Skip to main content Accessibility help
×
Home

Surface deformation and rebound for normal single-particle collisions in a surrounding fluid

  • Angel Ruiz-Angulo (a1), Shahrzad Roshankhah (a2) and Melany L. Hunt (a2)

Abstract

This article presents experimental measurements involving immersed collisions between a rigid impactor and a deformable target for a wide range of Reynolds and Stokes numbers. Three aluminium alloys are used as solid targets submerged in seven different fluids covering a wide range of viscosity and density. The collision and rebound velocities as well as the depth and diameter of the crater produced by the collisions are measured with high resolution. Most of the experiments in this study occur at velocities for which the deformation is within the elastic–plastic regime. Results of the experiments in air are analysed by elastic, plastic and elastic–plastic theories, and demonstrate the complexities of modelling elastic–plastic collisions. For collisions in a liquid, the measurements show that the size of the crater is independent of the fluid characteristics if the Stokes number is beyond a critical value. The normal coefficient of restitution can be estimated by including both viscous losses and plasticity effects and assuming that the collision time scale is significantly shorter than the hydrodynamic time scale. The results of the crater dimensions are also used to develop an analytical expression for the volume of deformation of the material as a function of material properties and the impact and critical Stokes numbers.

Copyright

Corresponding author

Email address for correspondence: hunt@caltech.edu

References

Hide All
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.
Bitter, J. G. A. 1963a A study of erosion phenomena. Part I. Wear 6 (1), 521.
Bitter, J. G. A. 1963b A study of erosion phenomena. Part II. Wear 6 (3), 169190.
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3–4), 242251.
Burgoyne, H. A. & Daraio, C. 2014 Strain-rate-dependent model for the dynamic compression of elastoplastic spheres. Phys. Rev. E 89, 032203.
Chatanantavet, P. & Parker, G. 2009 Physically based modeling of bedrock incision by abrasion, plucking, and macroabrasion. J. Geophys. Res. 114, F04018.
Clark, H. M. 1991 On the impact rate and impact energy of particles in a slurry pot erosion tester. Wear 147 (1), 165183.
Cox, R. G. & Brenner, H. 1967a Effect of finite boundaries on Stokes resistance of an arbitrary particle. Part 3. Translation and rotation. J. Fluid Mech. 28, 391411.
Cox, R. G. & Brenner, H. 1967b The slow motion of a sphere through a viscous fluid towards a plane surface. Part 2. Small gap widths, including inertial effects. Chem. Engng Sci. 22 (12), 17531777.
Davis, R. H., Serayssol, J. M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479497.
Desale, G. R., Gandhi, B. K. & Jain, S. C. 2011 Development of correlations for predicting the slurry erosion of ductile materials. Trans. ASME J. Tribol. 133 (3), 031603.
Finnie, I. 1960 Erosion of surfaces by solid particles. Wear 3 (2), 87103.
Finnie, I. 1972 Some observations on the erosion of ductile metals. Wear 19 (1), 8190.
Hertz, H. 1881 Über die Beürhrung fester elastischer Körper (On the contact of elastic solids). J. Reine Angew. Math. 92, 156171.
Hutchings, I. M. 1981 A model for the erosion of metals by spherical particles at normal incidence. Wear 70 (3), 269281.
Jackson, R. L. & Green, I. 2005 A finite element study of elasto-plastic hemispherical contact against a rigid flat. Trans. ASME J. Tribol. 127 (2), 343354.
Jackson, R. L., Green, I. & Marghitu, D. B. 2010 Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dynam. 60 (3), 217229.
Johnson, K. L. 1985 Contact mechanics. In Contact Mechanics, pp. 351369. Cambridge University Press.
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle-wall collisions in a viscous fluid. J. Fluid Mech. 433, 329346.
Kempe, T. & Frohlich, J. 2014 Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids. J. Fluid Mech. 709, 445489.
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.
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, 35433549.
Ma, D. L. & Liu, C. S. 2015 Contact law and coefficient of restitution in elastoplastic spheres. Trans. ASME J. Appl. Mech. 82 (12), 121006.
Parsi, M., Najmi, K., Najafifard, F., Hassani, S., McLaury, B. S. & Shirazi, S. A. 2014 A comprehensive review of solid particle erosion modeling for oil and gas wells and pipelines applications. J. Nat. Gas Sci. Engng 21, 850873.
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 (2), 185191.
Scheingross, J. S., Brun, F., Lo, D. Y., Omerdin, K. & Lamb, M. P. 2014 Experimental evidence for fluvial bedrock incision by suspended and bedload sediment. Geology 42 (6), 523526.
Sklar, L. S. & Dietrich, W. E. 2001 Sediment and rock strength controls on river incision into bedrock. Geology 29 (12), 10871090.
Sklar, L. S. & Dietrich, W. E. 2004 A mechanistic model for river incision into bedrock by saltating bed load. Water Resour. Res. 40 (6), W06301.
Stronge, W. J. 2000 Impact mechanics. In Impact Mechanics, pp. 116145. Cambridge University Press.
Thornton, C. 1997 Coefficient of restitution for collinear collisions of elastic perfectly plastic spheres. Trans. ASME J. Appl. Mech. 64 (2), 383386.
Wang, E. H., Geubelle, P. & Lambros, J. 2013 An experimental study of the dynamic elasto-plastic contact behavior of metallic granules. Trans. ASME J. Appl. Mech. 80 (2), 021009.
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 (1873), 22052218.
Zhao, Y. & Davis, R. H. 2002 Interaction of two touching spheres in a viscous fluid. Chem. Engng Sci. 57 (11), 19972006.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed