Suspensions with a tunable effective viscosity: A numerical study

Journal of Fluid Mechanics

Volumn 693, Issue , 2012, Pages 345-366

  Jibuti, L ^a   Rafai S ^a   Peyla, P ^a  

^a LIPHY   (France)

Author keywords

low Reynolds number flows; rheology; suspensions

Indexed keywords

ANGULAR VELOCITY; NUMERICAL METHODS; REYNOLDS NUMBER; RHEOLOGY; SHEAR FLOW; TORQUE; VOLUME FRACTION;

CONCENTRATED SUSPENSION; DIMENSIONLESS NUMBER; EFFECTIVE VISCOSITY; LOW REYNOLDS NUMBER FLOW; NUMERICAL INVESTIGATIONS; PARTICLE ROTATIONS; SPHERICAL PARTICLE; STRONG ENHANCEMENT;

SUSPENSIONS (FLUIDS);

ANGULAR MOMENTUM; FLUID MECHANICS; NUMERICAL MODEL; PARTICLE MOTION; REYNOLDS NUMBER; RHEOLOGY; SHEAR FLOW; TORQUE; VISCOSITY; VORTICITY;

EID: 84858680491     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2011.535     Document Type: Article

References (43)

1. BACRI, J. C., PERZYNSKI, R., SHLIOMIS, M. I. & BURDE, G. 1995 Negative-viscosity effect in a magnetic fluid. Phys. Rev. Lett. 75, 2128-2131.
2. BARTOK, W. & MASON, S. G. 1957 Particle motions in sheared suspensions. J. Colloid Sci. 12, 243-262.
3. BATCHELOR, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545-570.
4. BATCHELOR, G. K. & GREEN, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401-427.
5. BRADY, J. F., PHILIPS, R. J., LESTER, J. C. & BOSSIS, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257-280.
6. BRENNER, H. 1970 Rheology of a dilute suspension of dipolar spherical particles in an external field. J. Colloid Interface Sci. 32, 141-158.
7. CICHOCKI, B. & FELDERHOF, B. U. 1988 Short-time diffusion coefficients and high frequency viscosity of dilute suspensions of spherical Brownian particles. J. Chem. Phys. 89, 1049-1054.
8. CONDIFF, D. W. & DAHLER, J. S. 1964 Fluid mechanical aspects of antisymmetric stress. Phys. Fluids 7, 842-854.
9. DA CUNHA, F. R. & HINCH, E. J. 1996 Shear-induced dispersion in a dilute suspension of rough spheres. J. Fluid Mech. 309, 211-223. (Pubitemid 126469118)
10. DAVIT, Y. & PEYLA, P. 2008 Intriguing viscosity effects in confined suspensions: a numerical study. Eur. Phys. Lett. 83, 64001.
11. EINSTEIN, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. (Leipzig) 19, 289-306.
12. EINSTEIN, A. 1911 Berichtigung zu meiner Arbeit: 'Eine neue Bestimmung der Moleküldimensionen'. Ann. Phys. (Leipzig) 34, 591-592.
13. FENG, S., GRAHAM, A. L., ABBOTT, J. R. & BRENNER, H. 2006 Antisymmetric stresses in suspensions: vortex viscosity and energy dissipation. J. Fluid Mech. 563, 97-122. (Pubitemid 44322721)
14. GADALA-MARIA, F. 1979 The rheology of concentrated suspensions. PhD thesis, Stanford University.
15. HAPPEL, J. & BRENNER, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff.
16. ICHIKI, K. & PROSPERETTI, A. 2004 Faxen-like relations for a non-uniform suspension. Phys. Fluids 16, 2483-2496.
17. ISHIKAWA, T. & PEDLEY, T. J. 2007 The rheology of a semi-dilute suspension of swimming model micro-organisms. J. Fluid Mech. 588, 399-435.
18. JEFFERY, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. 102, 161-179.
19. KRIEGER, I. M. & DOUGHERTY, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137-152.
20. KROMKAMP, J., VAN DEN ENDE, D., KANDHAI, D., VAN DER SMAN, R. & BOOM, R. 2006 Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow. Chem. Engng Sci. 61, 858-873. (Pubitemid 41498044)
