  Nearly all dense suspensions undergo dramatic and abrupt thickening
transitions in their flow behaviour when sheared at high stresses. Such
transitions occur when the dominant interactions between the suspended
particles shift from hydrodynamic to frictional. Here, 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. The
material-specific behaviour due to the microscale particle interactions is
incorporated into 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.
