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Simultaneous and sequential collisions of three wetted spheres

  • Robert H. Davis (a1)

Abstract

Rectilinear collisions of three wetted spheres are considered under conditions of high capillary numbers, for which viscous lubrication forces dominate over capillary forces. The viscous forces resist the relative motion, as characterized by the Stokes number (a dimensionless ratio of particle inertia and viscous forces). At high Stokes numbers, the particles penetrate the fluid layers between them with sufficient inertia that they collide and rebound. Both simultaneous and sequential collisions are simulated, and various outcomes are demonstrated: full agglomeration of the three spheres at low Stokes numbers, full separation or Newton’s cradle at large Stokes numbers and even reverse Newton’s cradle at intermediate Stokes numbers when there is a thicker combined fluid layer between the two target spheres than between the striker sphere and the first target sphere. When there is an initial air gap between the two target spheres, even more exotic outcomes are predicted, such as full separation after the initial collisions followed by full agglomeration or reverse Newton’s cradle (intermediate Stokes numbers) or Newton’s cradle (large Stokes numbers) after the subsequent collisions when the striker sphere catches back up to the target spheres. The approach and findings of this work are expected to provide input and guidance to future work on discrete-element modelling of collisions of many wet particles.

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Corresponding author

Email address for correspondence: robert.davis@colorado.edu

References

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Anand, A., Curtis, J. S., Wassgren, C. R., Hancock, B. C. & Ketterhagen, W. R. 2009 Predicting discharge dynamics of wet cohesive particles from a rectangular hopper using the discrete element method (DEM). Chem. Engng Sci. 64, 52685275.
Angel, R. J., Bujak, M., Zhao, J., Gatta, G. D. & Jacobsen, S. D. 2007 Effective hydrostatic limits of pressure media for high-pressure crystallographic studies. J. Appl. Crystallogr. 40, 2632.
Bair, S. 2019 The viscosity at the glass transition of a liquid lubricant. Friction 7, 8691.
Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31, 13241329.
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, 501519.
Bordbar, M. H. & Hyppänen, T. 2007 Modeling of binary collisions between multisize viscoelastic spheres. J. Numer. Anal. Ind. Appl. Maths 2, 115118.
Brake, M. R. W., Reu, P. L. & Aragon, D. S. 2017 A comprehensive set of impact data for common aerospace metals. J. Comput. Nonlinear Dyn. 12, 061011.
Buck, B., Lunewski, J., Tang, Y., Deen, N. G., Kuipers, J. A. M. & Heinrich, S. 2018 Numerical investigation of collision dynamics of wet particles via force balance. Chem. Engng Res. Des. 132, 11431159.
Buck, B., Tang, Y., Heinrich, S., Deen, N. G. & Kuipers, J. A. M. 2017 Collision dynamics of wet solids: rebound and rotation. Powder Technol. 316, 218224.
Cruger, B., Salikov, V., Heinrich, S., Antonyuk, S., Sutkar, V., Deen, N. & Kuipers, J. A. M. 2016 Coefficient of restitution for particles impacting on wet surfaces: an improved experimental approach. Particuology 25, 19.
Davis, R. H., Rager, D. A. & Good, B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107119.
Davis, R. H., Serayssol, J. M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479497.
Donahue, C. M., Brewer, W. M., Davis, R. H. & Hrenya, C. M. 2012a Agglomeration and de-agglomeration of rotating wet doublets. J. Fluid Mech. 708, 128148.
Donahue, C. M., Davis, R. H., Kantak, A. A. & Hrenya, C. M. 2012b Mechanisms for agglomeration and de-agglomeration following oblique collisions of wet particles. Phys. Rev. E 86, 021303.
Donahue, C. M., Hrenya, C. M. & Davis, R. H. 2010a Stokes’ cradle: Newton’s cradle with liquid coating. Phys. Rev. Lett. 105, 034501.
Donahue, C. M., Hrenya, C. M., Davis, R. H., Nakagawa, K. J., Zelinskaya, A. P. & Joseph, G. G. 2010b Stokes’ cradle: normal three-body collisions between wetted particles. J. Fluids Mech. 650, 479504.
Joseph, G. G. & Hunt, M. L. 2004 Oblique particle–wall collisions in a liquid. J. Fluid Mech. 510, 7193.
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329346.
Kantak, A. A. & Davis, R. H. 2004 Oblique collisions and rebound of spheres from a wetted surface. J. Fluid Mech. 509, 6381.
Kantak, A. A. & Davis, R. H. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 4252.
Kantak, A. A., Hrenya, C. M. & Davis, R. H. 2009 Initial rates of aggregation for dilute, granular flows of wet (cohesive) particles. Phys. Fluids 21, 023301.
Lian, G., Adams, M. J. & Thornton, C. 1996 Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311, 141152.
Liu, P. Y., Yang, R. Y. & Yu, A. B. 2013 The effect of liquids on radial segregation of granular mixtures in rotating drums. Granul. Matt. 15, 427436.
Ma, J., Liu, D. & Chen, X. 2016 Normal and oblique impacts between smooth spheres and liquid layers: liquid bridge and restitution coefficient. Power Technol. 301, 747759.
Marston, J. O., Yong, W., Ng, W. K., Tan, R. B. H. & Thoroddsen, S. T. 2011 Cavitation structures formed during the rebound of a sphere from a wetted surface. Exp. Fluids 50, 729746.
Mikami, T., Kamiya, H. & Horio, M. 1998 Numerical simulation of cohesive powder behavior in a fluidized bed. Chem. Engng Sci. 53, 19271940.
Radl, S., Kalyoda, E., Glasser, B. J. & Khinast, J. G. 2010 Mixing characteristics of wet granular matter in a bladed mixer. Powder Technol. 200, 171189.
Weber, M. W. & Hrenya, C. M. 2006 Square-well model for cohesion in fluidized beds. Chem. Engng Sci. 61, 45114527.
Xu, Q., Orpe, A. V. & Kudrolli, A. 2007 Lubrication effects on the flow of wet granular materials. Phys. Rev. E 76, 031302.
Yang, F. L. & Hunt, M. L. 2006 Dynamics of particle–particle collisions in a viscous liquid. Phys. Fluids 18, 121506.
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Simultaneous and sequential collisions of three wetted spheres

  • Robert H. Davis (a1)

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