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Phys. Fluids 26, 035109 (2014);
Leigh T. Wardhaugh1 , Michael C. Williams2,a
1 CSIRO Energy Technology, Steel River Estate, Mayfield West, NSW 2304, Australia and
2 Chemical and Materials Engineering Department, University of Alberta, Edmonton, Alberta T6G 2G6, Canada.
Abstract
Spherical particles immersed in liquids were observed in their descent along a glass wall inclined at various angles {Alpha}, over a range of particle-based Reynolds numbers (Rep) extending to high values (15 < Re p < 50 000), rarely reported in such flows. Plastic, ceramic, and metal spheres were used, characterized as to surface roughness and their friction coefficients against the glass. Liquids were selected to achieve a viscosity variation by a factor of 300, as well as having widely differing chemical natures. A drag coefficient (C p ) used to correlate sphere velocity data was found to define a near-universal curve C p (Re p ) over the entire Re p -range, provided that spheres rolled down the wall without slipping, and here there was no need to accommodate roughness effects of solid-to-solid friction explicitly. This correlation was especially good for Re p > 103. For lower Re p , deviations appeared in systematic fashion, falling below the universal curve when slip was present. Several unexpected features were observed: (a) a threshold angle, {Alpha}0, needed before sphere motion could begin; (b) spheres lifting off from the wall at high Re p , but always at the same maximum angle {Alpha} m = 74°; and (c) prior to lift-off, a buzzing sound (not reported previously) for which explanations are offered.
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