Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T05:15:25.520Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous dissipation in the collision between a sphere and a textured wall

Published online by Cambridge University Press:  27 May 2020

Anne Mongruel Open the ORCID record for Anne Mongruel [Opens in a new window]  and
Philippe Gondret Open the ORCID record for Philippe Gondret [Opens in a new window]
Anne Mongruel
Affiliation:
PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris,75005Paris, France
Philippe Gondret*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire FAST, 91405, Orsay, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A model is presented for the bouncing dynamics of a fluid-immersed sphere impacting normally a textured wall with micropillars. By taking into account the hydrodynamic and contact interactions between the smooth sphere and the textured wall, the complete motion of the sphere is recovered when approaching, colliding with and bouncing off the wall. We demonstrate that the critical Stokes number for the bouncing transition, $St_{c}$, is the sum of two contributions corresponding to dissipation prior to and during the collision, both contributions being critically influenced by the geometrical parameters of the model roughness. The experimental data obtained from interferometric measurements are found to be in agreement with the theoretical predictions. In the bouncing regime, the coefficient of restitution is also derived analytically and shows a linear evolution with the Stokes number, $St$, just above the bouncing transition, in agreement with the experimental data obtained very close to $St_{c}$.

JFM classification

Complex Fluids: Suspensions Low-Reynolds-number flows: Lubrication theory Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ardekani, A. M. & Rangel, R. H. 2008 Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid. J. Fluid Mech. 596, 437–466.CrossRefGoogle Scholar
Barnoky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31, 1324–1329.CrossRefGoogle Scholar
Biegert, E., Vowinckel, B. & Meiburg, E. 2017 A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys. 340, 105–127.CrossRefGoogle Scholar
Birwa, S. K., Rajalakshmi, G., Govindarajan, R. & Menon, N. 2018 Solid-on-solid contact in a sphere-wall collision in a viscous fluid. Phys. Rev. Fluids 3, 044302.CrossRefGoogle Scholar
Cawthorn, C. J. & Balmforth, N. J. 2010 Contact in a viscous fluid. Part 1. A falling wedge. J. Fluid Mech. 646, 327–338.CrossRefGoogle Scholar
Chastel, T.2015 Interactions hydrodynamiques entre une sphère et une paroi texturée: approche, collision et rebond. PhD thesis, Université Pierre et Marie Curie.Google Scholar
Chastel, T., Gondret, P. & Mongruel, A. 2016 Texture-driven elastohydrodynamic bouncing. J. Fluid Mech. 805, 577–590.CrossRefGoogle Scholar
Chastel, T. & Mongruel, A. 2016 Squeeze flow between a sphere and a textured wall. Phys. Fluids 28, 023301.CrossRefGoogle Scholar
Chastel, T. & Mongruel, A. 2019 Sticking collision between a sphere and a textured wall in a viscous fluid. Phys. Rev. Fluids 4, 014301.CrossRefGoogle Scholar
Costa, P., Boersma, B. J., Westerweel, J. & Breugem, W.-P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92, 053012.Google ScholarPubMed
Davis, R. H., Serayssol, J.-M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.CrossRefGoogle Scholar
Falcon, E., Laroche, C., Fauve, S. & Coste, C. 1998 Behavior of one inelastic ball bouncing repeatedly off the ground. Eur. Phys. J. B 3, 45–57.CrossRefGoogle Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.CrossRefGoogle Scholar
Hunter, S. C. 1957 Energy absorbed by elastic waves during impact. J. Mech. Phys. Solids 5, 162–171.CrossRefGoogle Scholar
Izard, E., Bonometti, T. & Lacaze, L. 2014 Modelling the dynamics of a sphere approaching and bouncing on a wall in a viscous fluid. J. Fluid Mech. 747, 422–446.CrossRefGoogle Scholar
Johnson, K. L. 1985 Contact Mechanics. Cambridge University Press.CrossRefGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
King, H., White, R., Maxwel, I. & Menon, N. 2011 Inelastic impact of a sphere on a massive plane: nonmonotonic velocity-dependence of the restitution coefficient. Eur. Phys. Lett. 93, 14002.CrossRefGoogle Scholar
Kuwabara, S. 1959 The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. J. Phys. Soc. Japan 14, 527–532.CrossRefGoogle Scholar
Lecoq, N., Anthore, R., Cichocki, B., Szymczak, P. & Feuillebois, F. 2004 Drag force on a sphere moving towards a corrugated wall. J. Fluid Mech. 513, 247–264.CrossRefGoogle Scholar
Lecoq, N., Feuillebois, F., Anthore, N., Anthore, R., Bostel, F. & Petipas, C. 1993 Precise measurement of particle-wall hydrodynamic interactions at low Reynolds number using laser interferometry. Phys. Fluids A 5, 3–12.CrossRefGoogle Scholar
Ledesma-Alonso, R., Raphaël, E., Léger, L., Restagno, F. & Poulard, C. 2016 Stress concentration in periodically rough Hertzian contact: Hertz to soft-flat-punch transition. Proc. R. Soc. Lond. A 472, 20160235.CrossRefGoogle ScholarPubMed
Legendre, D., Zenit, R., Daniel, C. & Guiraud, P. 2006 A note on the modelling of the bouncing of spherical drops or solid spheres on a wall in viscous fluid. Chem. Engng Sci. 61, 3543–3549.CrossRefGoogle Scholar
Lian, G., Adams, M. J. & Thornton, C. 1996 Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311, 141–152.CrossRefGoogle Scholar
Marshall, J. S. 2011 Viscous damping force during head-on collision of two spherical particles. Phys. Fluids 23, 013305.CrossRefGoogle Scholar
Maruoka, H. 2019 Intermediate asymptotics on dynamical impact of solid sphere on militextured surface. Phys. Rev. E 100, 053004.Google ScholarPubMed
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Dover.CrossRefGoogle Scholar
Mongruel, A., Lamriben, C., Yahiaoui, S. & Feuillebois, F. 2010 The approach of a sphere to a wall at finite Reynolds number. J. Fluid Mech. 661, 229–238.CrossRefGoogle Scholar
Ruiz-Angulo, A., Roshankhah, S. & Hunt, M. L. 2019 Surface deformation and rebound for normal single-particle collisions in a surrounding fluid. J. Fluid Mech. 871, 1044–1066.CrossRefGoogle Scholar
Seiwert, J., Clanet, C. & Quéré, D. 2011 Coating of a textured solid. J. Fluid Mech. 669, 55–63.CrossRefGoogle Scholar
Simeonov, J. A. & Calantoni, J. 2012 Modeling mechanical contact and lubrication in Direct Numerical Simulations of colliding particles. Intl J. Multiphase Flow 46, 38–53.CrossRefGoogle Scholar
Smart, J. R. & Leighton, D. T. 1989 Measurement of the hydrodynamic surface roughness of noncolloidal spheres. Phys. Fluids A 1, 52–60.CrossRefGoogle Scholar
Yang, F.-L. & Hunt, M. L. 2008 A mixed contact model for an immersed collision between two solid surfaces. Phil. Trans. R. Soc. Lond. A 366, 2205–2218.CrossRefGoogle ScholarPubMed