Dynamic Jamming Point for Shear Thickening Suspensions

Abstract

We report on rheometry measurements to characterize critical behavior in two model shear thickening suspensions: cornstarch in water and glass spheres in oil. The slope of the shear thickening part of the viscosity curve is found to increase dramatically with packing fraction and diverge at a critical packing fraction φc. The magnitude of the viscosity and the yield stress are also found to have scalings that diverge at φc. We observe shear thickening as long as the yield stress is less than the stress at the viscosity maximum. Above this point the suspensions transition to purely shear thinning. Based on these data we present a dynamic jamming phase diagram for suspensions and show that a limiting case of shear thickening corresponds to a jammed state.In Newtonian fluids the viscosity does not change with applied shear rate, while non-Newtonian fluids usually show a decrease of viscosity when sheared faster, i. e., they shear thin. The opposite behavior, shear thickening, is less common but can be quite dramatic: beyond a certain shear rate the viscosity increases potentially by orders of magnitude. This behavior is reversible so the stress relaxes when the shear is removed. Reported shear thickening fluids are usually densely packed colloids or suspensions [1,2,3]. Strong shear thickening can be observed for example with cornstarch in water. Shear thickening is a concern across a range of industrial processes [1,4] and is of interest for the ability to absorb energy from impacts [5].It has been suggested [3,6,7,8,9,10,11,12,13,14,15,16,17] that shear thickening is related to the phenomenon of jamming. The concept of a jamming transition, however, applies to the limit of vanishing shear rate and is exemplified by the onset of glassy behavior with a seemingly diverging viscosity in molecular liquids, dense packings of colloids, or macroscopic granular materials, leading to the appearance of a yield stress below which there is no flow [18,19,20]. Shear thickening, on the other hand, occurs at non-zero shear rate. While a yield stress has been measured in some shear thickening fluids [8], no linkage has been established between such yield stress and the observed shear thickening behavior. Dense shear thickening fluids have been reported to exhibit seemingly discontinuous jumps in stress with increasing shear rate [7,14,17,21,22,23,24,25]. However, this discontinuity has not yet been characterized quantitatively. Phenomenological shear thickening models have shown stress distributions that are similar to those of force chains in jammed systems [6,10]. However, the mild shear thickening behavior found in simulations [10,26,27,28] so far cannot reproduce the dramatic increases in viscosity with shear rate observed in many experiments. As a result, the connection between shear thickening and the onset of jamming has been qualitative and many details of the relationship remain unresolved.Here we characterize the stress-shear rate discontinuity and the relationship to the yield stress through rheological measurements. T...

Granular suspension avalanches. I. Macro-viscous behavior

“…The most recent experimental investigations into the rheological behavior of granular suspensions comprising neutrally buoyant particles 16,17,21,38,39 have led to the hypothesis that the continuous fluid phase imparts most of its properties to the bulk, that is, the stresses are linearly dependent on the shear rate and the disperse solid phase does not play a significant role in the rheological response except to generate normal stress differences and enhance energy dissipation. In the limit of high concentrations, the suspension approaches a jammed solid state, which is characterized by the formation of load-bearing force chains throughout large clusters or particle networks.…”

Effect of particle collisions in dense suspension flows

“…However, the dilute regime breaks down upon densification as steric-hindrance effects become dominant. At larger packing fractions [2,3] the viscosity even diverges at the jamming point φ c where the suspension jams into an amorphous solid. Critical exponents governing the rheology of dense suspensions as well as a diverging correlation length scale have been observed in experiments [2][3][4][5][6] and in numerical models [7][8][9][10][11][12][13][14][15][16].…”

Discontinuous shear thickening in Brownian suspensions by dynamic simulation

“…In turn, the locations of these singularities shape the large ϕ-portion of the rheological landscape, i.e., the effective viscosity and the normal stresses as functions of ϕ and σ. In particular, in the "stress-induced friction" scenario (4,(6)(7)(8)(9)(10)(11)(12)(13), shear thickening is a transition from a rheological response dominated by frictionless jamming to one controlled by frictional jamming upon increase of the shear stress. This transition is argued to be due to the creation of frictional contacts between particles at high stresses; the contacts are prevented at low stresses by a short-range stabilizing repulsive force, as would be expected to be present to stabilize a colloidal dispersion against aggregation by, for example, attractive van der Waals forces (14,15).…”