Nonequilibrium Fluctuations in Sedimenting Suspensions: A Dynamical Renormalization Group Theory
Alex Levine, Sriram Ramaswamy, Robijn Bruinsma
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 L1/2 obtained in the linearized theory of Caflisch and Luke [Phys. Fluids 28, 785 (1985)]. This is an important step towards resolving a ten-year old puzzle in the field.
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