Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere-wall and sphere-sphere interactions

Journal of Rheology

Volumn 57, Issue 3, 2013, Pages 857-880

  Eisenberg, D A ^a   Klink, I M ^a   Phillips, R J ^a  

^a University of California Davis   (United States)

Author keywords

hydrodynamic interactions; sedimentation

Indexed keywords

HYDRODYNAMIC INTERACTION; LOW REYNOLDS NUMBER; NEWTONIAN FLUIDS; NEWTONIAN SOLUTIONS; POLYISOBUTYLENES; SEDIMENTATION RATES; SPHERICAL PARTICLE; VIS-COELASTIC FLUIDS;

DRAG; REYNOLDS NUMBER; SEDIMENTATION; SEDIMENTS; SEPARATION;

SPHERES;

EID: 84877252446     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.4798625     Document Type: Article

References (35)

1. Adrian, R. J., and J. Westerweel, Particle Image Velocimetry (Cambridge University Press, New York, 2011).
2. Allen, E., and P. Uhlherr, Nonhomogeneous sedimentation in viscoelastic fluids., J. Rheol. 33, 627-638 (1989). 10.1122/1.550030
3. Ardekani, A. M., R. H. Rangel, and D. D. Joseph, Motion of a sphere normal to a wall in a second-order fluid., J. Fluid Mech. 587, 163-172 (2007). 10.1017/S0022112007007549
4. Arigo, M. T., and G. H. McKinley, The effects of viscoelasticity on the transient motion of a sphere in a shear-thinning fluid., J. Rheol. 41, 103-128 (1997). 10.1122/1.550803
5. Becker, L. E., G. H. McKinley, and H. A. Stone, Sedimentation of a sphere near a plane wall: Weak non-Newtonian and inertial effects., J. Non-Newtonian Fluid Mech. 63, 201-233 (1996). 10.1016/0377-0257(95)01424-1
6. Binous, H., and R. J. Phillips, Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells., J. Non-Newtonian Fluid Mech. 83, 93-130 (1999a). 10.1016/S0377-0257(98)00141-4
7. Binous, H., and R. J. Phillips, The effect of sphere-wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells., J. Non-Newtonian Fluid Mech. 85, 63-92 (1999b). 10.1016/S0377-0257(98)00190-6
8. Bird, R. B., R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids 1. Fluid Mechanics (Wiley, New Nork, 1987).
9. Bisgaard, C., Velocity fields around spheres and bubbles investigated by laser-Doppler anemometry., J. Non-Newtonian Fluid Mech. 12, 283-302 (1983). 10.1016/0377-0257(83)85003-4
10. Bobroff, S., and R. J. Phillips, Nuclear magnetic resonance imaging investigation of sedimentation of concentrated suspensions in non-Newtonian fluids., J. Rheol. 42, 1419-1436 (1998). 10.1122/1.550895
11. Bot, E. T. J., M. A. Hulsen, and B. H. A. A. Van den Brule, The motion of two spheres falling along their line of center in a Boger fluid., J. Non-Newtonian Fluid Mech. 79, 191-212 (1998). 10.1016/S0377-0257(98)00106-2
12. Brenner, H., The slow motion of a sphere through a viscous fluid towards a plane surface., Chem. Eng. Sci. 16, 242-251 (1961). 10.1016/0009-2509(61) 80035-3
13. Chhabra, R. P., and J. F. Richardson, Non-Newtonian Flow and Applied Rheology: Engineering Applications (Butterworth-Heinemann, Burlington, MA, 2008).
14. Daugan, S., L. Talini, B. Herzhaft, Y. Peysson, and C. Allain, Sedimentation of suspensions in shear-thinning fluids., Oil Gas Sci. Technol. Rev. IFP 59, 71-80 (2004). 10.2516/ogst:2004007
15. Gheissary, G., and B. H. A. A. van den Brule, Unexpected phenomena observed in particle settling in non-Newtonian media., J. Non-Newtonian Fluid Mech. 67, 1-18 (1996). 10.1016/S0377-0257(96)01436-X
16. Gondret, P., M. Lance, and L. Petit, Bouncing motion of spherical particles in fluids., Phys. Fluids 14, 643-652 (2002). 10.1063/1.1427920
17. Guala, M., and A. Stocchino, Large-scale flow structures in particle-wall collision at low Deborah numbers., Eur. J. Mech. B/Fluids 26, 511-530 (2007). 10.1016/j.euromechflu.2006.10.004
