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.
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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.
This paper marks MEC’s grateful receipt of the 2013 Weissenberg Award.
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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