Hydrodynamic interactions between a sphere and a number of small particles

TL;DR

This paper derives exact formulas for hydrodynamic interactions involving a sphere and multiple small particles in a viscous fluid, using classical solutions of Stokes flow and Green's functions.

Contribution

It provides new explicit expressions for pair and three-body hydrodynamic interactions in low Reynolds number conditions, combining classical solutions with Green tensor methods.

Findings

Exact expressions for pair interactions

Explicit formulas for three-body interactions

Enhanced understanding of hydrodynamics in particle-sphere systems

Abstract

Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds number hydrodynamics. The results follow by a combination of the solutions for flow about a sphere with no-slip boundary condition derived by Stokes and Kirchhoff, and the result derived by Oseen for the Green tensor of Stokes' equations in the presence of a fixed sphere.