Torsional oscillations of a sphere in a Stokes flow

TL;DR

This study experimentally investigates torsional oscillations of a sphere in Stokes flow using a novel magnetic control setup, developing a mathematical model and confirming flow behavior aligns with theoretical predictions.

Contribution

Introduces a new experimental setup for remotely controlling sphere oscillations in viscous flow and validates a mathematical model with experimental data.

Findings

Flow velocity inversely proportional to square of radial distance

Good agreement between experimental results and theoretical model

Flow remains within the Stokes flow regime

Abstract

The results of an experimental investigation of a sphere performing torsional oscillations in a Stokes flow are presented. A novel experimental set up was developed which enabled the motion of the sphere to be remotely controlled through application of an oscillatory magnetic field. The response of the sphere to the applied field was characterised in terms of the viscous, magnetic and gravitational torques acting on the sphere. A mathematical model of the system was developed and good agreement was found between experimental and theoretical results. The flow resulting from the motion of the sphere was measured and the fluid velocity was found to have an inverse square dependence on radial distance from the sphere. Agreement between measurements and the analytical solution for the fluid velocity indicates that the flow may be considered Stokesian.