Jamming transitions in a schematic model of suspension rheology

– We study the steady-state response to applied stress in a simple scalar model of sheared colloids. Our model is based on a schematic (F2) model of the glass transition, with a memory term that depends on both stress and shear rate. For suitable parameters, we find transitions from a fluid to a nonergodic, jammed state, showing zero flow rate in an interval of applied stress. Although the jammed state is a glass, we predict that jamming transitions have an analytical structure distinct from that of the conventional mode coupling glass transition. The static jamming transition we discuss is also distinct from hydrodynamic shear thickening. When subjected to an applied shear stress, concentrated hard-sphere colloids are known to shear-thicken [1, 2, 3, 4]. An understanding of this in terms of hydrodynamic interactions has been developed [5,6]. Recently, a different (although seemingly related) phenomenon has been found. Bertrand and co-workers [7] report an experiment in which shearing a concentrated suspension induces a transition from a fluid to a metastable solid which persists after cessation of shear. Vibration of the sample restores it to a fluid state. Because the solid paste persists in the absence of flow, such ‘static jamming’ cannot be explained by hydrodynamic forces alone. An alternative view is that after cessation of flow the material remains stressed; this stress is what maintains the arrest. Indeed, jammed suspensions often take on a lumpy dry appearance as particles protrude partially from the fluid surface (a dilatancy effect). This entails large capillary stresses which might maintain the jam; lumps of paste removed from a rheometer would then remain solid. Vibration could destroy the jammed structure and restore both the fluidity and a wet appearance, as is observed [7, 8, 9]. Rather than model all this directly, we focus here on the simpler case of stress-induced jamming within an idealised rheometer, with no free surfaces. It was recently proposed that jamming in granular materials [10] might be closely connected to the glass transition [11,12]. If so, the jammed colloidal state found by Bertrand et al could resemble a glass, albeit one which is stressed and hence anisotropic. (Colloidal glasses are well-documented [13].) A speculative scenario for the formation of a shear-induced glass is as follows: the applied shear stress alters the structure of the material, initially through shear flow and hydrodynamics. But as the material thickens, its structure becomes more susceptible to