The slow motion of two or more spheres through a viscous fluid

Abstract

Expressions are derived for the velocity of two spheres, moving slowly under external forces through a viscous fluid, as a function of their separation and radii. They compare favourably with the available experimental data. A discussion of the interactions of three particles and some general comments on the settling of a swarm of spheres are also included.

Lubrication approximation in completed double layer boundary element method

“…These authors developed a general scheme for evaluating the mobility tensor for any three-dimensional con®guration of spheres and derived explicit expressions up to order R À7 , where R is the interparticle spacing. Their expressions are identical with those previously obtained by Kynch (1959) using the method of re¯ections. Applications of the theory have been reported by Kamel and Tory (1989) for special planar con®gurations of sedimenting spheres and by Ladd (1988) for periodic con®gurations.…”

Drag force of interacting coaxial spheres in viscoplastic fluids

“…Kynch [10] delivered a theoretical treatment of creeping motions of three or more spheres. Zick and Homsy [11] numerically investigated interacting characteristics of the simple and periodic arrays of spheres in a Newtonian creeping flow by formulating the problem as a set of two-dimensional integral equations and determined the average drag forces.…”

Dynamic simulation of hydrodynamically interacting particles

“…Kynch (1959) extended the method of reflections to account for effects from third and fourth bodies, showing that when relating the velocity disturbance of one sphere to the external force applied to another (i.e. the mobility interaction), third-body effects do not appear until O(l/.P), where r is a characteristic particle spacing, and fourth-body effects until O ( l / r 7 ) .…”