Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-25T11:59:43.976Z Has data issue: false hasContentIssue false
  • English
  • Français

An analytical determination of microstructure and stresses in a dense, sheared monolayer of non-Brownian spheres

Published online by Cambridge University Press:  12 December 2014

J. T. Jenkins  and
L. La Ragione
J. T. Jenkins*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
L. La Ragione
Affiliation:
Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura, Politecnico di Bari, 70125 Bari, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose an analytical model for the determination of the microstructure and stresses in a sheared suspension that consists of a dense monolayer of identical spheres in a viscous fluid. We calculate the anisotropy in the orientational distribution of spheres, associated with a short-range repulsive force assumed to act between the spheres, and a particle pressure and normal stress difference that result from this anisotropy. The microstructure and stresses are similar to those measured in Stokesian dynamics simulations.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 218 - 236
Check for updates
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brady, J. F. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Dratler, D. I. & Schowalter, W. R. 1996 Dynamic simulations of suspensions of non-Brownian hard spheres. J. Fluid Mech. 325, 53–77.CrossRefGoogle Scholar
Drazer, G., Koplik, J., Khusid, B. & Acrivos, A. 2004 Microstructure and velocity fluctuations in sheared suspensions. J. Fluid Mech. 511, 237–263.CrossRefGoogle Scholar
Goddard, J. D. 2006 A dissipative anisotropic fluid model for non-colloidal particle suspensions. J. Fluid Mech. 568, 1–17.CrossRefGoogle Scholar
Jeffrey, D. J. 1992 The calculation of low Reynolds number resistance functions for two unequal spheres. Phys. Fluids A 4, 16–29.CrossRefGoogle Scholar
Jeffrey, D. J., Morris, J. F. & Brady, J. F. 1993 The pressure moments for two rigid spheres in low-Reynolds-number flow. Phys. Fluids A 5, 2317–2325.CrossRefGoogle Scholar
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261–290.CrossRefGoogle Scholar
Jenkins, J. T., La Ragione, L., Johnson, D. & Makse, H.A. 2005 Fluctuations and effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J. Mech. Phys. Solids 53, 197–225.CrossRefGoogle Scholar
Love, A. E. H. 1944 A Treatise on the Mathematical Theory of Elasticity, 3rd edn. Cambridge University Press.Google Scholar
Nazockdast, E. & Morris, J. F. 2012a Microstructural theory and rheology of concentrated suspensions. J. Fluid Mech. 713, 420–452.CrossRefGoogle Scholar
Nazockdast, E. & Morris, J. F. 2012b Effect of repulsive interaction on structure and rheology of sheared colloidal suspensions. Soft Matt. 8, 4223–4234.CrossRefGoogle Scholar
Nazockdast, E. & Morris, J. F. 2013 Pair-particle dynamics and microstructure in sheared colloidal suspensions: simulation and Smoluchowski theory. Phys. Fluids 25, 25070601.CrossRefGoogle Scholar
Phan-Thien, N. 1995 Constitutive relation for concentrated suspensions in Newtonian liquids. J. Rheol. 39, 679–695.CrossRefGoogle Scholar
Sierou, A. & Brady, J. F. 2001 Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448, 115–146.CrossRefGoogle Scholar
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46, 1031–1056.CrossRefGoogle Scholar
Singh, A. & Nott, P. R. 2000 Normal stresses and microstructure in bounded sheared suspensions via Stokesian dynamics simulations. J. Fluid Mech. 412, 279–301.CrossRefGoogle Scholar
Stickel, J. J., Phillips, R. J. & Powell, R. L. 2006 A constitutive model for microstructure and total stress in particulate suspensions. J. Rheol. 50, 379–413.CrossRefGoogle Scholar
Torquato, S. 1995 Nearest-neighbor statistics for packings of hard spheres and disks. Phys. Rev. E 51, 3170–3184.CrossRefGoogle ScholarPubMed