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Nonequilibrium Fluctuations in Sedimenting Suspensions: A Dynamical Renormalization Group Theory

Alex Levine·Sriram Ramaswamy·Robijn Bruinsma
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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.

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Alex Levine, Sriram Ramaswamy, Robijn Bruinsma. 1996-10-07. Nonequilibrium Fluctuations in Sedimenting Suspensions: A Dynamical Renormalization Group Theory. https://arxiv.org/abs/cond-mat/9610042

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