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TECHNICAL PAPERS

A Numerical Investigation of the Detachment of the Trailing Particle From a Chain Sedimenting in Newtonian and Viscoelastic Fluids

[+] Author and Article Information
N. A. Patankar

Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455e-mail: patankar@aem.umn.edu

H. H. Hu

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315

J. Fluids Eng 122(3), 517-521 (Apr 18, 2000) (5 pages) doi:10.1115/1.1287269 History: Received October 20, 1999; Revised April 18, 2000
Copyright © 2000 by ASME
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References

Goldman,  A. J., Cox,  R. G., and Brenner,  H., 1966, “The slow motion of two identical arbitrarily oriented spheres through a viscous fluid,” Chem. Eng. Sci., 21, pp. 1151–1170.
Riddle,  M. J., Narvaez,  C., and Bird,  R. B., 1977, “Interactions between two spheres falling along their line of centers in a viscoelastic fluid,” J. Non-Newtonian Fluid Mech., 2, pp. 23–35.
Leal,  L. G., 1979, “The motion of small particles in non-Newtonian fluids,” J. Non-Newtonian Fluid Mech., 5, pp. 33–78.
Brunn,  P., 1980, “The motion of rigid particles in viscoelastic fluids,” J. Non-Newtonian Fluid Mech., 7, pp. 271–288.
Brunn,  P., 1977, “Interaction of spheres in a viscoelastic fluid,” Rheol. Acta, 16, pp. 461–465.
Joseph, D. D., 1996, “Flow induced microstructure in Newtonian and viscoelastic fluids,” Keynote presentation (paper no. 95a) at the 5th World Congress of Chemical Engineering, Particle Technology Track, Second Particle Technology Forum, San Diego, CA.
Feng,  J., Huang,  P. Y., and Joseph,  D. D., 1996, “Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid,” J. Non-Newtonian Fluid Mech., 63, pp. 63–88.
Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymeric Liquids, Vol. 1, Wiley-Interscience, New York.
Liu,  Y. J., and Joseph,  D. D., 1993, “Sedimentation of particles in polymer solutions,” J. Fluid Mech., 255, pp. 565–595.
Hu,  H. H., 1996, “Direct simulation of flows of solid-liquid mixtures,” Int. J. Multiphase Flow, 22, pp. 335–352.
Hu, H. H., and Patankar, N. A., 1999, “Simulation of particulate flows in Newtonian and viscoelastic fluids,” to appear in the Int. J. Multiphase Flow.

Figures

Grahic Jump Location
Phenomenon of critical distance with two spheres settling in a viscoelastic fluid. The mechanism of attraction is explained by compressive normal stresses (Joseph 6). The mechanism of separation is yet unresolved.
Grahic Jump Location
Formation of long chains in Newtonian and viscoelastic fluids. This chain configuration is unstable in Newtonian fluids whereas it is stable in viscoelastic fluids in slow flows.
Grahic Jump Location
Phenomenon of critical distance for chains settling in viscoelastic fluids
Grahic Jump Location
Numerical simulations are performed in a channel with the walls wide apart (the channel width is 15 times the particle diameter)
Grahic Jump Location
Phenomenon of critical distance in Newtonian fluids, N=2,ρsf=1.01 and Fr0.5/Re=0.026
Grahic Jump Location
Effect of number of particles in the leading chain. Initial separation ∼0, ρsf=1.005 and Fr0.5/Re=0.026.
Grahic Jump Location
Effect of density ratio. Initial separation ∼0, N=3 and Fr0.5/Re=0.026.
Grahic Jump Location
Effect of viscosity. Initial separation ∼0, N=3 and ρsf=1.01.
Grahic Jump Location
Effect of fluid elasticity. Initial separation ∼0, N=2,ρsf=1.003 and Fr0.5/Re=0.026.
Grahic Jump Location
Sequential separation of particles from a chain of six particles in a viscoelastic fluid, ρsf=1.001,Fr0.5/Re=0.026 and De/Re=2.4

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