Screened and unscreened phases in sedimenting suspensions

Abstract

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 that there exist a dynamical, non-equilibrium phase transition from an "unscreened" phase in which we recover the Caflisch-Luke (R.E. Calflisch and J.H.C. Luke, Phys. Fluids 28, 759 (1985)) divergence of the velocity variance to a "screened" phase where the velocity fluctuations have a finite correlation length growing as φ^-⅓ where φ is the particle volume fraction, in agreement with segré et al, [Phys. Rev. Lett. 79, 2574 (1997)] and the velocity variance is independent of system size. Detailed predictions are made for the correlation function in both phases and at the transition.