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Cylinder rolling on a wall at low Reynolds numbers

Published online by Cambridge University Press:  22 September 2011

Alain Merlen  and
Christophe Frankiewicz
Alain Merlen
Affiliation:
Joint International Laboratory LEMAC, Institut d’Électronique Microélectronique et Nanotechnologie UMR CNRS 8520, Université des Sciences et Technologies de Lille, Ecole Centrale de Lille, France
Christophe Frankiewicz*
Affiliation:
Joint International Laboratory LEMAC, Institut d’Électronique Microélectronique et Nanotechnologie UMR CNRS 8520, Université des Sciences et Technologies de Lille, Ecole Centrale de Lille, France
*
†Email address for correspondence: christophefrankiewicz@msn.com
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Abstract

The flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 461 - 494
Copyright
Copyright © Cambridge University Press 2011

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