Screened and Unscreened Phases in Sedimenting Suspensions

TL;DR

This paper models sedimenting suspensions revealing a phase transition from an unscreened phase with diverging velocity fluctuations to a screened phase with finite correlation length, using advanced hydrodynamical and renormalization techniques.

Contribution

It introduces a coarse-grained stochastic hydrodynamical framework to analyze phase transitions in sedimenting suspensions, connecting previous theoretical and experimental findings.

Findings

Identification of a non-equilibrium phase transition

Finite correlation length in the screened phase

Velocity variance becomes system size independent

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 $\phi^{-1/3}$ 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.