Screened and Unscreened Phases in Sedimenting Suspensions

A coarse-grained stochastic hydrodynamical description of velocity and concentration fluctuations in steadily sedimenting suspensions is constructed and analyzed using self-consistent and renormalization-group methods. We find a nonequilibrium phase transition from an “unscreened” phase in which we recover the Caflisch-Luke [Phys. Fluids 28, 759 (1985)] divergence of the velocity variance to a “screened” phase where the fluctuations have a finite correlation length depending on the volume fraction $\phi$ as ${\phi }^{-1\mathrm{}/3}$, in agreement with Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)] (if their observation of a $\phi$-independent diffusivity is used), and the velocity variance is independent of system size.