Abstract
The results of an experimental investigation into 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, numerical 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. The good agreement between measurements and the analytical solutions for both fluid velocity and angular displacement of the sphere indicates that the flow may be considered Stokesian, thus providing an excellent basis for experimental and theoretical characterisation of hydrodynamic interactions between multiple oscillating spheres at low Reynolds number.
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Notes
Mondy et al. (2005) measured the couple experienced by a rotating ball immersed in a concentrated suspension of comparatively sized, neutrally buoyant spheres and compared it to the torque on a sphere spinning in a Newtonian fluid, uncovering an apparent slip which reduced the measured torque when the radius of the spinning ball becomes comparable with that of the suspended spheres.
Hollerbach et al. (2002) define \(Re=a\omega \delta /\nu\), where the penetration depth of the boundary layer \(\delta = (2\nu /\omega )^{1/2}\), and provide an interesting discussion of the appropriate choice of Re.
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Acknowledgments
The authors would like to acknowledge the technical assistance of P. Tipler and to thank Professor Sir K. Novoselov FRS and Professor A. Murray for the loan of equipment. The completion of the experimental work was supported by an EPSRC studentship (EP/P505631/1), and the writing of the manuscript by a David Crighton Fellowship.
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Box, F., Thompson, A.B. & Mullin, T. Torsional oscillations of a sphere in a Stokes flow. Exp Fluids 56, 209 (2015). https://doi.org/10.1007/s00348-015-2075-7
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DOI: https://doi.org/10.1007/s00348-015-2075-7