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Screened and Unscreened Phases in Sedimenting Suspensions

Alex Levine·Sriram Ramaswamy·Erwin Frey·Robijn Bruinsma
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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 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 $ϕ^{-1/3}$ where $ϕ$ is the particle volume fraction, in agreement with Segrè 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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Alex Levine, Sriram Ramaswamy, Erwin Frey, Robijn Bruinsma. 1998-01-16. Screened and Unscreened Phases in Sedimenting Suspensions. https://doi.org/10.1103/physrevlett.81.5944

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