Three Simple Stokeslet Trajectories

TL;DR

This paper presents exact analytical results for three distinct trajectories of particles interacting hydrodynamically via Stokeslets, revealing constant velocities, finite displacements, and periodic orbits in different sedimentation scenarios.

Contribution

It provides new exact solutions for particle trajectories in Stokes flow, including sedimentation and flow-induced oscillations, expanding understanding of hydrodynamic interactions.

Findings

Middle particle sediments at constant velocity

Horizontal pair undergoes finite constant displacement near a wall

Particles in quadratic flow oscillate periodically

Abstract

Exact results for three trajectories of small numbers of particles interacting hydrodynamically through Stokeslets are presented. First, the middle particle in a vertical trio of particles sediments at a constant velocity for all time. Second, a horizontal pair of particles sedimenting toward a rigid wall undergo a finite and surprisingly constant horizontal displacement in the limit of large initial separations. Third, a pair of particles sedimenting in a quadratic flow, such as that of a fluid pumped in the direction of gravity, oscillates in a periodic orbit and admits a Hamiltonian formulation.