Shear thickening and jamming in densely packed suspensions of different particle shapes

We investigated the effects of particle shape on shear thickening in densely packed suspensions. Collaborating with Joseph DeSimone's group at UNC (link) and Liquidia Technologies, NC (link), rods of different aspect ratios and unique non-convex hooked rods were fabricated in gram quantities using the PRINT® (Particle Replication in Non-wetting Templates) process. Having such large quantities of well-controlled particles made it possible to use a rheometer for measuring viscosity curves and normal stresses for a wide range of packing fractions. Suspensions of each shape exhibit qualitatively similar Discontinuous Shear Thickening. The logarithmic slope of the stress/shear-rate relation increases dramatically with packing fraction and diverges at a critical packing fraction \phi_c which depends on particle shape. The packing fraction dependence of the viscosity curves for different convex shapes can be collapsed when the packing fraction is normalized by \phi_c. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. The value of \phi_c is found to coincide with the onset of a yield stress at the jamming transition, suggesting the jamming transition also controls shear thickening. The yield stress is found to correspond with trapped air in the suspensions, and the scale of the stress can be attributed to interfacial tension forces which dramatically increase above \phi_c due to the geometric constraints of jamming. The relationship between shear and normal stresses is found to be linear in both the shear thickening and jammed regimes, indicating that the shear stresses come from friction. In the limit of zero shear rate, normal stresses pull the rheometer plates together due to the surface tension of the liquid below \phi_c, but push the rheometer plates apart due to jamming above \phi_c.

• Eric Brown, Hanjun Zhang, Nicole A. Forman, Benjamin W. Maynor , Douglas E. Betts, Joseph M. DeSimone, and Heinrich M. Jaeger, ““Shear thickening and jamming in densely packed suspensions of different particle shapes”, submitted to Phys. Rev. E (2011), arXiv pdf

Giant Electro-Rheological Effect in Dense Strontium Titanyl Oxalate Suspensions

In suspensions of polarizable particles the addition of polar molecules can dramatically increase the yield stress under an applied electric field, leading to a giant electrorheological (GER) effect. We report experiments on dense suspensions of strontium titanyl oxalate in silicon oil, where we find a yield stress of up to 200kPa at 5kV/mm. The magnitude of this yield stress directly correlates with the water content in the particles. In the dynamic response we observe behavior not previously reported for GER fluids and similar to sheared granular materials, including a direct proportionality between shear and normal stresses and the creation of a shear band a few particles in width. An important consequence is that the dynamic response can be varied dramatically by changing the confinement of the suspension or by imposing a normal stress.

• Carlos S. Orellana, Jinbo He, and Heinrich M. Jaeger, “Electrorheological response of dense strontium titanyl oxalate suspensions”, Soft Matter, June 29 (2011). pdf

Discontinuous Shear Thickening in Dense Suspensions: A "granular" perspective

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.

• Eric Brown and Heinrich M. Jaeger, “Dilation and confining stresses in shear thickening of dense suspensions”, subm. to J. Rheology (2010) pdf

Shear Thickening in Very Thin Suspension Films

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers.Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed-shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.

• Eric Brown, Hanjun Zhang, Nicole A. Forman, Benjamin W. Maynor , Douglas E. Betts, Joseph M. DeSimone, and Heinrich M. Jaeger, “Shear thickening in densely packed suspensions of spheres and rods confined to few layers”, J. Rheology 54, 1023-1046 (2010) pdf

Why Shear Thickening is a Generic Property of Dense Suspensions that Often is Masked by a Yield Stress

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, that is, they shear thin. Few are reported to do the opposite, that is, shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behaviour. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response. This work relied, in part, on unique "designer particles" (such as carbonironyl-loaded PEG rods; see data on the left) which were fabricated in close collaboration with Prof. Joe DeSimone's group at UNC and Liquidia Technologies.

• Eric Brown, Nicole A. Forman, Carlos S. Orellana, Hanjun Zhang, Ben Maynor, Douglas Betts, Joseph M. DeSimone, and Heinrich M. Jaeger, “Generality of shear thickening in suspensions”, Nature Materials 9, 220 - 224 (2010). pdf (main text) / pdf (supplement)