  Many densely packed suspensions and colloids exhibit a behavior known as
Discontinuous Shear Thickening in which the shear stress jumps dramatically and
reversibly as the shear rate is increased. We performed rheometry and video
microscopy measurements on a variety of suspensions to determine the mechanism
for this behavior. Shear profiles and normal stress measurements indicate that,
in the shear thickening regime, stresses are transmitted through frictional
rather than viscous interactions, and come to the surprising conclusion that
the local constitutive relation between stress and shear rate is not
necessarily shear thickening. If the suspended particles are heavy enough to
settle we find the onset stress of shear thickening tau_min corresponds to a
hydrostatic pressure from the weight of the particle packing where neighboring
particles begin to shear relative to each other. Above tau_min, dilation is
seen to cause particles to penetrate the liquid-air interface of the sheared
sample. The upper stress boundary tau_max of the shear thickening regime is
shown to roughly match the ratio of surface tension divided by a radius of
curvature on the order of the particle size. These results suggest a new model
in which the increased dissipation in the shear thickening regime comes from
frictional stresses that emerge as dilation is frustrated by a confining stress
from surface tension at the liquid-air interface. When instead the suspensions
are confined by solid walls and have no liquid-air interface, we find tau_max
is set by the stiffness of the most compliant boundary which frustrates
dilation. This rheology can be described by a non-local constitutive relation
in which the local relation between stress and shear rate is shear thinning,
but where the stress increase comes from a normal stress term which depends on
the global dilation.
