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An experimental study of the motion of a light sphere in a rotating viscous fluid

Published online by Cambridge University Press:  21 May 2018

T. Sauma-Pérez ,
C. G. Johnson ,
L. Yang  and
T. Mullin Open the ORCID record for T. Mullin [Opens in a new window]
T. Sauma-Pérez
Affiliation:
Manchester Centre for Nonlinear Dynamics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
C. G. Johnson
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
L. Yang
Affiliation:
Manchester Centre for Nonlinear Dynamics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
T. Mullin*
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
*
†Email address for correspondence: tom.mullin@maths.ox.ac.uk
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Abstract

We present the results of an experimental investigation of the motion of a light, solid sphere in a horizontal rotating cylinder filled with viscous fluid. At high rotation rates, the sphere sits near the axis of the cylinder. At lower rotation rates, a set of off-axis fixed points are observed for a range of sphere radii. The locations of these fixed points are in quantitative agreement with the predictions of a model based on available theory. The fixed points are observed to become unstable to periodic orbits below a critical Reynolds number $Re_{c}$. The radius of the observed orbits increases with Reynolds number more slowly than a typical Hopf bifurcation, in this case, growing as $1/Re^{2}$.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Particle/fluid flow Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 119 - 133
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Copyright
© 2018 Cambridge University Press 

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