Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces

TL;DR

This paper presents a stable equilibrium solution for three heavy spheres in Stokes flow, contrasting with the collapse behavior of point particles, highlighting the importance of finite size effects in low Reynolds number hydrodynamics.

Contribution

It introduces a stable equilibrium configuration for three heavy spheres in Stokes flow, which does not occur in the point-particle approximation, revealing new insights into particle interactions.

Findings

Stable equilibrium configuration identified for three heavy spheres.

Point-particle model predicts collapse, unlike finite-sized spheres.

Finite size effects prevent collapse, enabling equilibrium.

Abstract

A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances evolve towards the equilibrium relative configuration while the point particles collapse onto a single point in a finite time.