Screening mechanisms in sedimentation

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Abstract
This paper considers a mixture of sedimenting particles at low Reynolds numbers and volume fractions. Simple theoretical arguments have long suggested that for a random suspension of particles in an infinite system, the fluctuations in the velocity about the mean should diverge with system size. On the other hand, experiments have shown no such divergence. The primary goal of this paper is to examine the effect of side walls on the predicted divergence in fluctuations, through theory, scaling arguments, and numerical simulations. Side walls lead to important modifications of the standard arguments. A scaling argument (based on wall effects) is presented to rationalize recent experiments by Segré et al. [Phys. Rev. Lett. 79, 2574 (1997)]. The paper also briefly discusses the role of inertia in screening fluctuations in infinite systems when the particle Reynolds number is very low, and also the coupling between the velocity fluctuations and the mean sedimenting velocity. A physical argument suggests that in some circumstances the fluctuations give a leading order correction to the mean sedimenting velocity as a function of volume fraction.