Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-24T21:59:05.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid

Published online by Cambridge University Press:  17 January 2008

A. M. ARDEKANI  and
R. H. RANGEL
A. M. ARDEKANI
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
R. H. RANGEL
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of particle–particle collisions and the bouncing motion of a particle colliding with a wall in a viscous fluid is numerically investigated. The dependence of the effective coefficient of restitution on the Stokes number and surface roughness is analysed. A distributed Lagrange multiplier-based computational method in a solid–fluid system is developed and an efficient method for predicting the collision between particles is presented. A comparison between this method and previous collision strategies shows that the present approach has some significant advantages over them. Comparison of the present methodology with experimental studies for the bouncing motion of a spherical particle onto a wall shows very good agreement and validates the collision model. Finally, the effect of the coefficient of restitution for a dry collision on the vortex dynamics associated with this problem is discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 437 - 466
Copyright
Copyright © Cambridge University Press 2008

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. 2006 Unsteady motion of two solid spheres in Stokes flow. Phys. Fluids 18, 103306.CrossRefGoogle Scholar
Ardekani, A. M., Rangel, R. H. & Joseph, D. D. 2007 Motion of a sphere normal to a wall in a second-order fluid. J. Fluid Mech. 587, 163–172.CrossRefGoogle Scholar
Arp, A. P. & Mason, S. G. 1977 The kinetics of flowing dispersions: IX. Doublets of rigid spheres (experimental). J. Colloid Interface Sci. 61, 44.CrossRefGoogle Scholar
Barnocky, G. & Davis, R. H. 1989 The influence of pressure-dependent density and viscosity on the elastohydrodynamic collision and rebound of two spheres. J. Fluid Mech. 209, 501–519.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16, 242.CrossRefGoogle Scholar
Davis, R. H. 1987 Elastohydrodynamic collisions of particles. PCH PhysicoChem. Hydrodyn. 9, 41–52.Google Scholar
Davis, R. H. 1992 Effect of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Phys. Fluids A 4, 2607–2619.CrossRefGoogle Scholar
Davis, R. H., Serayssol, J. M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479.CrossRefGoogle Scholar
Davis, R. H., Zhao, Y., Galvin, K. P. & Wilson, H. J. 2003 Solid–solid contacts due to surface roughness and their effects on suspension behaviour. Phil. Trans. R. Soc. Lond. A 361, 871–894.CrossRefGoogle ScholarPubMed
Eames, I. & Dalziel, S. B. 2000 Dust resuspension by the flow around an impacting sphere. J. Fluid Mech. 403, 305.CrossRefGoogle Scholar
Ekiel-Jezewska, M. L., Feuillebois, F., Lecoq, N., Masmoudi, K., Anthore, R., Bostel, F. & Wajnryb, E. 1999 Hydrodynamic interactions between two spheres at contact. Phys. Rev. E 59, 3182.Google Scholar
Ekiel-Jezewska, M. L., Lecoq, N., Anthore, R., Bostel, F. & Feuillebois, F. 2002 Rotation due to hydrodynamic interactions between two spheres in contact. Phys. Rev. E 66.Google ScholarPubMed
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1. Sedimentation. J. Fluid. Mech. 261, 95–134.CrossRefGoogle Scholar
Foerster, S. F., Lounge, M. Y., Chang, H. & Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 3, 1108.CrossRefGoogle Scholar
Glowinski, R., Pan, T. W., Hesla, T. I. & Joseph, D. D. 1999 A distributed Lagrange multiplier fictitious domain method for particulate flows. Intl J. Multiphase Flow 25, 755–794.CrossRefGoogle Scholar
Glowinski, R., Pan, T. W. & Periaux, J. 1998 distributed Lagrange multiplier method for incompressible viscous flow around moving rigid bodies. Comput. Methods Appl. Mech. Engng 151, 181–194.CrossRefGoogle Scholar
Gondret, P., Hallouin, E., Lance, M. & Petit, L. 1999 Experiments on the motion of a solid sphere toward a wall: From viscous dissipation to elastohydrodynamic bouncing. Phys. Fluids 11, 2803–2805.CrossRefGoogle Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.CrossRefGoogle Scholar
