Nonmonotonic flow curves of shear thickening suspensions.

The discontinuous shear thickening (DST) of dense suspensions is a remarkable phenomenon in which the viscosity can increase by several orders of magnitude at a critical shear rate. It has the appearance of a first-order phase transition between two hypothetical "states" that we have recently identified as Stokes flows with lubricated or frictional contacts, respectively. Here we extend the analogy further by means of stress-controlled simulations and show the existence of a nonmonotonic steady-state flow curve analogous to a nonmonotonic equation of state. While we associate DST with an S-shaped flow curve, at volume fractions above the shear jamming transition the frictional state loses flowability and the flow curve reduces to an arch, permitting the system to flow only at small stresses. Whereas a thermodynamic transition leads to phase separation in the coexistence region, we observe a uniform shear flow all along the thickening transition. A stability analysis suggests that uniform shear may be mechanically stable for the small Reynolds numbers and system sizes in a rheometer.