Dynamic structures in concentrated suspensions of spherical squirmers*

Concentrated suspensions of micro-organisms exhibit striking collective motions, but characterisation of the bulk rheological properties have been limited by a lack of suitably efficient numerical methods. A vertical monolayer of identical spherical squirmers, which may be bottom-heavy, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. The effective suspension viscosity is calculated for monolayers subjected to either a linear shear flow or pressure-driven flow, as functions of the areal fraction of spheres, the squirmers’ swimming properties, and external torque conditions. We characterise ephemeral structures, force chains and jamming events within the suspension, and reconcile these with the bulk rheological properties. This work suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and successfully connects microscale structural features in the suspension with bulk rheological attributes.