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Many densely packed suspensions and colloids exhibit Discontinuous ShearThickening, in which the viscosity jumps dramatically and reversibly as theshear rate is increased. We performed rheometry and video microscopymeasurements on a variety of suspensions to determine the mechanism for thisbehavior. For large particles, we find the onset of shear thickening tau_mincorresponds to a hydrostatic pressure from the weight of the particle packing.Combined with previous results this suggests that generally tau_min correspondsto the stress required to shear neighboring particles apart. Shear profiles andnormal stress measurements indicate that stresses are transmitted throughfrictional rather than viscous interactions. Above tau_min, dilation causesparticles to penetrate the liquid-air interface of the sheared sample. Theupper stress boundary tau_max of the shear thickening regime is shown toroughly match the ratio of surface tension divided by a radius of curvature onthe order of the particle size. This scaling suggests the viscosity jump comesfrom the confining stress due to surface tension as the liquid-air interface atthe boundary is deformed by dilation. A similar transition in rheology withboundary conditions happens when the packing fraction is increased beyond thejamming transition. We generalize this shear thickening mechanism to othersources of a confining stress by showing that, when instead the suspensions areconfined by solid walls and have no liquid-air interface, tau_max is set by thestiffness of the most compliant boundary. With these new scaling laws, we candelineate the shear thickening regime in a phase diagram and describe it with anon-local constitutive relation that encompass the scalings found not only forsuspensions but also colloids with Brownian and electrostatic interactions.

The role of dilation and confining stresses in shear thickening of dense suspensions