Tim Pedley

Title

Towards the rheology of a concentrated array of spherical squirmers

Abstract

Continuum models of dilute suspensions of swimming micro-organisms are well established and can incorporate external (gravitational) forces and torques as well as the particle stress generated by the swimming activity. In a semi-dilute suspension of steady spherical squirmers, hydrodynamic and steric interactions between cells can be computed in a pairwise manner, and Stokesian Dynamics (SD) has been developed for higher concentrations. The stress response to externally applied simple shear has been computed for semi-dilute suspensions. Recently we have examined the stability of a concentrated planar array of identical bottom-heavy squirmers, accounting for cell-cell interactions by the use of lubrication theory. Here we seek to extend this theory to externally driven simple shear, in order to represent the macroscopic shear stress and normal stresses as functions of the shear-rate, the orientation of the applied shear to gravity, and the dimensionless parameters of the squirming motion. Preliminary results are compared with those of a full SD computation.