Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T21:06:09.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Agglomeration and de-agglomeration of rotating wet doublets

Published online by Cambridge University Press:  21 August 2012

Carly M. Donahue ,
William M. Brewer ,
Robert H. Davis  and
Christine M. Hrenya
Carly M. Donahue
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
William M. Brewer
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
Robert H. Davis
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
Christine M. Hrenya*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
*
†Email address for correspondence: hrenya@colorado.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this work, experiments using a pendulum apparatus were conducted for two particles engaged in oblique, wetted collisions over a range of impact angles, impact velocities, coating thicknesses, liquid viscosities, particle materials, and particle radii. From previous studies on normal or head-on collisions, the two particles bounce apart if the Stokes number (a ratio of particle inertia to viscous forces) exceeds a critical value, whereas they stick together if the Stokes number is below this critical value. However, for oblique collisions, an additional outcome is observed at moderate Stokes numbers and impact angles, in which the spheres initially stick together, rotate as a doublet, and then separate due to centrifugal forces. We refer to this outcome as ‘stick–rotate–separate’. For subcritical Stokes numbers exhibiting this new outcome, the experimental results for the apparent coefficient of normal restitution and angle of rotation from impact to separation show only weak dependence on the fluid viscosity and thickness and the dry restitution coefficient, whereas they both decrease with increasing particle radius. These results are in contrast with those for supercritical Stokes numbers in which the spheres bounce upon impact. An accompanying theory based on lubrication forces, the glass transition of the liquid layer, and solid deformation and rebound agrees well with experimental results and gives insight into the observed trends.

JFM classification

Granular media: Granular media Low-Reynolds-number flows: Lubrication theory Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 128 - 148
Copyright
Copyright © Cambridge University Press 2012

