Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

Abstract

Lattice-Boltzmann simulations are employed to determine the mean settling velocity and pair distribution function for spheres settling in a liquid. The Reynolds number based on the terminal velocity ranges from 1 to 20, the solid-to-fluid density ratio is ρp∕ρf=2.0, and the solid volume fraction is varied from 0.005 to 0.40. At volume fractions larger than about 0.05, the ratio of the mean settling velocity to the terminal velocity u* can be fit by a power-law expression u*=k(1−ϕ)n, where k and n are functions of the Reynolds number based on the terminal velocity. The constant k is typically about 0.86–0.92 and u* deviates from the power-law behavior in dilute suspensions. The extent of this deviation increases with increasing Reynolds number. We show that the hindered settling velocity follows a power law when the particle microstructure is similar to that in a hard-sphere suspension. The deviation from the power-law behavior can be correlated with an anisotropic microstructure resulting from wake interactions among the spheres. This microstructure, which occurs in dilute suspensions and is most pronounced at the higher Reynolds numbers explored in our study, consists of a decreased pair distribution function for pairs with vertical separation vectors and a peak in the pair distribution function for horizontal separations corresponding to about two particle diameters.