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 three-dimensional squirmers. The system of vertically oriented squirmers is unstable if there is no short-range repulsive force between them, even when there is a strong gravitational torque on them because they are bottom-heavy. When there is a repulsive force the positions of the squirmers are stable, but the orientations are unstable unless the bottom-heaviness parameter is sufficiently large. The predictions of instability and possible long time behavior are qualitatively the same for monolayers confined between two parallel rigid planes as for unconfined monolayers. The predictions compare favorably with published numerical simulations, and reveal the existence of additional dynamic structures not previously observed; puller-type squirmers show a greater range of structures than pushers. The use of pairwise lubrication interactions provides an efficient means of assessing stability of dense suspensions usually tackled using full numerical simulations.
4 More- Received 12 December 2018
DOI:https://doi.org/10.1103/PhysRevFluids.4.053102
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