Pair-sphere trajectories in finite-Reynolds-number shear flow

Journal of Fluid Mechanics

Volumn 596, Issue , 2008, Pages 413-435

  Kulkarni, Pandurang M ^a   Morris, Jeffrey F ^a  

^a Benjamin Levich Institute for Physico Chemical Hydrodynamics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOLTZMANN EQUATION; NEWTONIAN FLOW; REYNOLDS NUMBER; SPHERES; VISCOSITY;

FLUID MOTION; LATTICE-BOLTZMANN METHOD; NEWTON DYNAMICS; STOKES FLOW;

SHEAR FLOW;

BOLTZMANN EQUATION; NEWTONIAN FLOW; REYNOLDS NUMBER; SHEAR FLOW; SPHERES; VISCOSITY;

NEWTONIAN FLUID; REYNOLDS NUMBER; SHEAR FLOW; SPHERE; STOKES FORMULA; TRAJECTORY;

EID: 38349191759     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007009627     Document Type: Article

References (44)

1. AIDUN, C. K., LU, Y. & DING, E. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287-311.
2. BATCHELOR, G. K. 1977 The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97-117.
3. BATCHELOR, G. K. & GREEN, J. T. 1972 The hydrodynamic interation of two small freely-moving spheres in a linear flow field. J. Fluid. Mech. 56, 375-400.
4. BRADY, J. F. & Bossis, G. 1988 Stokesian Dynamics. Annu. Rev. Fluid Mech. 20, 111-157.
5. BRADY, J. F. & MORRIS, J. F. 1997 Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid. Mech. 348, 103-139.
6. BRENNER, H. & O'NEILL, M. E. 1972 On the Stokes resistance of multiparticle systems in a linear shear field. Chem. Engng Sci. 27, 1421.
7. CHUN, B. & LADD, A. J. C. 2006 Inertial migration of neutrally buoyant particles in a square duct: An investigation of multiple equilibrium positions. Phys. Fluids 18, 031704.
8. DA CUNHA, F. R. & HINCH, E. J. 1996 Shear induced dispersion in a dilute suspension of rough spheres. J. Fluid Mech. 309, 211-223.
9. DARABANER, C. L. & MASON, S. G. 1967 Particle motions in sheared suspensions XXII: Interaction of rigid spheres (Experimental). Rheol. Acta. 6, 273-284.
10. DING, E. & AIDUN, C. K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317-344.
11. FENG, J., HU, H. H. & JOSEPH, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 277 271-301.
12. FRISCH, U., D'HUMIERS, D., HASSLACHER, B., LALLEMAND, P., POMEAU, Y. & RIVET, J. P. 1987 Lattice gas hydrodynamics in two and three dimension. Complex Systems 1, 649.
13. HIGUERA, F., SUCCI, S. & BENZI, R. 1989 Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345-349.
14. HU, H. H. 1996 Direct simulation of flows of solid-liquid mixtures. Intl J. Multiphase Flow 22, 335-352.
15. HU, H. H., JOSEPH, D. D. & CROCHET, M. J. 1992 Direct simulation of fluid particle motions. Theor. Comput. Fluid Dyn. 3, 285-306.
16. HU, H. H., PATANKAR, N. A. & ZHU, M. Y. 2001 Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J. Comput. Phys 169, 427-462.
17. HUANG, P. Y. & JOSEPH, D. D. 2000 Effects of shear thinning on migration of neutrally-buoyant particles in pressure driven flow of Newtonian and viscoelastic fluid. J. Non-Newtonian Fluid Mech. 90, 159-185.
18. JEFFREY, D. J. 1992 The calculation of the low Reynolds number resistance functions for two unequal spheres. Phys. Fluids A 4 16-29.
19. JEFFREY, D. J. & ONISHI, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-n umber flow. J. Fluid. Mech. 139, 261-290.
20. KIM, S. & MIFFLIN, R. T. 1985 The resistance and mobility functions of two equal spheres in low-Reynolds-number flow. Phys. Fluids 28, 2033-2045.
21. KOCH, D. L. & HILL, R. J. 2001 Inertial effects in suspension and porous media flows. Annu. Rev. Fluid Mech. 33, 619-647.
