The suspension balance model revisited

Physics of Fluids

Volumn 23, Issue 4, 2011, Pages

  Nott, Prabhu R ^a   Guazzelli, Elisabeth ^b   Pouliquen, Olivier ^b  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

TWO PHASE FLOW;

INTER-PHASE DRAG; MICROMECHANICAL RELATIONS; PARTICLE MIGRATION; PARTICLE STRESS; PARTICLE-PHASE STRESS; SHEAR-INDUCED MIGRATION; SUSPENSION BALANCE; VOLUME-AVERAGING;

SUSPENSIONS (FLUIDS);

EID: 84981275733     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3570921     Document Type: Article

References (34)

1. Leighton D.T. Acrivos A. The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 1987, 181:415. JFLSA7, 0022-1120, 10.1017/S0022112087002155.
2. Nott P.R. Brady J.F. Pressure-driven flow of suspensions: Simulation and theory. J. Fluid Mech. 1994, 275:157. JFLSA7, 0022-1120, 10.1017/S0022112094002326.
3. Batchelor G.K. The stress system in a suspension of force-free particles. J. Fluid Mech. 1970, 41:545. JFLSA7, 0022-1120, 10.1017/S0022112070000745.
4. Buyevich Y.A. Shchelchkova I.N. Flow of dense suspensions. Prog. Aerosp. Sci. 1978, 18:121. PAESD6, 0376-0421, 10.1016/0376-0421(77)90004-5.
5. Drew D.A. Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 1983, 15:261. ARVFA3, 0066-4189, 10.1146/annurev.fl.15.010183.001401.
6. Jackson R. Locally averaged equations of motion for a mixture of identical particles and a Newtonian fluid. Chem. Eng. Sci. 1997, 52:2457. CESCAC, 0009-2509, 10.1016/S0009-2509(97)00065-1.
7. Zhang D.Z. Prosperetti A. Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Int. J. Multiphase Flow 1997, 23:425. IJMFBP, 0301-9322, 10.1016/S0301-9322(96)00080-8.
8. Prosperetti A. The average stress in incompressible disperse flow. Int. J. Multiphase Flow 2004, 30:1011. IJMFBP, 0301-9322, 10.1016/j.ijmultiphaseflow.2004.05.003.
9. Anderson T.B. Jackson R. Fluid mechanical description of fluidized beds. equations of motion. Ind. Eng. Chem. Fundam. 1967, 6:527. IECFA7, 0196-4313, 10.1021/i160024a007.
10. Lhuillier D. Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 2009, 21:023302. PHFLE6, 1070-6631, 10.1063/1.3079672.
11. Jeffrey D.J. Morris J.F. Brady J.F. The pressure moments for two spheres in a low-Reynolds-number flow. Phys. Fluids A 1993, 5:2317. PFADEB, 0899-8213, 10.1063/1.858795.
12. Brady J.F. Morris J.F. Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid Mech. 1997, 348:103. JFLSA7, 0022-1120, 10.1017/S0022112097006320.
13. Singh A. Nott P.R. Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 2000, 412:279. JFLSA7, 0022-1120, 10.1017/S0022112000008375.
14. Zarraga I.E. Hill D.A. Leighton D.T. The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 2000, 44:185. JORHD2, 0148-6055, 10.1122/1.551083.
15. Sierou A. Brady J.F. Rheology and microstructure in concentrated non-colloidal suspensions. J. Rheol. 2002, 46:1031. JORHD2, 0148-6055, 10.1122/1.1501925.
16. Singh A. Nott P.R. Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 2003, 490:293. JFLSA7, 0022-1120, 10.1017/S0022112003005366.
17. Brady J.F. Brownian motion, hydrodynamics, and the osmotic pressure. J. Chem. Phys. 1993, 98:3335. JCPSA6, 0021-9606, 10.1063/1.464105.
18. Morris J.F. Boulay F. Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 1999, 43:1213. JORHD2, 0148-6055, 10.1122/1.551021.
19. Miller R.M. Singh J.P. Morris J.F. Suspension flow modeling for general geometries. Chem. Eng. Sci. 2009, 64:4597. CESCAC, 0009-2509, 10.1016/j.ces.2009.04.033.
20. Morris J.F. Brady J.F. Pressure-driven flow of a suspension: Bbuoyancy effects. Int. J. Multiphase Flow 1998, 24:105. IJMFBP, 0301-9322, 10.1016/S0301-9322(97)00035-9.
21. Miller R.M. Morris J.F. Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions. J. Non-Newtonian Fluid Mech. 2006, 135:149. JNFMDI, 0377-0257, 10.1016/j.jnnfm.2005.11.009.
22. Norman J.T. Nayak H.V. Bonnecaze R.T. Migration of buoyant particles in low-Reynolds-number pressure-driven flows. J. Fluid Mech. 2005, 523:1. JFLSA7, 0022-1120, 10.1017/S0022112004000886.
23. Norman J.T. Oguntade B.O. Bonnecaze R.T. Particle-phase distributions of pressure-driven flows of bidisperse suspensions. J. Fluid Mech. 2008, 594:1. JFLSA7, 0022-1120, 10.1017/S0022112007008804.
24. Yapici K. Powell R.L. Phillips R.J. Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow. Phys. Fluids 2009, 21:053302. PHFLE6, 1070-6631, 10.1063/1.3119802.
25. Ramachandran A. Leighton D.T. The effect of gravity on the meniscus accumulation phenomenon in a tube. J. Rheol. 2007, 51:1073. JORHD2, 0148-6055, 10.1122/1.2754309.
26. Ramachandran A. Leighton D.T. The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 2008, 603:207. JFLSA7, 0022-1120, 10.1017/S0022112008000980.
27. Ramachandran A. Loewenberg M. Leighton D.T. A constitutive equation for droplet distribution in unidirectional flows of dilute emulsions for low capillary numbers. Phys. Fluids 2010, 22:083301. PHFLE6, 1070-6631, 10.1063/1.3466577.
28. Kim S. Russel W.B. Modelling of porous media by renormalization of the stokes equations. J. Fluid Mech. 1985, 154:269. JFLSA7, 0022-1120, 10.1017/S0022112085001525.
29. Batchelor G.K. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 1977, 83:97. JFLSA7, 0022-1120, 10.1017/S0022112077001062.
30. Brady J.F. Bossis G. Stokesian dynamics. Annu. Rev. Fluid Mech. 1988, 20:111. ARVFA3, 0066-4189, 10.1146/annurev.fl.20.010188.000551.
31. Brady J.F. Philips R.J. Lester J.C. Bossis G. Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 1988, 195:257. JFLSA7, 0022-1120, 10.1017/S0022112088002411.
32. Kim S. Karrila S.J. Microhydrodynamics: Principles and Selected Applications 2005, and (Dover, New York, ).
33. Frank M. Anderson D. Weeks E.R. Morris J.F. Particle migration in pressure-driven flow of a Brownian suspension. J. Fluid Mech. 2003, 493:363378. JFLSA7, 0022-1120, 10.1017/S0022112003006001, and.
34. Brown J.R. Fridjonsson E.O. Seymour J.D. Codd S.L. Nuclear magnetic resonance measurement of shear-induced particle migration in Brownian suspensions. Phys. Fluids 2009, 21:093301. PHFLE6, 1070-6631, 10.1063/1.3230498.