Suspensions in a tilted trough: Second normal stress difference

Journal of Fluid Mechanics

Volumn 686, Issue , 2011, Pages 26-39

  Couturier, Étienne ^a   Boyer, François ^a   Pouliquen, Olivier ^a   Guazzelli, Élisabeth ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

Author keywords

particle fluid flow; rheology; suspensions

Indexed keywords

NEWTONIAN LIQUIDS; RHEOLOGY; SHEAR STRESS; VOLUME FRACTION;

BEHAVIOURAL CHANGES; BUOYANT RIGID SPHERE; FIRST NORMAL STRESS DIFFERENCE; FREE SURFACES; NEWTONIAN FLUIDS; NORMAL STRESS DIFFERENCE; PARTICLE/FLUID FLOWS; STRESS INCREASE;

SUSPENSIONS (FLUIDS);

BUOYANCY; FLUID FLOW; FLUID MECHANICS; NEWTONIAN FLUID; PARTICLE MOTION; RHEOLOGY; SHEAR STRESS;

EID: 84855509373     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2011.315     Document Type: Article

References (23)

1. ARP, A. P. & MASON, S. G. 1977 The kinetics of flowing dispersions. IX. Doublets of rigid spheres (experimental). J. Colloid Interface Sci. 61, 44-61.
2. 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, 401-27.
3. BEAVERS, G. S. & JOSEPH, D. D. 1975 The rotating-rod viscometer. J. Fluid Mech. 69, 475-512.
4. BIRD, R. B., ARMSTRONG, R. C. & HASSAGER, O. 1987 Dynamics of Polymeric Liquids, 2nd edn. Fluid Dynamics, vol. 1. John Wiley & Sons.
5. BOYER, R, POULIQUEN, O. & GUAZZELLI, E. 2011 Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686, 5-25.
6. BRADY, J. F & CARPEN, I. C. 2001 Second normal stress jump instability in non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 2075, 1-14.
7. 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. (Pubitemid 127474225)
8. DAVIS, R. H. 1992 Effects of surface roughness on a sphere sedimenting through a dilute suspension of neutrally buoyant spheres. Phys. Fluids A 4, 2607-2619.
9. GADALA-MARIA, F. 1979 The rheology of concentrated suspensions. PhD thesis, Stanford University.
10. LEIGHTON, D. T. & ACRIVOS, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415-439.
11. MORRIS, J. F. & BOULAY, F. 1999 Curvilinear flows of non-colloidal suspensions: The role of normal stresses. J. Rheol. 43, 1213-1237.
12. PARSI, F. & GADALA-MARIA, F. 1987 Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J. Rheol. 31, 725-732.
13. PRESS, W. H., TEUKOLSKY, S. A., FLANNERY, B. , P. & VETTERLING, W. T. 2007 Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.
14. RAMACHANDRAN, A. & LEIGHTON, D. T. 2008 The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 603, 207-243. (Pubitemid 351622232)
15. RAMPALL, I., SMART, J. R. & LEIGHTON, D. T. 1997 The influence of surface roughness on the particle-pair distribution function of dilute suspensions of non-colloidal spheres in simple shear flow. J. Fluid Mech. 339, 1-24.
16. SIEROU, A. & BRADY, J. F. 2002 Rheology and microstructure in concentrated non-colloidal suspensions. J. Rheol. 46, 1031-1056.
17. SINGH, A. & NOTT, P. R. 2000 Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 412, 279-301.
18. SINGH, A. & NOTT, P. R. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293-320. (Pubitemid 37164470)
19. STICKEL, J. J. & POWELL, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129-149. (Pubitemid 40301254)
20. TANNER, R. I. 1970 Some methods for estimating the normal stress functions in viscometric flows. Trans. Soc. Rheol. 14 (4), 483-507.
21. WILSON, H. J. 2005 An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. J. Fluid Mech. 534, 97-114. (Pubitemid 40990515)
22. WINEMAN, A. & PIPKIN, A. 1966 Slow viscoelastic flow in tilted troughs. Acta Mechanica 2, 104-115.
23. ZARRAGA, I. E., HILL, D. A. & LEIGHTON, D. T. 2000 The characterization of the total stress of concentrated suspensions of non-colloidal spheres in Newtonian fluids. J. Rheol. 44, 185-220.