TITLE GOES HERE: UNOFFICIAL WORD TEMPLATE FOR APS JOURNAL GOES HERE 1 S-Shaped Discontinuous Shear Thickening Flow Curve in Granular Suspensions Zhongcheng Pan 1 , Henri de Cagny 1 , Bart Weber 1 , Daniel Bonn 1 1 Van der Waals-Zeeman Institute, IoP, Science Park 904, Amsterdam, Netherlands We study the rheological behavior of concentrated granular suspensions of simple spherical particles that show discontinuous shear thickening. Under controlled stress, the system exhibits an S-shaped flow curve (stress vs. shear rate) in which the low-viscosity Newtonian regime is connected to the shear thickening regime through a line with negative slope. Under controlled shear rate, a discontinuous transition between the two states is observed. We observe hysteresis in the negative slope section of the flow curve. This hysteresis is sensitive to the rate at which data is taken: by changing the shear rate rapidly, the Newtonian branch can be “overheated” and the shear thickened branch can be “undercooled”. Experiments with a novel fluorescent viscosity probe show that the system remains homogeneous if a stress is imposed that is intermediate between the high-and low-viscosity branches, which indicates the continuous formation of a force network due to the frictional forces between particles if the stress is increased towards shear thickening. The phenomenon of shear thickening is important for many industrial applications [1] and exists in a wide range of systems, including wormlike micelle solutions [2-4], cornstarch [5-7] and colloidal [8,9] and non-colloidal suspensions [1,7,10-12]. Granular suspensions made of spherical particles dispersed in a Newtonian liquid are arguably the simplest of these systems; nonetheless its rheological behavior is very rich. If the particles and solvent are not perfectly density matched, such suspensions will exhibit a yield stress and pronounced shear thinning [12]; in addition the measured viscosity can be significantly affected by particle migration [1]. For a perfectly density matched system without migration, besides a Newtonian flow regime, both continuous shear thickening (CST) and discontinuous shear thickening (DST) can be observed depending on the volume fraction of particles [13,14]. All this makes it difficult to predict the flow behavior of a given suspension, while understanding the rheological behavior of granular suspensions is of considerable significance, since the handling and transport of granular materials in general is responsible for a significant fraction of the world energy consumption [15]. From a fundamental point of view, shear thickening is of great interest since it is an interesting exception to the general rule that most complex fluids organize themselves in flow to minimize the flow resistance. Shear thickening, its opposite, is often described as a shear-induced jamming transition [7]; however, other mechanisms are also under debate [6,16]. Consequently, to precisely predict the thickening behavior remains a challenge. For instance, an understanding that shear thickening is due to the inertia of the particles predicts that the thickening happens at a Stokes number    as observed in some simulations [17- 18], in stark contrast to     observed in experiments [1,19]; recent simulations, on the other hand, suggest that inertia is not important for shear thickening [20]. It is even harder to estimate which systems will shear thicken [1] or whether the thickening is monotonic or not. For the type of suspensions that we consider here, the viscosity can increase either continuously (which happens at low volume fractions) or discontinuously (for high volume fractions). Recent theory and simulations [13,20] considers hard spherical particles and incorporates particle-particle frictional forces into the hydrodynamic description, predicting both the transition from continuous to discontinuous thickening and a non-monotonic S-shaped flow curve (stress vs. shear rate) for DST at high volume fractions. The significance of the friction is evident from models that take a finite-range interaction into account [13], and suggests that the S-shaped shear thickening flow curve arises due to frictional contacts between particles which are formed when the finite-range particle-particle repulsion is overcome by the applied shear stress. This stress induced contact proliferation model also indicates that the non- monotonic flow behavior is characterized by hysteresis in the flow curve. Recent simulations [14] also indicate that DST does occur due to a stress induced transition from a state where the contacts between particles are lubricated to the thickened state for which frictional contacts are dominant. All this of course calls for experimental confirmation. In this Letter, we show that concentrated suspensions indeed exhibit an S-shaped flow curve under controlled shear stress with a hysteresis that depends on the rate at which the data points are taken. This flow curve is quite different from that under controlled shear rate, which exhibits a discontinuous jump. In analogy with shear- thickening micellar systems [2-4], this suggests that under controlled stress a coexistence between low-and high viscosity material might be observed. However visualization experiments using a novel fluorescent probe whose fluorescence intensity depends on the viscosity show