Numerical Simulation and Modeling of Particle Motions in Three-Dimensional Stokes Flow

In this dissertation, the particles motion and interactions in 3D Stokes flow have been studied. There two types of particles studied: one type is rigid-body particles and the other type is porous particles. For the rigid-body type particle, a novel distributed Lagrange multiplier/fictitious domain (DLM/FD) method for simulating fluid-particle interactions in three-dimensional (3D) Stokes flow is applied. The method is validated by comparing the numerical results for a neutrally buoyant particle, of either spherical or prolate shape, with the associated Jeffery's analytical solutions for a simple shear flow. The results concerning two balls, interacting under creeping flow conditions in a bounded shear flow, are consistent with those available in the literature. For the porous type particles, two novel numerical methods have been developed for simulating fluid/porous particle interactions in three-dimensional (3D) Stokes flow. The Brinkman-Debye-Bueche model is adapted for the fluid flow inside the porous particle, being coupled with the Stokes equations for the fluid flow outside the particle. The rotating of a porous ball and the interaction of two porous balls in bounded shear flows have been studied by these two new methods, respectively. The numerical results show that the permeability of the porous particle does have strong effect on the interaction of two porous balls.