On the slow broadside motion of a thin disc along the axis of a fluid-filled circular duct

Abstract

The study of the slow motion of a solid body through a viscous fluid is of importance in many fields. We may instance viscometry and chemical engineering as two subjects in which a quantitative understanding of such motions is essential. Thus, in recent years systematic attempts have been made to calculate the drag force and couple on slowly sedimenting particles in a bounded viscous fluid. Using the ‘method of reflexions’ Brenner (1) has obtained formulae which give, for a wide class of sedimenting particles, an estimate of the effect of the container walls on the drag force, the error being O(c/l)3, where c is a characteristic particle dimension and l the distance from the centre of the particle to the nearest boundary wall. The reader is referred to the recent book by Happel and Brenner (2) for a complete account of these and other pertinent investigations; also to Williams (3) for an alternative integral equation approach to these results.