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Stokes' cradle: normal three-body collisions between wetted particles

  • C. M. DONAHUE (a1), C. M. HRENYA (a1), R. H. DAVIS (a1), K. J. NAKAGAWA (a1), A. P. ZELINSKAYA (a1) and G. G. JOSEPH (a1)...

Abstract

In this work, a combination of experiments and theory is used to investigate three-body normal collisions between solid particles with a liquid coating (i.e. ‘wetted’ particles). Experiments are carried out using a Stokes' cradle, an apparatus inspired by the Newton's cradle desktop toy except with wetted particles. Unlike previous work on two-body systems, which may either agglomerate or rebound upon collision, four outcomes are possible in three-body systems: fully agglomerated, Newton's cradle (striker and target particle it strikes agglomerate), reverse Newton's cradle (targets agglomerate while striker separates) and fully separated. Post-collisional velocities are measured over a range of parameters. For all experiments, as the impact velocity increases, the progression of outcomes observed is fully agglomerated, reverse Newton's cradle and fully separated. Notably, as the viscosity of the oil increases, experiments reveal a decrease in the critical Stokes number (the Stokes number that demarcates a transition from agglomeration to separation) for both sets of adjacent particles. A scaling theory is developed based on lubrication forces and particle deformation and elasticity. Unlike previous work for two-particle systems, two pieces of physics are found to be critical in the prediction of a regime map that is consistent with experiments: (i) an additional resistance upon rebound of the target particles due to the pre-existing liquid bridge between them (which has no counterpart in two-particle collisions), and (ii) the addition of a rebound criterion due to glass transition of the liquid layer at high pressure between colliding particles.

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Corresponding author

Email address for correspondence: hrenya@colorado.edu

References

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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.
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 2 spheres. J. Fluid Mech. 209, 501519.
Chu, P. S. Y. & Cameron, J. 1962 Pressure viscosity characteristics of lubricating oils. J. Inst. Petrol. 48, 147155.
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 2 spheres. J. Fluid Mech. 163, 479497.
Donahue, C. M., Hrenya, C. M. & Davis, R. H. 2010 Stokes' cradle: adding a layer of complexity to Newton's cradle. Submitted.
Donahue, C. M., Hrenya, C. M., Zelinskaya, A. P. & Nakagawa, K. J. 2008 Newton's cradle undone: experiments and collision models for the normal collision of three solid spheres. Phys. Fluids 20, 113301.
Ennis, B. J., Tardos, G. & Pfeffer, R. 1991 A microlevel-based characterization of granulation phenomena. Powder Technol. 65, 257272.
Hertz, H. 1882 On the contact of rigid elastic solids and on hardness. J. Reine Angew. Math. 94, 156171.
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. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 4252.
Lian, G., Adams, M. J. & Thornton, C. 1996 Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311, 141152.
Lian, G. P., Thornton., C. & Adams, M. J. 1993 A theoretical-study of the liquid bridge forces between 2 rigid spherical bodies. J. Colloid Interface Sci. 161, 138147.
Lundberg, J. & Shen, H. H. 1992 Collisional restitution dependence on viscosity. J. Engng Mech.-ASCE 118, 979989.
Mikami, T., Kamiya, H. & Horio, M. 1998 Numerical simulation of cohesive powder behaviour in a fluidized bed. Chem. Engng Sci. 53, 19271940.
Pepin, X., Rossetti, D. & Iveson, S. 2000 Modelling the evolution and rupture of pendular liquid bridges in the presence of large wetting hysteresis. J. Colloid Interface Sci. 232, 289297.
Stevens, A. B. & Hrenya, C. M. 2005 Comparison of soft-sphere models to measurements of collision properties during normal impacts. Powder Technol. 154, 99109.
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Stokes' cradle: normal three-body collisions between wetted particles

  • C. M. DONAHUE (a1), C. M. HRENYA (a1), R. H. DAVIS (a1), K. J. NAKAGAWA (a1), A. P. ZELINSKAYA (a1) and G. G. JOSEPH (a1)...

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