18. Happel, J., and H. Brenner, Low Reynolds Number Hydrodynamics (Kluwer, Hingham, MA, 1986).
19. Harlen, O. G., High-Deborah-number flow of a dilute polymer solution past a sphere falling along the axis of a cylindrical tube., J. Non-Newtonian Fluid Mech. 37, 157-173 (1990). 10.1016/0377-0257(90)90003-T
20. Harlen, O. G., The negative wake behind a sphere sedimenting through a viscoelastic fluid., J. Non-Newtonian Fluid Mech. 108, 411-430 (2002). 10.1016/S0377-0257(02)00139-8
21. Joseph, D. D., Y. J. Liu, M. Poletto, and J. Feng, Aggregation and dispersion of spheres falling in viscoelastic liquids., J. Non-Newtonian Fluid Mech. 54, 45-86 (1994). 10.1016/0377-0257(94)80015-4
22. Mora, S., L. Talini, and C. Allain, Structuring sedimentation in a shear-thinning fluid., Phys. Rev. Lett. 95, 088301 (2005). 10.1103/PhysRevLett. 95.088301
23. Phillips, R. J., Dynamic simulation of hydrodynamically interacting spheres in a quiescent second-order fluid., J. Fluid Mech. 315, 345-365 (1996). 10.1017/S0022112096002455
24. Phillips, R. J., A singularity method for calculating time-dependent viscoelastic flows with integral constitutive equations., J. Fluid Mech. 481, 77-104 (2003). 10.1017/S0022112002003592
25. Phillips, R. J., Structural instability in the sedimentation of particulate suspensions through viscoelastic fluids., J. Non-Newtonian Fluid Mech. 165, 479-488 (2010). 10.1016/j.jnnfm.2010.02.003
26. Phillips, R. J., and L. Talini, Chaining of weakly interacting particles suspended in viscoelastic fluids., J. Non-Newtonian Fluid Mech. 147, 175-188 (2007). 10.1016/j.jnnfm.2007.08.007
27. Riddle, M. J., C. Narvaez, and R. B. Bird, Interactions between two spheres falling along their line of centers in a viscoelastic fluid., J. Non-Newtonian Fluid Mech. 2, 23-35 (1977). 10.1016/0377-0257(77)80030-X
28. Sigli, D., and M. Coutanceau, Effect of finite boundaries on the slow laminar flow of a viscoelastic fluid around a spherical obstacle., J. Non-Newtonian Fluid Mech. 2, 1-21 (1977). 10.1016/0377-0257(77)80029-3
29. Singh, P., D. D. Joseph, T. I. Hesla, R. Glowinski, and T.-W. Pan, Distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows., J. Non-Newtonian Fluid Mech. 91, 165-188 (2000). 10.1016/S0377-0257(99)00104-4
30. Solomon, M. J., and S. J. Muller, Flow past a sphere in polystyrene-based Boger fluids: The effect on the drag coefficient of finite extensibility, solvent quality, and polymer molecular weight., J. Non-Newtonian Fluid Mech. 62, 81-94 (1996). 10.1016/0377-0257(95)01398-9
31. Stimson, M., and G. B. Jeffery, The motion of two spheres in a viscous fluid., Proc. R. Soc. London, Ser. A 111, 110-116 (1926). 10.1098/rspa.1926.0053
32. Stocchino, A., and M. Guala, Particle-wall collision in shear-thinning fluids., Exp. Fluids 38, 476-484 (2005). 10.1007/s00348-005-0928-1
33. Ten Cate, A., C. H. Nieuwstad, J. J. Derhsen, and H. E. A. Van den Akker, Particle imaging velocimetry experiments and lattice Boltzmann simulations on a single sphere settling under gravity., Phys. Fluids 14, 4012-4025 (2002). 10.1063/1.1512918
34. Verneuil, E., R. J. Phillips, and L. Talini, Axisymmetric two-sphere sedimentation in a shear-thinning viscoelastic fluid: Particle interactions and induced velocity fields., J. Rheol. 51, 1343-1359 (2007). 10.1122/1.2780799
35. Yu, Z., A. Wachs, and Y. Peysson, Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method., J. Non-Newtonian Fluid Mech. 136, 126-139 (2006). 10.1016/j.jnnfm.2006.03.015