Universal scaling in shear thickening suspensions

Nearly all dense suspensions undergo dramatic thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we give a complete theory of the shear thickening viscosity in terms of a universal crossover scaling from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes, due to a crossover between frictionless isotropic jamming and a frictional shear jamming point, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into an additive analytic background and a scaling variable governing the proximity to shear jamming that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.