Concentration effects on sedimentation velocity of monodispersed aerosol particles

An analytical study is investigated for the quasisteady sedimentation in a suspension of identical aerosol particles. The Knudsen and Reynolds numbers are assumed to be small, so that the fluid flow can be described by a continuum model with a hydrodynamic slip at the particle surfaces, with the flow field being governed by Stokes equations. A unit cell model is applied to predict the hydrodynamic behavior for a monodispersed system of spherical particles. Three different boundary conditions at the shell of a unit cell are discussed: no-slip, Happel-type cell and Kuwabara-type cell. Our analytical expressions of the average sedimentation velocity of particles are obtained in a closed form as functions of the volume fraction of particles. In general, as the volume fraction of particles increases, the effect of particle concentration on the mean translational velocity becomes significant.