Sedimentation of a dilute suspension in low Reynolds number hydrodynamics

Sedimentation of a dilute disordered suspension of spherical particles in a viscous incompressible fluid is studied in the limit of low Reynolds number. The static structure factor and the velocity correlation functions of the suspended particles are shown to exhibit screening for a class of sedimentation states corresponding to definite values of the mean sedimentation velocity and horizontal and vertical velocity variance. The mean velocity and the variances, as well as the density and velocity correlation functions, are calculated in continuum approximation for given parameters characterizing the distribution in configuration space. The parameters corresponding to steady sedimentation are determined by comparison with experiment. The experimental data suggest that for given force, viscosity, and number density the parameters take unique values.