Numerical Simulation of the Coherent Structures in a Homogeneous Sedimenting Suspension

Abstract

Long-range hydrodynamic interactions of the particles sedimenting in the fluid under gravity force with small Reynolds numbers lead to the large-scale velocity disturbances. Behaviour of the disturbances of the fluid velocity due to fluctuations of particle concentration is described commonly on the basis of solution of the steady Stokes equations. A stability problem for a dilute homogeneous suspension of spherical particles was considered by Koch & Shaqfeh (1989). The orientation of a particle pair are affected by a fluid shear field induced by particle density disturbances. The coupling between the pairs’ velocities and their relative position was suggested as the possible mechanism of the instability. However the linear-stability analysis based on the steady Stokes equations indicated that the suspension is neutrally stable. Nevertheless Segre et al. (1997) in their recent experiments observed the structures in a sedimenting suspension which prove that the instability still occurs.