The Lateral Force on a Small Sphere Sedimenting in a Viscous Fluid Bounded by a Cylindrical Wall

Abstract

A theoretical study is made of the lateral force on a spherical rigid particle sedimenting with a constant velocity in an incompressible viscous fluid bounded by a vertical cylindrical wall. Results are obtained up to the first-order effects of boundaries using the method of matched asymptotic expansions. The sphere experiences a lateral force towards the axis everywhere and its magnitude is proportional to the distance from the axis to the position of the sphere when the distance is not so large and has a maximum value near the wall.