Higher-order corrections to the axisymmetric interactions of nearly touching spheres

Abstract

Two unequal spheres are immersed in an axisymmetric low-Reynolds-number flow and are separated by a small nondimensional distance ∈. The forces and stresslets exerted by the spheres on the fluid are calculated asymptotically to O(∈ ln ∈), in order to improve the convergence of numerical calculations of the same quantities. The main obstacle to the extension to O(∈ ln ∈) was the breakdown of the usual lubrication approach at higher orders in ∈. The method adopted here obtains expressions for the functions of immediate interest, but does so by postponing the resolution of the fundamental difficulties until a higher order in ∈. © 1989 American Institute of Physics.