Screening in sedimenting suspensions

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Abstract
Caflisch & Luke (1985) showed that, owing to the long range of the hydrodynamie interactions, the variance of the sedimentation velocity in a random suspension with uniform probability for the positions of the particles is divergent in the sense that it grows without bound as the macroscopic linear dimension of the settling vessel is increased. It is shown here, however, that a Debye-like screening of a particle's velocity disturbance, leading to a finite variance, will occur if the pair probability reflects a net deficit of one particle in the vicinity of each particle. The three-particle interactions, which determine the structure of a dilute, monodisperse suspension of spheres, lead to a deficit of neighbouring particles. The magnitude and range of this deficit are shown to be sufficient to lead to a Debye-like screening of the velocity disturbance at a radial distance of order aϕ−1, where a is the particle radius and ϕ their volume fraction. A self-consistent approximation to the screened conditional average velocity field and pair distribution is presented. The screening leads to a variance of the particle velocity and a particle tracer diffusion coefficient that are finite and of order Us2 and Usaϕ−1, respectively, where Vs is the Stokes settling velocity of the particles in unbounded fluid.