Hostname: page-component-6bf8c574d5-rwnhh Total loading time: 0 Render date: 2025-02-26T18:45:29.626Z Has data issue: false hasContentIssue false
  • English
  • Français

Rheology of dense granular suspensions

Published online by Cambridge University Press:  14 August 2018

Élisabeth Guazzelli Open the ORCID record for Élisabeth Guazzelli [Opens in a new window]  and
Olivier Pouliquen
Élisabeth Guazzelli*
Affiliation:
Aix-Marseille Université, CNRS, IUSTI, Marseille, France
Olivier Pouliquen
Affiliation:
Aix-Marseille Université, CNRS, IUSTI, Marseille, France
*
†Email address for correspondence: Elisabeth.Guazzelli@univ-amu.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Suspensions are composed of mixtures of particles and fluid and are omnipresent in natural phenomena and in industrial processes. The present paper addresses the rheology of concentrated suspensions of non-colloidal particles. While hydrodynamic interactions or lubrication forces between the particles are important in the dilute regime, they become of lesser significance when the concentration is increased, and direct particle contacts become dominant in the rheological response of concentrated suspensions, particularly those close to the maximum volume fraction where the suspension ceases to flow. The rheology of these dense suspensions can be approached via a diversity of approaches that the paper introduces successively. The mixture of particles and fluid can be seen as a fluid with effective rheological properties but also as a two-phase system wherein the fluid and particles can experience relative motion. Rheometry can be undertaken at an imposed volume fraction but also at imposed values of particle normal stress, which is particularly suited to yield examination of the rheology close to the jamming transition. The response of suspensions to unsteady or transient flows provides access to different features of the suspension rheology. Finally, beyond the problem of suspension of rigid, non-colloidal spheres in a Newtonian fluid, there are a great variety of complex mixtures of particles and fluid that remain relatively unexplored.

JFM classification

Complex Fluids: Complex Fluids Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
JFM Perspectives
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , P1
Copyright
© 2018 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

