Screened and Unscreened Phases in Sedimenting Suspensions

Alex Levine; Sriram Ramaswamy; Erwin Frey; Robijn Bruinsma

doi:10.1103/PhysRevLett.81.5944

Screened and Unscreened Phases in Sedimenting Suspensions

Alex Levine, Sriram Ramaswamy, Erwin Frey, and Robijn Bruinsma

Phys. Rev. Lett. 81, 5944 – Published 28 December 1998

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 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 $φ$ as $φ^{- 1 / 3}$ , in agreement with Segrè et al. [Phys. Rev. Lett. 79, 2574 (1997)] (if their observation of a $φ$ -independent diffusivity is used), and the velocity variance is independent of system size.

Received 15 January 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.5944

Authors & Affiliations

Alex Levine^1,*, Sriram Ramaswamy², Erwin Frey^3,†, and Robijn Bruinsma⁴

¹Exxon Research and Engineering, Route 22E, Clinton Township, Annandale, New Jersey 08801
²Department of Physics, Indian Institute of Science, Bangalore 560 012, India
³Institut für Theoretische Physik, Physik-Department der Technischen, Universität München, D-85747 Garching, Germany
⁴Department of Physics, University of California, Los Angeles, California 90095

^*Present address: Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, PA 19104.
^†Present address: Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138.