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Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall

Published online by Cambridge University Press:  14 August 2015

Thomas Salez  and
L. Mahadevan
Thomas Salez
Affiliation:
School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, MA 02138, USA PCT Lab, UMR CNRS 7083 Gulliver, ESPCI ParisTech, PSL Research University, 75005 Paris, France
L. Mahadevan*
Affiliation:
School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds-number feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation–sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows us to generalize the results to account for additional effects such as wall poroelasticity.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 181 - 196
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Copyright
© 2015 Cambridge University Press 

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