Abstract
In granulation, a dense colloidal suspension is converted into pasty lumps by application of flow. Often, such lumps are bistable: each can exist either as a fluid droplet (with a shiny surface) or as a jammed granule, whose rough surface creates a bulk stress via capillary action. Such bistability can be explained if the bulk steady-state flow curve is sufficiently nonmonotonic that, above some threshold of stress, flow ceases entirely. This is a stronger condition than the one required to see discontinuous shear thickening, but closely related to it. For instance, inertia can play a role in shear thickening, but not in static bistability. Suitable flow curves were previously found in a phenomenological model of the colloidal glass transition, in which Brownian motion is arrested at high stresses. However, granulation often involves particles too large for Brownian motion to be significant, so that another nonmonotonicity mechanism is needed. A very recent theory, in which the proportion of frictional rather than lubricated contacts increases with stress, provides just such a mechanism, and we use it here to give a simple explanation of granular bistability in non-Brownian suspensions, which requires knowledge only of the steady-state flow curve. However, jamming is in general a history-dependent phenomenon which allows bistability to arise under broader conditions than those just described, possibly including systems that do not shear-thicken at all. In this paper, we focus on explanations of granular bistability based on steady-state shear-thickening, but also discuss alternative explanations based on flow history effects.
Similar content being viewed by others
References
Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc A 225:49
Barnes HA (1989) Shear-thickening (Dilatancy) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J Rheol 33:329
Batchelor GK (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech 83:97
Batchelor GK, Green JT (1972) The determination of the bulk stress in a suspension of spherical particles to order c 2. J Fluid Mech 56:401
Bender J, Wagner NJ (1996) Reversible shear thickening in monodisperse and bidisperse colloidal dispersions. J Rheol 40:899– 916
Bergenholtz J, Brady JF, Vicic M (2002) The non-Newtonian rheology of dilute colloidal suspensions. J Fluid Mech 456:239–275
Bertrand E, Bibette J, Schmitt V (2002) From shear thickening to shear-induced jamming. Phys Rev E 66:60401R
Besseling R, Isa L, Ballesta P, Petekidis G, Cates ME, Poon WCK (2010) Shear banding and flow-concentration coupling in colloidal glasses. Phys Rev Lett 105:268301
Boyer F, Guazzelli E, Pouliquen O (2011) Unifying suspension and granular rheology. Phys Rev Lett 107:188301
Brady JF, Morris JF (1997) Structure of strongly sheared suspensions and its impact on rheology and diffusion. J Fluid Mech 348:103–139
Brady JF, Bossis G (1988) Stokesian dynamics. Annual Rev Fluid Mech 20:111
Brown E, Jaeger HM (2014) Shear thickening in concentrated suspensions: phenomenology, mechanisms, and relations to jamming. Rept Prog Phys 77:046602
Cates ME, Haw MD, Holmes CB (2005) Dilatancy, jamming, and the physics of granulation. J Phys Cond Mat 17:S2517–S2531
Einstein A (1906) Eine neue bestimmung der molekueldimensionen. Annalen der Physik 19:289
Fernandez N, Mani R, Rinaldi D, Kadau D, Mosquet M, Lombois-Burger H, Cayer-Barrioz J, Herrmann HJ, Spencer ND, Isa L (2013) Microscopic mechanism for shear thickening of non-Brownian suspensions. Phys Rev Lett 111:108301
Goddard JD (2006) A dissipative anisotropic fluid model for non-colloidal particle dispersions. J Fluid Mech 568:1–17
Haw MD (2004) Jamming, two-fluid behavior, and “self-filtration” in concentrated particulate suspensions. Phys Rev Lett 92:185506
Holmes CB, Cates ME, Fuchs M, Sollich P (2005) Glass transitions and shear thickening suspension rheology. J Rheol 49:237
Laun HM (1994) Normal stresses in extremely shear thickening polymer dispersions. J Non-Newtonian Fluid Mech 54:8– 108
Lemaitre A, Roux J-N, Chevoir F (2009) What do dry granular flows tell us about dense non-Brownian suspension rheology? Rheologica Acta 48:925
Lerner E, During G, Wyart M (2012a) A unified framework for non-Brownian suspension flows and soft amorphous solids. Proc Nat Acad Sci 109:4798
Lerner E, During G, Wyart M (2012b) Toward a microscopic description of flow near the jamming threshold. Europhys Lett 99:58003
Lerner E, During G, Wyart M (2014) Length scales and self-organization in dense suspension flows. Phys Rev E 89:022305
Mari R, Seto R, Morris JF, Denn MM (2014) Shear thickening, frictionless and frictional rheologies. arXiv: 1403.6793
Melrose JR, Ball RC (1995) The pathological behavior of sheared hard-spheres with hydrodynamic interactions. Europhys Lett 32:535
Neto C, Evans DR, Bonaccurso E, Butt H-J, Craig VJS (2005) Boundary slip in Newtonian liquids: a review of experimental studies. Rept Prog Phys 68:2859
Poon WCK (2000) A day in the life of a hard-sphere suspension. In: Cates ME, Evans MR (eds) In soft and fragile matter: nonequilibrium dynamics, metastability and flow. CRC Press, Bristol, pp 1–9
Russel WB, Saville DA, Schowalter WR (1989) Colloidal dispersions. Cambridge University Press
Seto R, Mari R, Morris JF, Denn MM (2013) Discontinuous shear thickening of frictional hard-sphere suspensions. Phys Rev Lett 111:218301
Warren PB (2001) Private communication
Wyart M, Cates ME (2014) Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys Rev Lett 112:098302
Acknowledgements
We thank Bruno Andreotti, Paul Chaikin, Eric DeGiuli, Mort Denn, Nicolas Fernandez, Ben Guy, Michiel Hermes, Gary Hunter, Lucio Isa, Edan Lerner, Jie Lin, Jeff Morris, Wilson Poon, and Le Yan for discussions. MW thanks NSF CBET Grant 1236378, NSF DMR Grant 1105387, and MRSEC Program of the NSF DMR-0820341 for partial funding. MEC holds a Royal Society Research Professorship; he thanks EPSRC J/007404 for funding and NYU for hospitality.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper marks MEC’s grateful receipt of the 2013 Weissenberg Award.
Rights and permissions
About this article
Cite this article
Cates, M.E., Wyart, M. Granulation and bistability in non-Brownian suspensions. Rheol Acta 53, 755–764 (2014). https://doi.org/10.1007/s00397-014-0795-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00397-014-0795-x