Numerical simulation of large populations of motile cells with the Force Coupling Method: effect of shape and concentration.

Abstract

The statistics of the collective motions in an active suspension depend highly on the length scale of observation. Obtaining representative and reliable statistics requires simulating large numbers of individual interacting swimmers beyond what most simulation methods can hardly afford. As coupling between individuals are mainly mediated through fluid flow perturbations, efficient solvers for many-body hydrodynamic interactions are required. In the context of HPC (high performance computing), a highly parallelized code has been developed on an extension of the Force Coupling Method (FCM) to active suspensions. This efficient tool uses the latest FFT libraries (P3DFFT) for the Stokes flow solver and can handle the many-body hydrodynamic interactions between O(105) swimmers while accounting also for finite size effects. Since its original development by Maxey & Patel (Int. J. Mult. Flows, 2001), the FCM has been improved further and extensively validated for particulate, non-motile suspensions. Each particle is modelled via a 3D Gaussian envelope related to the actual size of the particle. Using the FCM framework, we show that additional flow perturbations induced by motile particles (pushers, pullers, and squirmers) can be included through an appropriate regularized multipole expansion of the forcing terms in the Stokes equations. Preliminary FCM simulations with spherical swimmers show very good agreement with Stokesian Dynamics results (Ishikawa et al., J. Fluid Mech. 2008, Mehandia & Nott, J. Fluid Mech. 2008) whilst the number of swimmers in the FCM simulations is two orders of magnitude larger. Our approach also captures the influence of shape (spheroidal and ellipsoidal swimmers), swimming gait (pusher, puller and squirmer) and suspension concentration on the collective dynamics and bulk properties of the suspension. The resulting statistics reveal non-trivial unsteady spatial arrangements of swimmers. Preferential orientation of the swimmers and the contribution of particle stresses to non-Newtonian effects are also currently being investigated.