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Sedimenting sphere in a variable-gap Hele-Shaw cell

Published online by Cambridge University Press:  14 August 2007

Center for Nonlinear Dynamics and the Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
Center for Nonlinear Dynamics and the Department of Physics, University of Texas at Austin, Austin, TX 78712, USA Centro de Investigación en Energía, Universidad Nacional Autónoma de México, Ap.P. 34, 62580 Temixco Mor, México
Center for Nonlinear Dynamics and the Department of Physics, University of Texas at Austin, Austin, TX 78712, USA


We have measured the trajectory and visualized the wake of a single sphere falling in a fluid confined between two closely spaced glass plates (a Hele-Shaw cell). The position of a sedimenting sphere was measured to better than 0.001d, where d is the sphere diameter, for Reynolds numbers (based on the terminal velocity) between 20 and 330, for gaps between the plates ranging from 1.014d to 1.4d. For gaps in the range 1.01d–1.05d, the behaviour of the sedimenting sphere is found to be qualitatively similar to that of an unconfined cylinder in a uniform flow, but our sedimenting sphere begins to oscillate and shed von Kármán vortices for Re>200, which is far greater than the Re = 49 for the onset of vortex shedding behind cylinders in an open flow. When the gap is increased to 1.10d–1.40d, the vortices behind the sphere are different – they are qualitatively similar to those behind a sphere sedimenting in the absence of confining walls. Our precision measurements of the velocity of a sedimenting sphere and the amplitude and frequency of the oscillations provide a benchmark for numerical simulations of the sedimentation of particles in fluids.

Copyright © Cambridge University Press 2007

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