Nonequilibrium Fluctuations in Sedimenting Suspensions: A Dynamical Renormalization Group Theory

TL;DR

This paper develops a nonlinear hydrodynamical model for sedimenting suspensions, using RG and SC methods, revealing how velocity fluctuations scale with system size and addressing a longstanding puzzle in the field.

Contribution

It introduces a nonlinear two-fluid stochastic hydrodynamical framework analyzed via RG and SC methods for sedimenting suspensions, advancing understanding of fluctuation scaling.

Findings

Velocity fluctuations are relevant in all dimensions below 6.

Strong reduction in fluctuation dependence on system size compared to linear theory.

Addresses a ten-year-old puzzle about fluctuation scaling in sedimentation.

Abstract

A nonlinear two-fluid stochastic hydrodynamical description of velocity and concentration fluctuations in sedimenting suspensions is constructed, and analyzed using self-consistent (SC) and renormalization group (RG) methods. The advection of particles by velocity fluctuations is shown to be ``relevant'' in all dimensions $d < 6$ . Both RG and SC analyses predict a strong reduction in the dependence of velocity fluctuations on system-size $L$ relative to the $L^{1/2}$ obtained in the linearized theory of Caflisch and Luke [Phys. Fluids {\bf 28}, 785 (1985)]. This is an important step towards resolving a ten-year old puzzle in the field.