21. LADD, A. J. C. 1990 Hydrodynamic transport coefficients of random dispersions of hard spheres. J. Chem. Phys. 93, 3484-3494.
22. LANDAU, L. & LIFSCHITZ, E. 1959 Fluid Mechanics. Pergamon.
23. LEMAIRE, E., LOBRY, L. N., PANNACCI, F. & PETERS, 2008 Viscosity of an electro-rheological suspension with internal rotations. J. Rheol. 52, 769-785.
24. LIM, S., PARK, S. M. & KIM, K. I. 2005 AI vibration control of high-speed rotor systems using electrorheological fluid. J. Sound Vib. 284, 685-703. (Pubitemid 40643833)
25. MARCHIORO, M., TANKSLEY, M. & PROSPERETTI, A. 2000 Flow of spatially non-uniform suspensions. Part I. Phenomenology. Intl J. Multiphase Flow 26, 783-831. (Pubitemid 30306328)
26. MARCHIORO, M., TANKSLEY, M., WANG, M. & PROSPERETTI, A. 2001 Flow of spatially non-uniform suspensions. Part II. Systematic derivation of closure relations. Intl J. Multiphase Flow 27, 237-276.
27. MARSHALL, L., ZUKOVSKI, C. F. & GOODWIN, J. W. 1989 Effects of electric fields on the rheology of non-aqueous concentrated suspensions. J. Chem. Soc. Faraday Trans. 85, 2785-2795.
28. MAURY, B. 2006 A time stepping scheme for inelastic collisions. Numer. Math. 102, 649-679.
29. MAURY, B. 2009 Numerical analysis of a finite element/volume penalty method. SIAM J. Numer. Anal. 47, 1126-1148.
30. 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. (Pubitemid 40107036)
31. PEYLA, P. 2007 Rheology and dynamics of a deformable object in a microfluidic configuration: a numerical study. Eur. Phys. Lett. 80, 34001.
32. PEYLA, P. & VERDIER, C. 2011 New confinement effects on the viscosity of suspensions. Eur. Phys. Lett. 94, 44001.
33. PEYRET, R. & TAYLOR, T. D. 1963 Computational Methods for Fluid Flow. Springer.
34. PHANI, A. S. & VENKATRAMAN, K. 2005 Damping characteristics of electro-rheological fluid sandwich beams. Acta. Mechanica 180, 195-201. (Pubitemid 41813054)
35. RAFAÏ, S., JIBUTI, L. & PEYLA, P. 2010 Effective viscosity of microswimmer suspensions. Phys. Rev. Lett. 104, 098102.
36. ROSENSWEIG, R. E., KAISER, R. & MISKOLCZY, C. 1969 Viscosity of magnetic fluid in a magnetic field. J. Colloid Interface Sci. 29, 680-686.
37. RUSSEL, W. B., SAVILLE, D. A. & SCHOWALTER, W. R. 1989 Colloidal Dispersions. Cambridge University Press.
38. SIEROU, A. & BRADY, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46, 1031-1056.
39. TAN, K. P., STANWAY, R. & BULLOUGH, W. A. 2006 Dynamic velocity response of an electro-rheological (ER) clutch for robotic applications. Mech. Adv. Mater. Struct. 13, 1-12. (Pubitemid 43019247)
40. TANAKA, H. & ARAKI, T. 2000 Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics. Phys. Rev. Lett. 85, 1338-1341.
41. THOMAS, D. G. 1969 Transport characteristics of suspensions. Part VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J. Colloid Sci. 20, 267-277.
42. WANG, W. & PROSPERETTI, A. 2001 Flow of spatially non-uniform suspensions. Part III. Closure relations for porous media and spinning particles. Intl J. Multiphase Flow 27, 1627-1653. (Pubitemid 32644082)
43. YEO, K. & MAXEY, M. R. 2010 Rheology and ordering transitions of non-Brownian suspensions in a confined shear flow: effects of external torques. Phys. Rev. E 81, 062501.