Analysis and Computation of Sedimentation and Erosion in Viscous Flow

Particulate flows at very small scales are dominated by viscous effects. The Stokes system of partial differential equations is an appropriate model for such flows, and the linearity of these equations allows for the use of the powerful mathematical techniques known as Green's functions and boundary integral equations. In the work presented herein we apply these tools to study the sedimentation of a single spheroidal particle near a flat wall and the shear stress driven erosion of one or several particles in various flow configurations. The main theoretical results include the following: the far-field mobility of a spheroidal particle near a wall, the reduction of the sedimentation problem to a three-dimensional system of ordinary differential equations, and a new completed traction boundary integral equation adapted for the case of nontrivial background flows and wall-bounded geometries. These results lead to improved numerical methods, which we develop and deploy to explore several processes related to viscous sedimentation and erosion. We conclude with a discussion of erosion in the special case of axisymmetric flow.