Simulation und Modellierung von mono- und bidispersen Suspensionen

We present a numerical simulation technique which allows us to study three-dimensional, non-Brownian particle suspensions at low Reynolds numbers. We use this simulation technique to study mono- and bidisperse suspensions. And extend the Kynch theory of sedimentation to a advection-diffusion model, which is able to describe the evolution of the concentrations of polydisperse suspensions. The simulation technique couples the particles and the fluid by means of constraint forces and is verified on various test cases like fluid flow through a bed of fixed spheres and the calculation of the volume fraction dependency of the mean sedimentation velocity. We study the velocity fluctuations of monodisperse suspensions and find that the velocity fluctuations in systems with periodic boundary conditions diverge with the system size L. The increase of the velocity fluctuations is in agreement with theoretical arguments. In the case of monodisperse suspensions where the container is bounded by walls in the directions perpendicular to gravity no such scaling is found. Based on Kynch's one-dimensional theory for the evolution of concentrations in monodisperse suspension, we formulate an extension for polydisperse suspensions. The choice of the flux function is based on Batchelor's sedimentation coefficients, which reproduces the basic features of the results of three-dimensional simulations of batch sedimentation. We extended the Kynch model to an advection-diffusion model, where the volume fraction dependency of the diffusion coefficient is described by a phenomenological expression, which shows a good agreement with experimental data. The system of coupled partial differential equations resembles the results of simulations to a high degree and allows to describe the experimental concentration profiles of monodisperse particle suspensions of a given size distribution