Steady-state sedimentation of non-Brownian particles with finite Reynolds number

Abstract

The sedimentation of non-Brownian particles has been studied extensively, both experimentally and through computer simulations. Currently there is quite a good understanding of statistical properties of sedimentation of spherical particles under low Reynolds number conditions. The research of the effects of finite Reynolds number is, however, quite limited.

The aim of this thesis is to study the significance of inertial effects in steady state sedimentation under conditions where the particle size based Reynolds number is small but significant. The known analytical results for single or few sedimenting bodies show that the inertial effects affect some quantities only by an additional correction term that is proportional to the Reynolds number. There are, however, certain type of interactions that entirely vanish in the zero Reynolds number limit.

In this thesis the many-body sedimentation is studied by numerical simulations. From the large variety of possible simulation techniques an immersed boundary method has been used since it allows the study of finite Reynolds number sedimentation efficiently and does not restrict the shape of the suspended particles. The method is based on solving the partial differential equations governing the time evolution of the continuum fluid phase. The embedded solid particles are not treated by explicite boundary conditions but by introducing an equivalent force density to the fluid.

First, we study the case of spherical particles in a system with periodic boundaries in all directions. We show that the velocity distribution of the particles is non-Gaussian and explain this as an effect arising from the local fluctuations in the density of the suspension. Next, we consider the effect of system size by confining the suspension in one horizontal dimension by solid walls. We show the effect of the wall to the particle density and discuss how the system size affects the velocity fluctuations. Finally we consider the sedimentation of spheroidal particles where the orientation of the particles plays an important role altering the average sedimentation velocity significantly from the one measured for spherical particles. We show a transition in the orientational behavior of the spheroids when the volume fraction of the particles is increased and show how it depends on the Reynolds number. This transition is also connected to observed increase in the density fluctuations.