Self-diffusion of particles in an alternatively sheared macroscopic suspension
Résumé
In this communication, we present the preliminary results of a study of the migration motions of macroscopic spherical particles (diameter 45 μm) in a suspension submitted to an alternating plane shear flow. The shear flow is applied in two directions which are both perpendicular and in phase quadrature (circularly polarized shear). By following the particles in time and analysing their trajectory, we can compute the mean-square displacement $\sigma^{2}=\langle ({\bf R}(t)-\langle {\bf R}(t)\rangle )^{2}\rangle$ which shows a linear behaviour with time. We interpret this diffusive behaviour as a result of the hydrodynamic interactions experienced by each particle from the other particles of the suspension. These interactions come from inertial corrections to the applied flow, of non-zero mean, over long times in comparison with the period of the alternating shear. We propose a simple model, based on macroscopic Brownian-like diffusion to give an estimate of the long-time self-diffusion coefficient.
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