Sedimentation of a Small Sphere in a Viscous Fluid Bounded by Two Perpendicular Walls

Abstract

A theoretical study is made of the sedimentation of a small sphere in a viscous fluid bounded by horizontal and vertical walls. The analysis is based on the quasi-steady equations of motion, and the first-order wall effect is taken into account. The trajectory of the particle slightly deviates from the vertical line, the magnitude of which is determined by the angular position of the sphere. When the ensemble of spheres with randomly distributed initial positions is considered, the spheres which originally lay at a height h are found most frequently at the distance 0.591 h from the side wall.