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Soft-lubrication interactions between a rigid sphere and an elastic wall

Published online by Cambridge University Press:  23 December 2021

Vincent Bertin Open the ORCID record for Vincent Bertin [Opens in a new window] ,
Yacine Amarouchene Open the ORCID record for Yacine Amarouchene [Opens in a new window] ,
Elie Raphaël Open the ORCID record for Elie Raphaël [Opens in a new window]  and
Thomas Salez Open the ORCID record for Thomas Salez [Opens in a new window]
Vincent Bertin
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
Yacine Amarouchene
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Elie Raphaël
Affiliation:
UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
Thomas Salez*
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Hokkaido 060-0808, Japan
*
†Email address for correspondence: thomas.salez@u-bordeaux.fr
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Abstract

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

JFM classification

Low-Reynolds-number flows: Lubrication theory Complex Fluids: Colloids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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