22. KOSSACK, C. & ACRIVOS A. 1974 Steady simple shear flow past a cirular cylinder at moderate Reynolds number: A numerical solution. J. Fluid Mech. 66, 353-376.
23. KROMKAMP, J., VAN DEN ENDE, D. T. M., KANDHAI, D., VAN DER SMAN, R. G. M. & BOOM, R. M. 2005 Shear-induced self-diffusion and microstructure in non-Brownian suspensions at non-zero Reynolds number. J. Fluid Mech. 529, 253-278.
24. LADD, A. J. C. 1988 Hydrodynamic interactions in a suspension of spherical particles. J. Chem. Phys. 88, 5051-5063.
25. LADD, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285-309.
26. LADD, A. J. C. 1994b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311-339.
27. LADD, A. J. C. & VERBERG, R. 2001 Lattice-Boltzmann simulations of particle-fluid suspensions. J. Statist. Phys. 104, 1191-1151.
28. LEAL, L. G. 1992 Laminar Flow and Convective Transport Processes. Butterworth-Heinemann.
29. LIN, C. J., LEE, K. J. & SATHER, N. F. 1970a Slow motion of two spheres in a shear field. J. Fluid. Mech. 43, 35-47.
30. LIN, C. J., PEERY, J. H. & SCHOWALTER, W R. 1970b Simple shear flow round a rigid sphere: Inertial effects and suspension rheology. J. Fluid Mech. 44, 1-17.
31. MATAS, J., GEEZER, V., GUAZZELLI, E. & MORRIS, J. F. 2004 Trains of particles in finite-Reynolds-number pipe flow. Phys. Fluids 16, 4192-4195.
32. MIKULENCAK, D. R. & MORRIS, J. F. 2004 Stationary shear flow around fixed and free bodies at finite Reynolds number. J. Fluid Mech. 520, 215-242.
33. NGUYEN, N. Q. & LADD, A. J. C. 2002 Lubrication corrections for lattice-Boltzmann simulation of particle suspensions. Phys. Rev. E 66, 046708.
34. NIRSCHL, H., DWYER, H. A. & DENK, V. 1995 Three-dimensional calculations of the simple shear flow around a single particle betwen two moving walls. J. Fluid Mech. 283, 273-285.
35. POE, G. G. & ACRIVOS, A. 1975 Closed streamline flows past rotating single spheres and cylinders: Inertia effects. J. Fluid. Mech. 72, 605-623.
36. ROBERTSON, C. R. & ACRIVOS, A. 1970 Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer. J. Fluid Mech. 40, 685-703.
37. SUBRAMANIAN, G. & BRADY, J. F. 2006 Trajectory analysis for non-Brownian inertial suspensions in simple shear flow. J. Fluid Mech. 559, 151-203.
38. SUBRAMANIAN, G. & KOCH, D. L. 2006a Centrifugal forces alter streamline topology and greatly enhance the rate of heat and mass transfer from neutrally buoyant particles to a shear flow. Phys. Rev. Lett 96, 134503.
39. SUBRAMANIAN, G. & KOCH, D. L. 2006b Inertial effects on the transfer of heat or mass from neutrally buoyant spheres in a steady linear velocity field. Phys. Fluids 18, 073302.
40. SWAMINATHAN, T. N., MUKUNDAKRISHNAN, K. & HU, H. H. 2006 Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers. J. Fluid Mech. 551, 357-385.
41. WAKIYA, S., DARABANER, C. L. & MASON, S. G. 1967 Particle motions in sheared suspensions XXI: Interaction of rigid spheres (Theoretical). Rheol. Acta. 6, 273-284.
42. ZARRAGA, I. E. & LEIGHTON, D. T. 2001 Normal stress and diffusion in a dilute suspension of hard spheres undergoing simple shear. Phys. Fluids 13, 565-577.
43. ZETTNER, C. M. & YODA, M. 2001 The circular cylinder in simple shear at moderate Reynolds number: An experimental study. Exps. Fluids 30, 346-353.
44. ZURITA-GOTOR, M., BLAWZDZIEWICZ, J. & WAJNRYB, E. 2007 Swapping trajectories: A new cross-streamline particle migration mechanism in a dilute suspension of spheres. J. Fluid Mech. 592, 447-469.