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

1. Barnocky, G. & Davis, R. H. 1988 Elastohydrodynamic collision and rebound of spheres – experimental-verification. Phys. Fluids 31, 1324–1329.CrossRefGoogle Scholar
2. 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, 501–519.CrossRefGoogle Scholar
3. Chaudhuri, B., Mehrotra, A., Muzzio, F. J. & Tomassone, M. S. 2006 Cohesive effects in powder mixing in a tumbling blender. Powder Technol. 165, 105–114.CrossRefGoogle Scholar
4. Cross, N. L. & Picknett, R. G. 1968 Comment on paper effect of capillary liquid on force of adhesion between spherical solid particles. J. Colloid Interface Sci. 26, 247–249.CrossRefGoogle Scholar
5. Davis, R. H. 1987 Elastohydrodynamic collisions of particles. Physico-Chem. Hydrodyn. 9, 41–52.Google Scholar
6. Davis, R. H., Rager, D. A. & Good, B. T. 2002 Elastohydrodynamic rebound of spheres from coated surfaces. J. Fluid Mech. 468, 107–119.CrossRefGoogle Scholar
7. Davis, R. H., Serayssol, J. M. & Hinch, E. J. 1986 The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497.CrossRefGoogle Scholar
8. Donahue, C. M., Davis, R. H., Kantak, A. A. & Hrenya, C. M. 2012 Mechanisms for agglomeration and deagglomeration following oblique collisions of wetted particles. Phys. Rev. E (submitted).CrossRefGoogle Scholar
9. Donahue, C. M., Hrenya, C. M. & Davis, R. H. 2010a Stokes’s cradle: Newton’s cradle with liquid coating. Phys. Rev. Lett. 105, 34501.CrossRefGoogle ScholarPubMed
10. 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. Fluid Mech. 650, 479–504.CrossRefGoogle Scholar
11. Ennis, B. J., Tardos, G. & Pfeffer, R. 1991 A microlevel-based characterization of granulation phenomena. Powder Technol. 65, 257–272.CrossRefGoogle Scholar
12. Fisher, R. A. 1926 On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines. J. Agric. Sci. 16, 492–505.CrossRefGoogle Scholar
13. Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14, 643–652.CrossRefGoogle Scholar
14. Iveson, S. M. 2002 Limitations of one-dimensional population balance models of wet granulation processes. Powder Technol. 124, 219–229.CrossRefGoogle Scholar
15. Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.CrossRefGoogle Scholar
16. Kantak, A. A. & Davis, R. H. 2004 Oblique collisions and rebound of spheres from a wetted surface. J. Fluid Mech. 509, 63–81.CrossRefGoogle Scholar
17. Kantak, A. A. & Davis, R. H. 2006 Elastohydrodynamic theory for wet oblique collisions. Powder Technol. 168, 42–52.CrossRefGoogle Scholar
18. Kantak, A. A., Hrenya, C. M. & Davis, R. H. 2009 Initial rates of aggregation for dilute, granular flows of wet particles. Phys. Fluids 21, 023301.CrossRefGoogle Scholar
19. Lekhal, A., Conway, S. L., Glasser, B. J. & Khinast, J. G. 2006 Characterization of granular flow of wet solids in a bladed mixer. AIChE J. 52 (8), 2757–2766.CrossRefGoogle Scholar
20. Li, H. M. & McCarthy, J. J. 2005 Phase diagrams for cohesive particle mixing and segregation. Phys. Rev. E 71, 021305-1–021305-8.CrossRefGoogle ScholarPubMed
21. Lian, G., Adams, M. & Thornton, C. 1996 Elastohydrodynamic collisions of solid spheres. J. Fluid Mech. 311, 141–152.CrossRefGoogle Scholar
22. Lian, G. P., Thornton, C. & Adams, M. J. 1993 A theoretical study of the liquid bridge forces between two rigid spherical bodies. J. Colloid Interface Sci. 161, 138–147.CrossRefGoogle Scholar
23. Liu, P. Y., Yang, R. Y. & Yu, A. B. 2011 Dynamics of wet particles in rotating drums: effect of liquid surface tension. Phys. Fluids 23, 013304.CrossRefGoogle Scholar
24. Marston, J., Wong, W. & Thoroddsen, S. 2010 Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall. J. Fluid Mech. 655, 515–526.CrossRefGoogle Scholar
25. Mason, G. & Clark, W. C. 1965 Liquid bridges between spheres. Chem. Engng Sci. 20, 859–866.CrossRefGoogle Scholar
26. Mikami, T., Kamiya, H. & Horio, M. 1998 Numerical simulation of cohesive powder behaviour in a fluidized bed. Chem. Engng Sci. 53, 1927–1940.CrossRefGoogle Scholar
27. O’Neill, M. E. & Majumdar, R. 1970 Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part I. The determination of exact solutions for any values of the ratio of radii and separation parameters. Z. Angew. Math. Phys. 21, 164–179.CrossRefGoogle Scholar
28. Saitoh, K., Bodrova, A., Hayakawa, H. & Brilliantov, N. V. 2010 Negative normal restitution coefficient found in simulation of nanocluster collisions. Phys. Rev. Lett. 105, 238001.CrossRefGoogle ScholarPubMed
29. Salcudean, M., Darabi, P., Pougatch, K. & Grecov, D. 2009 A novel coalescence model for binary collision of identical wet particles. Chem. Engng Sci. 64, 1868–1876.Google Scholar
30. Talu, I., Tardos, G. I. & Khan, M. I. 2000 Computer simulation of wet granulation. Powder Technol. 110, 59–75.CrossRefGoogle Scholar
31. Weber, M. W. & Hrenya, C. M. 2006 Square-well model for cohesion in fluidized beds. Chem. Engng Sci. 61, 4511–4527.CrossRefGoogle Scholar
32. Xu, Q., Orpe, A. V. & Kudrolli, A. 2007 Lubrication effects on the flow of wet granular materials. Phys. Rev. E 76, 31302.CrossRefGoogle ScholarPubMed