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A contact model for normal immersed collisions between a particle and a wall

Published online by Cambridge University Press:  01 December 2011

Xiaobai Li ,
Melany L. Hunt  and
Tim Colonius
Xiaobai Li
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Melany L. Hunt*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: hunt@caltech.edu
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Abstract

The incompressible Navier–Stokes equations are solved numerically to predict the coupled motion of a falling particle and the surrounding fluid as the particle impacts and rebounds from a planar wall. The method is validated by comparing the numerical simulations of a settling sphere with experimental measurements of the sphere trajectory and the accompanying flow field. The normal collision process is then studied for a range of impact Stokes numbers. A contact model of the liquid–solid interaction and elastic effect is developed that incorporates the elasticity of the solids to permit the rebound trajectory to be simulated accurately. The contact model is applied when the particle is sufficiently close to the wall that it becomes difficult to resolve the thin lubrication layer. The model is calibrated with new measurements of the particle trajectories and reproduces the observed coefficient of restitution over a range of impact Stokes numbers from 1 to 1000.

JFM classification

Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 123 - 145
Copyright
Copyright © Cambridge University Press 2011

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References

1. Al-Samieh, M. F. & Rahnejat, H. 2002 Physics of lubricated impact of a sphere on a plate in a narrow continuum to gaps of molecular dimensions. J. Phys. D: Appl. Phys. 35, 2311–2326.CrossRefGoogle Scholar
2. Ardekani, A. M. & Rangel, R. H. 2008 Numerical investigation of particle–particle and particle–wall collisions in a viscous fluid. J. Fluid Mech. 576, 437–466.CrossRefGoogle Scholar
3. Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31, 1324–1329.CrossRefGoogle Scholar
4. 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
5. Colonius, T. & Taira, K. 2008 A fast immersed boundary method using a nullspace approach and multi-domain far-field conditions. Comput. Meth. Appl. Mech. Engng 197, 2131–2146.CrossRefGoogle Scholar
6. Crowe, C., Sommerfeld, M. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC Press.Google Scholar
7. Davis, R. H., Rager, D. A. & Good, B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107–119.CrossRefGoogle Scholar
8. Davis, R. H., Serayssol, J. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.Google Scholar
9. Feng, Z., Michaelides, E. E. & Mao, S. 2010 A three-dimensional resolved discrete particle method for studying particle–wall collision in a viscous fluid. Trans. ASME: J. Fluids Engng 132, 091302.Google Scholar
10. Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14 (2), 643–652.CrossRefGoogle Scholar
11. Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
12. Joseph, G. G. & Hunt, M. L. 2004 Oblique particle–wall collisions in a liquid. J. Fluid Mech. 510, 71–93.CrossRefGoogle Scholar
13. Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 443, 329–346.CrossRefGoogle Scholar
14. Kim, I., Elghobashi, S. & Sirignano, W. A. 1998 On the equation for spherical-particle motion: effect of Reynolds and acceleration numbers. J. Fluid Mech. 367, 221–253.Google Scholar
15. Ladd, A. J. C. 1997 Sedimentation of homogeneous suspensions of non-Brownian sphere. Phys. Fluids 9, 491–499.CrossRefGoogle Scholar
16. Lamb, M. P., Dietrich, W. E. & Sklar, L. S. 2008 A model for fluvial bedrock incision by impacting suspended and bed load sediment. J. Geophys. Res. 113, F03025.Google Scholar
17. Leweke, T., Thompson, M. C. & Hourigan, K. 2004 Vortex dynamics associated with the collision of a sphere with a wall. Phys. Fluids 16 (9), L74–L77.CrossRefGoogle Scholar
18. Li, X. 2010 An experimental and numerical study of normal particle collisions in a viscous liquid. PhD thesis, California Institute of Technology.Google Scholar
19. Lorenzini, G. & Mazza, N. 2004 Debris Flow Phenomenology and Rheological Modelling. WIT Press.Google Scholar
20. Michaelide, E. E. 1997 Reviewcthe transient equation of motion for particles, bubbles, and droplets. Trans. ASME: J. Fluids Engng 119, 223–247.Google Scholar
21. Nguyen, N.-Q. & Ladd, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66 (046708).CrossRefGoogle ScholarPubMed
22. Ruiz-Angulo, A. & Hunt, M. L. 2010 Measurements of the coefficient of restitution for particle collisions with ductile surfaces in a liquid. Granul. Matt. 12, 185–191.CrossRefGoogle Scholar
23. Safa, M. M. A. & Gohar, A. 1986 Pressure distribution under a ball impacting a thin lubricant layer. Trans. ASME: J. Tribology 108, 372–376.CrossRefGoogle Scholar
24. Taira, K. & Colonius, T. 2007 The immersed boundary method: a projection approach. J. Comput. Phys. 225, 2118–2137.CrossRefGoogle Scholar
25. TenCate, A., Nieuwstad, C. H., Derksen, J. J. & Van Den Akker, H. E. A. 2002 Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys. Fluids 14 (11), 4012–4025.CrossRefGoogle Scholar
26. Thompson, M. C., Leweke, T. & Hourigan, K. 2007 Sphere-wall collisions: vortex dynamics and stability. J. Fluid Mech. 575, 121–148.CrossRefGoogle Scholar
27. Timoshenko, S. P. & Goodier, J. N. 1970 Theory of Elasticity, 3rd edn. McGraw Hill.Google Scholar
28. Yang, F.-L. 2006 Interaction law for a collision between two solid particles in a viscous liquid. PhD thesis, California Institute of Technology.Google Scholar
29. Yang, F.-L. & Hunt, M. L. 2006 Dynamics of particle–particle collisions in a viscous liquid. Phys. Fluids 18 (121506).CrossRefGoogle Scholar