Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-30T03:50:15.513Z Has data issue: false hasContentIssue false

Simultaneous and sequential collisions of three wetted spheres

Published online by Cambridge University Press:  25 October 2019

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.

Type
JFM Papers
Copyright
© 2019 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

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, 52685275.10.1016/j.ces.2009.09.001Google Scholar
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, 2632.10.1107/S0021889806045523Google Scholar
Bair, S. 2019 The viscosity at the glass transition of a liquid lubricant. Friction 7, 8691.10.1007/s40544-018-0210-1Google Scholar
Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres: experimental verification. Phys. Fluids 31, 13241329.10.1063/1.866725Google 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, 501519.10.1017/S0022112089003198Google Scholar
Bordbar, M. H. & Hyppänen, T. 2007 Modeling of binary collisions between multisize viscoelastic spheres. J. Numer. Anal. Ind. Appl. Maths 2, 115118.Google Scholar
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.Google Scholar
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, 11431159.10.1016/j.cherd.2018.02.026Google Scholar
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, 218224.10.1016/j.powtec.2016.12.088Google Scholar
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.Google Scholar
Davis, R. H., Rager, D. A. & Good, B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107119.10.1017/S0022112002001489Google Scholar
Davis, R. H., Serayssol, J. M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479497.10.1017/S0022112086002392Google Scholar
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, 128148.10.1017/jfm.2012.297Google Scholar
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.Google Scholar
Donahue, C. M., Hrenya, C. M. & Davis, R. H. 2010a Stokes’ cradle: Newton’s cradle with liquid coating. Phys. Rev. Lett. 105, 034501.10.1103/PhysRevLett.105.034501Google Scholar
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.Google Scholar
Joseph, G. G. & Hunt, M. L. 2004 Oblique particle–wall collisions in a liquid. J. Fluid Mech. 510, 7193.10.1017/S002211200400919XGoogle Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329346.10.1017/S0022112001003470Google Scholar
Kantak, A. A. & Davis, R. H. 2004 Oblique collisions and rebound of spheres from a wetted surface. J. Fluid Mech. 509, 6381.10.1017/S0022112004008900Google Scholar
Kantak, A. A. & Davis, R. H. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 4252.10.1016/j.powtec.2006.07.006Google Scholar
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, 023301.10.1063/1.3070830Google Scholar
Lian, G., Adams, M. J. & Thornton, C. 1996 Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311, 141152.Google Scholar
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, 427436.10.1007/s10035-013-0392-1Google Scholar
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.Google Scholar
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.Google Scholar
Mikami, T., Kamiya, H. & Horio, M. 1998 Numerical simulation of cohesive powder behavior in a fluidized bed. Chem. Engng Sci. 53, 19271940.Google Scholar
Radl, S., Kalyoda, E., Glasser, B. J. & Khinast, J. G. 2010 Mixing characteristics of wet granular matter in a bladed mixer. Powder Technol. 200, 171189.10.1016/j.powtec.2010.02.022Google Scholar
Weber, M. W. & Hrenya, C. M. 2006 Square-well model for cohesion in fluidized beds. Chem. Engng Sci. 61, 45114527.10.1016/j.ces.2006.02.008Google Scholar
Xu, Q., Orpe, A. V. & Kudrolli, A. 2007 Lubrication effects on the flow of wet granular materials. Phys. Rev. E 76, 031302.Google Scholar
Yang, F. L. & Hunt, M. L. 2006 Dynamics of particle–particle collisions in a viscous liquid. Phys. Fluids 18, 121506.10.1063/1.2396925Google Scholar