Rheology of a concentrated suspension of spherical squirmers: Monolayer in simple shear flow

Abstract

A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres, the squirming parameter (proportional to the ratio of a squirmer's active stresslet to its swimming speed), the ratio of swimming speed to a typical speed of the shear flow, the bottom-heaviness parameter, the angle that the shear flow makes with the horizontal and two parameters that define the repulsive force that is required computationally to prevent the squirmers from overlapping when their distance apart is less than a critical value. The Stokesian dynamics method allows the rheological quantities to be computed for values of up to; the lubrication-theory method can be used for 0.5]]>. For non-bottom-heavy squirmers, which are unaffected by gravity, the effective shear viscosity is found to increase more rapidly with than for inert spheres, whether the squirmers are pullers (0]]>) or pushers ( < \phi. This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.