Modeling and Direct Simulation of Velocity Fluctuations and Particle-Velocity Correlations in Sedimentation

Abstract

In this paper we present direct numerical simulations of monodisperse and polydisperse suspensions of non-Brownian particles sedimenting at low Reynolds number. We describe a scheme to generate ergodic ensembles of random particulate systems and a numerical procedure for computing interactions among spherical particles based on Ewald summation technique for hydrodynamic mobility tensors. From the generation process truly random both monodisperse and multimodal size distributions of particles were obtained for dilute and moderate densities based on a minimum energy criterion. Concerned with computations of the Ewald sums our numerical procedure drastically reduces the CPU simulation time providing results of the hindered settling function in good agreement with available experimental data and asymptotic results for ordered and random periodic arrays of particles. We show new computer simulations with no flux boundary perpendicular to gravity and periodic boundary conditions in horizontal direction. The simulations reproduce the experimental correlation-time and anisotropy of the velocity fluctuations, but have the magnitude of these fluctuations increasing proportional to the size of the system.