between a microswimmer and a wall have ubiquitous biological and technological applications. A plethora of gravity-induced dynamics of a squirming microswimmer 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 facing perpendicularly towards or away from the planar wall. We use these solutions to validate numerical code based on a boundary integral method for arbitrary squirmer-to-wall distances down to 0.1% of the squirmer radius. We then use this boundary integral code to investigate the rich gravity-induced dynamics of a squirmer near a wall with and without repulsion, mapping out the detailed bifurcation structures of a squirmer in terms of its orientation and distance to the wall. Simulation results show 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.