Acrivos, A., Mauri, R. & Fan, X. 1993 Shear-induced resuspension in a Couette device. Intl J. Multiphase Flow 19, 797–802.Google Scholar
Amarsid, L., Delenne, J. Y., Mutabaruka, P., Monerie, Y., Perales, F. & Radjai, F. 2017 Viscoinertial regime of immersed granular flows. Phys. Rev. E 96, 012901.Google Scholar
Andreotti, B., Forterre, Y. & Pouliquen, O. 2013 Granular Media: Between Fluid and Solid. Cambridge University Press.Google Scholar
Aussillous, P., Chauchat, J., Pailha, M., Médale, M. & Guazzelli, É. 2013 Investigation of the mobile granular layer in bedload transport by laminar shearing flows. J. Fluid Mech. 736, 594–615.Google Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49–63.Google Scholar
Batchelor, G. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. & Green, J. 1972a The determination of the bulk stress in a suspension of spherical particles to order c 2 . J. Fluid Mech. 56, 401–427.Google Scholar
Batchelor, G. & Green, J. 1972b The hydrodynamic interaction of two small freely-moving spheres in a linear flow field. J. Fluid Mech. 56, 375–400.Google Scholar
Blanc, F., Lemaire, É., Meunier, A. & Peters, F. 2013 Microstructure in sheared non-Brownian concentrated suspensions. J. Rheol. 57, 273–292.Google Scholar
Blanc, F., Peters, F. & Lemaire, É. 2011 Local transient rheological behavior of concentrated suspensions. J. Rheol. 55, 835–854.Google Scholar
Bonnoit, C., Darnige, T., Clement, É. & Lindner, A. 2010 Inclined plane rheometry of a dense granular suspension. J. Rheol. 54, 65–79.Google Scholar
Bounoua, S., Kuzhir, P. & Lemaire, É. 2016 Normal stress differences in non-Brownian fiber suspensions. J. Rheol. 60, 661–671.Google Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011a Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.Google Scholar
Boyer, F., Pouliquen, O. & Guazzelli, É. 2011b Dense suspensions in rotating-rod flows: normal stresses and particle migration. J. Fluid Mech. 686, 5–25.Google Scholar
Brown, E. & Jaeger, H. M. 2014 Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming. Rep. Prog. Phys. 77, 046602.Google Scholar
Butler, J. E. & Snook, B. 2018 Microstructural dynamics and rheology of suspensions of rigid fibers. Annu. Rev. Fluid Mech. 50, 299–318.Google Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined planes. Phys. Fluids 17, 103301.Google Scholar
Chateau, X., Ovarlez, G. & Trung, K. L. 2008 Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids. J. Rheol. 52, 489–506.Google Scholar
Clavaud, C., Bérut, A., Metzger, B. & Forterre, Y. 2017 Revealing the frictional transition in shear-thickening suspensions. Proc. Natl Acad. Sci. USA 114, 5147–5152.Google Scholar
Corté, L., Chaikin, P. M., Gollub, J. P. & Pine, D. J. 2008 Random organization in periodically driven systems. Nat. Phys. 4, 420–424.Google Scholar
Couturier, E., Boyer, F., Pouliquen, O. & Guazzelli, É. 2011 Suspensions in a tilted trough: second normal stress difference. J. Fluid Mech. 686, 26–39.Google Scholar
Dagois-Bohy, S., Hormozi, S., Guazzelli, É. & Pouliquen, O. 2015 Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids. J. Fluid Mech. 776, R2.Google Scholar
Dai, S.-C., Bertevas, E., Qi, F. & Tanner, R. I. 2013 Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices. J. Rheol. 57, 493–510.Google Scholar
Dbouk, T., Lobry, L. & Lemaire, É. 2013 Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715, 239–272.Google Scholar
Deboeuf, A., Gauthier, G., Martin, J., Yurkovetsky, Y. & Morris, J. F. 2009 Particle pressure in a sheared suspension: a bridge from osmosis to granular dilatancy. Phys. Rev. Lett. 102, 108301.Google Scholar
DeGiuli, E., Düring, G., Lerner, E. & Wyart, M. 2015 Unified theory of inertial granular flows and non-Brownian suspensions. Phys. Rev. E 91, 062206.Google Scholar
Düring, G., Lerner, E. & Wyart, M. 2016 Effect of particle collisions in dense suspension flows. Phys. Rev. E 94, 022601.Google Scholar
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 19, 289–306.Google Scholar
Einstein, A. 1911 Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 34, 591–592.Google Scholar
Fall, A., Lemaître, A., Bertrand, F., Bonn, D. & Ovarlez, G. 2010 Shear thickening and migration in granular suspensions. Phys. Rev. Lett. 105, 268303.Google Scholar
Forterre, Y. & Pouliquen, O. 2008 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24.Google Scholar
Gadala-Maria, F.1979 The rheology of concentrated suspensions. PhD thesis, Stanford University.Google Scholar
Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799–814.Google Scholar
Gallier, S., Lemaire, É., Lobry, L. & Peters, F. 2016 Effect of confinement in wall-bounded non-colloidal suspensions. J. Fluid Mech. 799, 100–127.Google Scholar
Gallier, S., Lemaire, É., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles. J. Fluid Mech. 757, 514–549.Google Scholar
Garland, S., Gauthier, G., Martin, J. & Morris, J. F. 2013 Normal stress measurements in sheared non-Brownian suspensions. J. Rheol. 57, 71.Google Scholar
Guazzelli, É. & Morris, J. F. 2012 A Physical Introduction to Suspension Dynamics. Cambridge University Press.Google Scholar
Iverson, R. M., Reid, M. E., Iverson, N. R., Lahusen, R. G., Logan, M., Mann, J. E. & Brien, D. L. 2000 Acute sensitivity of landslide rates to initial soil porosity. Science 290, 513–516.Google Scholar
Jackson, R. 1997 Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid. Chem. Engng Sci. 52, 2457–2469.Google Scholar
