Motion of a rigid cylinder between parallel plates in Stokes flow. Part 1: motion in a quiescent fluid and sedimentation.

A general numerical scheme for solution of two dimensional Stokes equations in a multiconnected domain of arbitrary shape, was applied to the motion of a rigid circular cylinder between plane parallel boundaries. Numerically generated boundary conforming coordinates are used to transform the flow domain into a domain with rectilinear boundaries. The transformed Stokes equations in vorticity stream function form were then solved on a uniform grid using an iterative algorithm. Coefficients of the resistance matrix representing the forces and torque on the cylinder due to its translational motion parallel or perpendicular to the boundaries or due to rotation about its axis were calculated. The solutions are obtained for a wide range of particle radii and positions across the channel. It was found that the force on a particle translating parallel to the boundaries without rotation exhibits a minimum at a position between the channel centerline and the wall and a local maximum on the centerline. (from authors' abstract)