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Dynamic Theory of Suspensions with Brownian Effects

We consider a suspension of particles in a fluid settling under the influence of gravity and dispersing by Brownian motion. A mathematical description is provided by the Stokes equations and a Fokker–Planck equation for the one-particle phase space density. This is a nonlinear system that depends on a number of parametric functions of the spatial concentration of the particles. These functions are known only empirically or for dilute suspensions. We analyze the system, its stability, its asymptotic behavior under different scalings and its validity from more microscopic description. We summarize our conclusions at the end.