This is a comprehensive account of our measurements on a wide variety of dense suspensions. These systems, as well as many colloids, exhibit a dramatic behavior known as Discontinuous Shear Thickening in which the viscosity jumps apparently dramatically and reversibly at a certain shear rate. We performed rheometry and video microscopy measurements several different densely packed suspensions to determine the mechanism for this behavior.

We distinguish Discontinuous Shear Thickening from inertial effects by showing that the latter are characterized by a Reynolds number but are only found up to packing fractions around 0.4, while the former are significant only at higher packing fractions. If the suspended particles are heavy enough to settle we find the onset of shear thickening tau_min corresponds to a hydrostatic pressure which is required to shear the particles against gravity and friction. Combined with previous results for colloids this suggests that generally tau_min corresponds to the stress required to shear neighboring particles apart. Shear profiles and normal stress measurements indicate that stresses are transmitted through frictional rather than viscous interactions implying the particles remain in contact via force chains while sheared. Above tau_min, dilation is observed as an apparent roughness of the surface, indicating the viscosity jump coincides with a change in the boundary condition.

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. This scaling suggests the viscosity jump comes from the confining stress due to capillary forces as the liquid-air interface at the boundary is deformed by dilation. A similar change in boundary conditions happens without shear when the packing fraction is increased beyond the jamming transition where a yield stress on the scale of tau_max develops as a result of particles penetrating the liquid-air interface.

We generalize this shear thickening mechanism to other sources of a confining stress by showing that when instead the suspensions are confined by solid walls and have no liquid-air interface, then tau_max is set by the stiffness of the wall. With these new scaling laws, we can delineate the shear thickening regime in a phase diagram that encompasses the scalings found not only for suspensions but also colloids with Brownian and electrostatic interactions.

1. •Eric Brown and Heinrich M. Jaeger,  “The role of dilation and confining stresses in shear thickening of dense suspensions”, J. Rheology 56(4), 875-923 (2012) pdf