Interactions between hard spheres sedimenting at low Reynolds number

The present article reports on experimental and numerical study for sedimentation of non-colloidal suspended particles in a viscous fluid. The hydrodynamic interactions between several particles sedimenting at low Reynolds numbers have been investigated. The numerical model is based on separation of the real velocity field into two parts. The first part is symmetrical and represents the conventional Stokes contribution. The second non-symmetrical part represents the net inertial contribution. The first contribution has been modelled using the Stokesian Dynamics method. Whereas the second one has been accounted for by assuming the validity of Faxen's first law. The numerical results agree with those from literature in the limit of the Stokes' flow regime (Re=0). Unfortunately, when Re>0, the simulation appears to quantitatively overestimate the influence of the real inertial effects. However, the accuracy of the results has been observed to be improved by introducing the empirical correction proposed by Happel et al. at the level of the individual particle. In this way, the proposed numerical tool becomes able to determine accurately the behaviour of several particles in different configurations. The agreement between the simulation results and the experimental ones is very satisfactory.