Analogies between colloidal sedimentation and turbulent convection at highPrandtl numbers

A set of coarse-grained equations of motion is proposed to describe concent ration and velocity fluctuations in a dilute sedimenting suspension of non- Brownian particles. With these equations, colloidal sedimentation is found to be analogous to turbulent convection at high Prandtl numbers. Using Krai chnan's mixing-length theory, scaling relations are obtained for the diffus ive dissipation length delta(d), the velocity variance <(delta u)over tilde > and the concentration variance <(delta phi)over tilde>. The obtained scal ing laws over varying particle radius a and-volume fraction phi(0) are in e xcellent agreement with the recent experiment by Segre et al. [Phys. Rev. L ett. 79, 2574 (1997)]. [S1063-651X(98)50912-9].