Particle distribution functions in suspensions

Abstract

Equations are derived for the temporal variation of the one- and two-particle position distribution functions in a suspension. The fluid is assumed to be incompressible, viscous, and in slow motion, i.e., to be undergoing Stokes flow. External forces such as gravity are included, but Brownian motion is omitted. The resulting system of equations for the one-particle distribution and for the mean velocity of a particle resemble the Vlasov-Poisson system for the charge density and the electric field in a plasma. The existence and uniqueness of the solution of this system is proved for a nearly uniform distribution of spherical particles. This shows that in this case the equations do not break down because of shock formation or other nonlinear effects. © 1989 American Institute of Physics.