Hu, H. H., Patankar, N. A. & Zhu, M. Y. 2001 Direct numerical simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian technique. J. Comput. Phys. 169, 427–462.CrossRefGoogle Scholar
Joseph, G. G. & Hunt, M. L. 2004 Oblique particle-wall collisions in a liquid. J. Fluid Mech. 510, 71–93.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
Kushch, V. I., Sangani, A. S., Spelt, P. D. M. & Koch, D. L. 2002 Finite-Weber-number motion of bubbles through a nearly inviscid liquid. J. Fluid Mech. 460, 241–280.CrossRefGoogle Scholar
Ladd, A. J. C. 1994 a Numerical simulation of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 271–309.Google Scholar
Ladd, A. J. C. 1994 b Numerical simulation of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Legendre, D., Daniel, C. & Guiraud, P. 2005 Experimental study of a drop bouncing on a wall in a liquid. Phys. Fluids 17, 1–13.CrossRefGoogle Scholar
Legendre, D., Magnaudet, J. & Mougin, G. 2003 Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497, 133–166.CrossRefGoogle Scholar
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
Lin, J. Z., Wang, Y. L. & Olsen, J. A. 2004 Sedimentation of rigid cylindrical particles with mechanical contacts. Chin. Phys. Lett. 22, 628–631.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Dover.CrossRefGoogle Scholar
Patankar, N. A. 2001 A formulation for fast computations of rigid particulate flows. Center for Turbulence Res., Annu. Res. Briefs 185–196.Google Scholar
Patankar, N. A., Singh, P., Joseph, D. D., Glowinski, R. & Pan, T. W. 2000 A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 26, 1509–1524.CrossRefGoogle Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.Google Scholar
Richard, D. & Quéré, D. 2000 Bouncing water drops. Europhys. Letters 50, 769–775.CrossRefGoogle Scholar
Sangani, A. S. & Mo, G. 1994 Inclusion of lubrication forces in dynamic simulations. Phys. Fluids 6, 1653.CrossRefGoogle Scholar
Sangani, A. S., Mo, G. B., Tsao, H. K. & Koch, D. L. 1996 Simple shear flows of dense gas-solid suspensions at finite Stokes numbers. J. Fluid Mech. 313, 309.CrossRefGoogle Scholar
Sharma, N., Chen, Y. & Patankar, N. A. 2005 A distributed Lagrange multiplier based computational method for the simulation of particulate-Stokes flow. Comput. Methods Appl. Mech. Engng 194, 4716–4730.CrossRefGoogle Scholar
Sharma, N. & Patankar, N. A. 2005 A fast computation technique for direct numerical simulation of rigid particulate flows. J. Comput. Phys. 205, 439–457.CrossRefGoogle Scholar
Singh, P., Hesla, T. I. & Joseph, D. D. 2003 Distributed Lagrange multiplier method for particulate flows with collisions. Intl J. Multiphase Flow 29, 495–509.CrossRefGoogle Scholar
Singh, P., Joseph, D. D., Hesla, T. I., Glowinski, R. & Pan, T. W. 2000 Direct numerical simulation of viscoelastic particulate flows. J. Non-Newtonian Fluid Mech. 91, 165–188.CrossRefGoogle Scholar
Smart, J. R. & Leighton, D. T. 1989 Measurement of the hydrodynamic surface-roughness of noncolloidal spheres. Phys. Fluids 1, 52–60.CrossRefGoogle Scholar
Sundararajakumar, R. R. & Koch, D. L. 1996 Non-continuum lubrication flows between particles colliding in a gas. J. Fluid Mech. 313, 283.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K., Cheung, A. & Leweke, T. 2006 Hydrodynamics of a particle impact on a wall. Appl. Math. Modelling 30, 1356.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Hourigan, K. 2007 Sphere-wall collisions: Vortex dynamics and stability. J. Fluid Mech. 575, 121.CrossRefGoogle Scholar
Tsao, H. K. & Koch, D. L. 1994 Collisions of slightly deformable, high Reynolds number bubbles with short range repulsive forces. Phys. Fluids 6, 2591–2605.CrossRefGoogle Scholar
Zeng, S., Kerns, E. T. & Davis, R. H. 1996 The nature of particle contact in sedimentation. Phys. Fluids 8, 1389.CrossRefGoogle Scholar
Zhang, J., Fan, L. S., Zhu, C., Pfeffer, R. & Qi, D. 1999 Dynamic behavior of collision of elastic spheres in viscous fluids. Powder Tech. 106, 98–109.CrossRefGoogle Scholar