Jerome, J. J. S., Vandenberghe, N. & Forterre, Y. 2016 Unifying impacts in granular matter from quicksand to cornstarch. Phys. Rev. Lett. 117, 098003.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The kinetics of flowing dispersions: I. Concentrated suspensions of rigid particles. J. Colloid Interface Sci. 22, 531–553.Google Scholar
Koh, C. J., Hookham, P. & Leal, L. G. 1994 An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 266, 1–32.Google Scholar
Kulkarni, S. D., Metzger, B. & Morris, J. F. 2010 Particle-pressure-induced self-filtration in concentrated suspensions. Phys. Rev. E 82, 010402.Google Scholar
Leighton, D. & Acrivos, A. 1986 Viscous resuspension. Chem. Engng Sci. 41, 1377–1384.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Lemaître, A., Roux, J. N. & Chevoir, F. 2009 What do dry granular flows tell us about dense non-Brownian suspension rheology? Rheol. Acta 48, 925–942.Google Scholar
Lerner, E., Düring, G. & Wyart, M. 2012 A unified framework for non-Brownian suspension flows and soft amorphous solids. Proc. Natl Acad. Sci. USA 109, 4798–4803.Google Scholar
Lhuillier, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.Google Scholar
Lyon, M. K. & Leal, L. G. 1998 An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J. Fluid Mech. 363, 25–56.Google Scholar
Madraki, Y., Hormozi, S., Ovarlez, G., Guazzelli, É. & Pouliquen, O. 2017 Enhancing shear thickening. Phys. Rev. Fluids 2, 033301.Google Scholar
Mari, R., Seto, R., Morris, J. F. & Denn, M. M. 2014 Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58, 1693–1724.Google Scholar
Mari, R., Seto, R., Morris, J. F. & Denn, M. M. 2015 Discontinuous shear thickening in brownian suspensions by dynamic simulation. Proc. Natl Acad. Sci. USA 112, 15326–15330.Google Scholar
Metzger, B. & Butler, J. E. 2012 Clouds of particles in a periodic shear flow. Nat. Phys. 24, 021703.Google Scholar
Mewis, J. & Wagner, N. J. 2011 Colloidal Suspension Rheology. Cambridge University Press.Google Scholar
Morris, J. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.Google Scholar
Nott, P. R. & Brady, J. 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157–199.Google Scholar
Nott, P. R., Guazzelli, É. & Pouliquen, O. 2011 The suspension balance model revisited. Phys. Fluids 23, 043304.Google Scholar
O’Hern, C. S., Silbert, L. E., Liu, A. J. & Nagel, S. R. 2003 Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E 68, 011306.Google Scholar
Olsson, P. & Teitel, S. 2007 Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99 (17), 178001.Google Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, É. 2009 Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows. J. Fluid Mech. 636, 295–319.Google Scholar
Ovarlez, G., Bertrand, F. & Rodts, S. 2006 Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J. Rheol. 50, 259–292.Google Scholar
Pailha, M. & Pouliquen, O. 2009 A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 633, 115–135.Google Scholar
Parsi, F. & Gadala-Maria, F. 1987 Fore-and-aft asymmetry in a concentrated suspension of solid spheres. J. Rheol. 31, 725–732.Google Scholar
Peters, F., Ghigliotti, G., Gallier, S., Blanc, F., Lemaire, E. & Lobry, L. 2016 Rheology of non-Brownian suspensions of rough frictional particles under shear reversal: a numerical study. J. Rheol. 60, 715–732.Google Scholar
Pine, D. J., Gollub, J. P., Brady, J. F. & Leshansky, A. M. 2005 Chaos and threshold for irreversibility in sheared suspensions. Nature 438, 997–1000.Google Scholar
Pitman, E. B. & Le, L. 2005 A two-fluid model for avalanche and debris flows. Phil. Trans. R. Soc. Lond. A 363, 1573–1601.Google Scholar
Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidization. Part I. Trans. Inst. Chem. Engrs 32, 35–53.Google Scholar
Rondon, L., Pouliquen, O. & Aussillous, P. 2011 Granular collapse in a fluid: role of the initial volume fraction. Phys. Fluids 23, 073301.Google Scholar
Sierou, A. & Brady, J. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46, 1031–1056.Google Scholar
Singh, A. & Nott, P. R. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293–320.Google Scholar
Snook, B., Butler, J. E. & Guazzelli, É. 2016 Dynamics of shear-induced migration of spherical particles in oscillatory pipe flow. J. Fluid Mech. 786, 128–153.Google Scholar
Snook, B., Davidson, L. M., Butler, J. E., Pouliquen, O. & Guazzelli, É. 2014 Normal stress differences in suspensions of rigid fibres. J. Fluid Mech. 758, 486–507.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Tapia, F., Shaikh, S., Butler, J. E, Pouliquen, O. & Guazzelli, É. 2017 Rheology of concentrated suspensions of non-colloidal rigid fibres. J. Fluid Mech. 827, R5.Google Scholar
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109, 118305.Google Scholar
Trulsson, M., DeGiuli, E. & Wyart, M. 2017 Effect of friction on dense suspension flows of hard particles. Phys. Rev. E 95, 012605.Google Scholar
Wagner, N. J. & Brady, J. F. 2009 Shear thickening in colloidal dispersions. Phys. Today 62, 27–32.Google Scholar
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.Google Scholar
Wyart, M. & Cates, M. E. 2014 Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys. Rev. Lett. 112, 098302.Google Scholar
Yeo, K. & Maxey, M. R. 2011 Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow. J. Fluid Mech. 682, 491–518.Google Scholar
Zarraga, I. E., Hill, D. A. & Leighton, D. T. Jr 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–220.Google Scholar