An Indirect Boundary Integral Method for an Oscillatory Stokes Flow Problem

The purpose of this paper is to present an indirect boundary integral method for the oscillatory Stokes flow provided by the translational oscillations of two rigid spheres in an incompressible Newtonian fluid of infinite expanse. 1. Introduction. The study of oscillatory Stokes flows has a key role in the understanding of the biomechanics of blood flow, the Brownian motion, the motion of swimming microorganisms, and other biological or chemical phenomena. The oscillatory Stokes flows have some important characteristics. For example, at low frequencies, they reduce to steady (more exactly quasi-steady) Stokes flows with diffusion of vorticity. At high frequencies, oscillatory Stokes flows reduce to potential flows, located outside of viscous boundary layers. Such a boundary layer, called the Stokes layer, appears in the vicinity of a solid boundary and has the thickness equal to (ν/Ω) 1/2 , where ν is the kinematic