The Oscillatory Motion of a Sphere in a Stokes Flow

We report results of an experimental investigation into the dynamic response of a single sphere to magnetic forcing and the resultant motion of the surrounding viscous fluid. Permanent magnets embedded into the surface of a neutrally buoyant sphere enable actuation of torsional oscillations of the sphere through the application of an alternating magnetic field. The applied field induces a torque on the embedded magnets, and the torsional response of the sphere to magnetic forcing has been systematically characterized as a function of the dimensionless forcing parameter F$=$8$\pi \mu $ a$^{\mathrm{3}}\omega $. Excellent agreement is found between the experimentally observed and numerically computed behavior of the sphere. Furthermore, the flow generated by the rotary motion of a sphere has visualized using Particle Image Velocimetry and good agreement is also found between the observed and the analytic solution for the fluid velocity as a function of radial distance.