Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia

Physics of Fluids

Volumn 18, Issue 8, 2006, Pages

  Verberg, Rolf ^a   Koch, Donald L ^a  

^a Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DRAG; KINETIC ENERGY; KINETIC THEORY; PARTICLES (PARTICULATE MATTER); REYNOLDS NUMBER; RHEOLOGY; VISCOSITY; VOLUME FRACTION;

FLUID INERTIA; PARTICLE SUSPENSIONS; STOKES NUMBER; VISCOUS DISSIPATION;

SUSPENSIONS (FLUIDS);

COMPUTER SIMULATION; DRAG; KINETIC ENERGY; KINETIC THEORY; PARTICLES (PARTICULATE MATTER); REYNOLDS NUMBER; RHEOLOGY; SUSPENSIONS (FLUIDS); VISCOSITY; VOLUME FRACTION;

EID: 33748278365     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2337318     Document Type: Article

References (30)

1. J. T. Jenkins and S. B. Savage, "A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles," J. Fluid Mech. JFLSA70022-112010.1017/S0022112083001044 130, 187 (1983).
2. C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, "Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield," J. Fluid Mech. JFLSA70022-112010.1017/S0022112084000586 140, 223 (1984).
3. J. T. Jenkins and M. W. Richman, "Grad's 13-moment system for a dense gas of inelastic spheres," Arch. Ration. Mech. Anal. AVRMAW0003-952710.1007/BF00250919 87, 355 (1985).
4. M. Babic, "On the stability of rapid granular flows," J. Fluid Mech. JFLSA70022-112010.1017/S002211209300206X 254, 127 (1993).
5. A. S. Sangani, G. Mo, H.-K. Tsao, and D. L. Koch, "Simple shear flows of dense gas-solid suspensions at finite Stokes numbers," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096002224 313, 309 (1996).
6. A. J. C. Ladd and R. Verberg, "lattice Boltzmann simulations of particle-fluid suspensions," J. Stat. Phys. JSTPBS0022-471510.1023/ A:1010414013942 104, 1191 (2001).
7. N.-Q. Nguyen and A. J. C. Ladd, "Lubrication corrections for lattice Boltzmann simulations of particle suspensions," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.66.046708 66, 046708 (2002).
8. J. J. Wylie, D. L. Koch, and A. J. C. Ladd, "Rheology of suspensions with high particle inertia and moderate fluid inertia," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002003531 480, 95 (2003).
9. N. F. Carnahan and K. E. Starling, "Equation of state for nonattracting rigid spheres," J. Chem. Phys. JCPSA60021-960610.1063/ 1.1672048 51, 635 (1969).
10. R. R. Sundararajakumar and D. L. Koch, "Non-continuum lubrication flows between spherical particles colliding in a gas," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096002212 313, 283 (1996).
11. H. Grad, "On the kinetic theory of rarified gas," Commun. Pure Appl. Math. CPMAMV0010-3640 2, 331 (1949).
12. U. Frisch, D. d'Humières, D. Hasslacher, and P. Lallemand, "Lattice gas hydrodynamics in two and three dimensions," Complex Syst. CPSYEN0891-2513 1, 649 (1987).
13. F. J. Higuera, S. Succi, and R. Benzi, "Lattice gas dynamics with enhanced collisions," Europhys. Lett. EULEEJ0295-5075 9, 345 (1989).
14. S. D. Chen, H. D. Chen, D. Martinez, and W. Matthaeus, "Lattice Boltzmann model for simulation of magnetohydrodynamics," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.67.3776 67, 3776 (1991).
15. Y. H. Qian, D. d'Humières, and P. Lallemand, "Lattice BGK models for Navier-Stokes equation," Europhys. Lett. EULEEJ0295-5075 17, 479 (1992).
16. D. d'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L.-S. Luo, "Multiple-relaxation-time lattice Boltzmann models in three dimensions," Philos. Trans. R. Soc. London, Ser. A PTRMAD0962-8428 360, 437 (2002).
17. P. Lallemand and L.-S. Luo, "Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.61.6546 61, 6546 (2000).
18. A. J. C. Ladd, "Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112094001771 271, 285 (1994).
19. X. He, Q. Zou, L.-S. Luo, and M. Dembo, "Analytic solutions of simple flows and analysis of nonslip for the lattice Boltzmann BGK model," J. Stat. Phys. JSTPBS0022-471510.1007/BF02181482 87, 115 (1997).
20. A. J. C. Ladd, "Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results," J. Fluid Mech. JFLSA70022-112010.1017/S0022112094001783 271, 311 (1994).
21. R. Verberg and A. J. C. Ladd, "Accuracy and stability of a lattice Boltzmann model with subgrid scale boundary conditions," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.65.016701 65, 016701 (2002).
22. E. J. Hinch, "An averaged-equation approach to particle interactions in a fluid suspension," J. Fluid Mech. JFLSA70022-112010.1017/S0022112077001414 83, 695 (1977).
23. S. Ergun, "Pressure drop through granular beds," Chem. Eng. Prog. CEPRA80360-7275 48, 84 (1952).
24. R. J. Hill, D. L. Koch, and A. J. C. Ladd, "Moderate-Reynolds-number flows in ordered and random arrays of spheres," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001003603 448, 243 (2001).
25. D. L. Koch and A. J. C. Ladd, "Moderate Reynolds number flows through periodic and random arrays of aligned cylinders," J. Fluid Mech. JFLSA70022-112010.1017/S002211209700671X 349, 31 (1997).
26. H. Xu, M. Y. Louge, and A. Reeves, "Solution of the kinetic theory for bounded collisional granular flows," Continuum Mech. Thermodyn. CMETEJ0935-117510.1007/s00161-003-0116-6 15, 321 (2003).
27. G. K. Batchelor, "The stress system in a suspension of force-free particles," J. Fluid Mech.JFLSA70022-112010.1017/S0022112070000745 41, 545 (1970).
28. I. E. Zarraga, D. A. Hill, and D. T. Leighton, Jr., "The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids," J. Rheol. JORHD20148-605510.1122/1.551083 44, 185 (2001).
29. A. J. C. Ladd, "Hydrodynamic transport coefficients of random dispersions of hard spheres," J. Chem. Phys. JCPSA60021-960610.1063/ 1.458830 93, 3484 (1990).
30. D. R. Mikulencak and J. F. Morris, "Stationary shear flow around fixed and free bodies at finite Reynolds number," J. Fluid Mech. JFLSA70022-112010.1017/S0022112004001648 520, 215 (2004).