Universality and Tunability in Shear Thickening Suspensions

Nearly all dense suspensions demonstrate shear thickening – an increase in the viscosity when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. We interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems -- cornstarch in glycerol and silica spheres in glycerol -- 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 frictional shear jamming, with different critical exponents. We further show that our scaling framework is broadly applicable and that the suspension dethickening observed upon adding in orthogonal shear perturbations (OSP) can be incorporated by simply altering the scaling variable to include a multiplicative term that decreases with the normalized OSP strain rate. Finally, we show how this understanding can be used to design viscosity metamaterials, with highly tunable properties including zero, infinite and negative viscosities.