Screened and Unscreened Phases in Sedimenting Suspensions

Details Screened and Unscreened Phases in Sedimenting Suspensions Screened and Unscreened Phases in Sedimenting Suspensions

1998-01-16

arxiv.org/abs/cond-mat/9801164v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, revtex 1 figure

Scientific paper

10.1103/PhysRevLett.81.5944

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 exists a dynamical, non-equilibrium phase transition from an "unscreened" phase in which we recover the Caflisch-Luke (R.E. Caflisch 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 $\phi^{-1/3}$ where $\phi$ is the particle volume fraction, in agreement with Segr\`e 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.

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