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

Published online by Cambridge University Press:  31 March 2010

C. M. DONAHUE ,
C. M. HRENYA ,
R. H. DAVIS ,
K. J. NAKAGAWA ,
A. P. ZELINSKAYA  and
G. G. JOSEPH
C. M. DONAHUE
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
C. M. HRENYA*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
R. H. DAVIS
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
K. J. NAKAGAWA
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
A. P. ZELINSKAYA
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
G. G. JOSEPH
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309–0424, USA
*
†Email address for correspondence: [email protected]
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 479 - 504
Copyright
Copyright © Cambridge University Press 2010

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