Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-08T16:36:19.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-induced forces in sphere doublets

Published online by Cambridge University Press:  11 July 2008

J. J. DERKSEN
J. J. DERKSEN*
Affiliation:
Chemical & Materials Engineering Department, University of Alberta, Edmonton, Alberta, T6G [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Motivated by applications in solids formation and handling processes we numerically investigate the force and torque required for maintaining a fixed contact between two equally sized solid spheres immersed in fluid flow. The direct numerical procedure applied is based on solving the Navier–Stokes equations by means of the lattice-Boltzmann method, with no-slip conditions at the surfaces of the moving spheres. It is validated by means of the analytical results due to Nir & Acrivos (1973) for sphere doublets in creeping flow. Subsequently, doublets are released in turbulent flows. In these cases, the contact force and torque strongly fluctuate, with peak levels much higher than would follow from simple dimensional analysis. The force fluctuation levels have been quantified by a linear relation in the ratio of sphere radius over Kolmogorov length scale.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 337 - 356
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Chen, S. & Doolen, G. D. 1998 Lattice-Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Delichatsios, M. A. & Probstein, R. F. 1976 The effect of coalescence on the average drop size in liquid–liquid dispersions. Ind. Engng. Chem. Fund. 14, 134–138.CrossRefGoogle Scholar
Derksen, J. & Van den Akker, H. E. A. 1999 Large-eddy simulations on the flow driven by a Rushton turbine. AIChE J. 45, 209–221.CrossRefGoogle Scholar
Derksen, J. J. & Sundaresan, S. 2007 Direct numerical simulations of dense suspensions: wave instabilities in liquid-fluidized beds. J. Fluid Mech. 587, 303–336.CrossRefGoogle Scholar
Goldstein, D. Handler, R. & Sirovich, L. 1993 Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366.CrossRefGoogle Scholar
Gopalkrishnana, P., Manas-Zloczowera, I. & Fekeb, D. L. 2005 Investigating dispersion mechanisms in partially infiltrated agglomerates: Interstitial fluid effects. Powder Tech. 156, 111–119.CrossRefGoogle Scholar
Guerrero-Sanchez, C., Erdmenger, T., Ereda, P., Wouters, D. & Schubert, U. S. 2006 Water-soluble ionic liquids as novel stabilizers in suspension polymerization reactions: Engineering polymer beads. Chemistry A 12, 9036–9045.CrossRefGoogle ScholarPubMed
Hollander, E. D., Derksen, J. J., Portela, L. M. & Van den Akker, H. E. A. 2001 A numerical scale-up study for orthokinetic agglomeration in stirred vessels. AIChE J. 47, 2425–2440.CrossRefGoogle Scholar
Hounslow, M. J., Mumtaz, H. S., Collier, A. P., Barrick, J. P. & Bramley, A. S. A. 2001 Micro-mechanical model for the rate of aggregation during precipitation from solution. Chem. Engng. Sc. 56, 2543–2552.CrossRefGoogle Scholar
Kusters, K. A. 1991. The influence of turbulence on aggregation of small particles in agitated vessel. PhD. Thesis Eindhoven University of Technology, Netherlands.Google Scholar
Kwade, A. & Schwedes, J. 2002 Breaking characteristics of different materials and their effect on stress intensity and stress number in stirred media mills. Powder Tech. 122, 109–121.CrossRefGoogle Scholar
Ladd, A. J. C. 1994 Numerical simulations of particle suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Marchisio, D. L., Soos, M. Sefcik, & Morbidelli, M. 2006 Role of turbulent shear rate distribution in aggregation and breakage processes. AIChE J. 52, 158–173.CrossRefGoogle Scholar
Mody, N. A., Lomakin, O., Doggett, T. A., Diacovo, T. G. & King, M. R. 2005 Mechanics of transient platelet adhesion to von Willebrand factor under flow. Biophys. J. 88, 1432–1443.CrossRefGoogle ScholarPubMed
Nir, A. & Acrivos, A. 1973 On the creeping motion of two arbitrary-sized touching spheres in a linear shear field. J. Fluid Mech. 59, 209–223.CrossRefGoogle Scholar
Obermair, S., Gutschi, C., Woisetschläger, J. & Staudinger, G. 2005 Flow pattern and agglomeration in the dust outlet of a gas cyclone investigated by Phase Doppler Anemometry. Powder Tech. 156, 34–42.CrossRefGoogle Scholar
Overholt, M. R. & Pope, S. B. 1998 A deterministic forcing scheme for direct numerical simulations of turbulence. Computers Fluids 27, 11–28.CrossRefGoogle Scholar
Qian, Y. H. d'Humieres, D. & Lallemand, P. 1992 Lattice BGK for the Navier-Stokes equations. Europhys. Lett. 17, 479–484.CrossRefGoogle Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties. Phys. Fluids 17, 095106.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.CrossRefGoogle Scholar
Saffman, P. G. 1968 Correction. J. Fluid Mech. 31, 624.Google Scholar
Somers, J. A. 1993 Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation. Appl. Sci. Res. 51, 127–133.CrossRefGoogle Scholar
Soos, M., Sefcik, J. & Morbidelli, M. 2006 Investigation of aggregation, breakage and restructuring kinetics of colloidal dispersions in turbulent flows by population balance modeling and static light scattering. Chem. Engng. Sci. 61, 2349–2363.CrossRefGoogle Scholar
Succi, S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Clarendon.CrossRefGoogle Scholar
Ten Cate, A. Nieuwstadt, C. H., Derksen, J. J. & Van den Akker, H. E. A. 2002 PIV experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys. Fluids 14, 4012–4025.CrossRefGoogle Scholar
Ten Cate, A. Derksen, J. J. Portela, L. M. & Van den Akker, H. E. A. 2004 Fully resolved simulations of colliding spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233–271.CrossRefGoogle Scholar
Wang, L. P., Wexler, A. S. & Zhou, Y. 2000 Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 415, 117–153.CrossRefGoogle Scholar