Stability of arrays of bottom-heavy spherical squirmers

Abstract

The incessant swimming motion of microbes in dense suspensions can give rise to striking collective motions and coherent structures. However, theoretical investigations of these structures typically utilize either computationally demanding numerical simulations or simplified continuum models. Here we analytically investigate the collective dynamics of a dense array of steady, spherical squirmers. We first calculate the forces and torques acting on two closely separated squirmers, through solving the Stokes equations to second order in the ratio of mean spacing to squirmer radius. This lubrication analysis is then used to assess the stability of a dense, vertical, planar array of identical th..