Analogies between colloidal sedimentation and turbulent convection at high Prandtl numbers

A set of coarse-grained equations of motion is proposed to describe concentration 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 Kraichnan’s mixing-length theory, scaling relations are obtained for the diffusive dissipation length ${\delta }_d,$ the velocity variance $\delta ũ,$ and the concentration variance $\delta \phi ̃.$ The obtained scaling laws over varying particle radius $a$ and volume fraction ${\phi }_0$ are in excellent agreement with the recent experiment by Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)].