skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Universal scaling of shear thickening transitions
Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.  more » « less
Award ID(s):
2026842
PAR ID:
10471990
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
Publisher / Repository:
AIP Publishing
Date Published:
Journal Name:
Journal of Rheology
Volume:
67
Issue:
6
ISSN:
0148-6055
Page Range / eLocation ID:
1189 to 1197
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Dense suspensions of particles in viscous liquid often demonstrate the striking phenomenon of abrupt shear thickening, where their viscosity increases strongly with increase of the imposed stress or shear rate. In this work, discrete-particle simulations accounting for short-range hydrodynamic, repulsive, and contact forces are performed to simulate flow of shear thickening bidisperse suspensions, with the packing parameters of large-to-small particle radius ratio δ = 3 and large particle fraction ζ = 0.15, 0.50, and 0.85. The simulations are carried out for volume fractions 0.54 ≤ ϕ ≤ 0.60 and a wide range of shear stresses. The repulsive forces, of magnitude F R , model the effects of surface charge and electric double-layer overlap, and result in shear thinning at small stress, with shear thickening beginning at stresses σ ∼ F R a −2 . A crossover scaling analysis used to describe systems with more than one thermodynamic critical point has recently been shown to successfully describe the experimentally-observed shear thickening behavior in suspensions. The scaling theory is tested here on simulated shear thickening data of the bidisperse mixtures, and also on nearly monodisperse suspensions with δ = 1.4 and ζ = 0.50. Presenting the viscosity in terms of a universal crossover scaling function between the frictionless and frictional maximum packing fractions collapses the viscosity for most of the suspensions studied. Two scaling regimes having different exponents are observed. The scaling analysis shows that the second normal stress difference N 2 and the particle pressure Π also collapse on their respective curves, with the latter featuring a different exponent from the viscosity and normal stress difference. The influence of the fraction of frictional contacts, one of the parameters of the scaling analysis, and its dependence on the packing parameters are also presented. 
    more » « less
  2. We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general. 
    more » « less
  3. null (Ed.)
    Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities ϕ j above the minimal density (or the J-point density) ϕ J leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings. Under constant pressure shear, the system evolves into a steady-state at sufficiently large strains, whose density only depends on the pressure and is insensitive to the initial jamming density ϕ j . In the limit of vanishing pressure, the steady-state exhibits critical behavior at ϕ J . While packings with different ϕ j values display equivalent scaling properties under compression, they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when ϕ j > ϕ J , contrary to the continuous behaviour in generic packings that jam at ϕ J . Our results thus lead to a more coherent, generalised picture of jamming in frictionless packings, which also have important implications on how dilatancy is understood in the context of frictional granular matter. 
    more » « less
  4. Discrete-particle simulations of bidisperse shear thickening suspensions are reported. The work considers two packing parameters, the large-to-small particle radius ratio ranging from [Formula: see text] (nearly monodisperse) to [Formula: see text], and the large particle fraction of the total solid loading with values [Formula: see text], 0.5, and 0.85. Particle-scale simulations are performed over a broad range of shear stresses using a simulation model for spherical particles accounting for short-range lubrication forces, frictional interaction, and repulsion between particles. The variation of rheological properties and the maximum packing fraction [Formula: see text] with shear stress [Formula: see text] are reported. At a fixed volume fraction [Formula: see text], bidispersity decreases the suspension relative viscosity [Formula: see text], where [Formula: see text] is the suspension viscosity and [Formula: see text] is the suspending fluid viscosity, over the entire range of shear stresses studied. However, under low shear stress conditions, the suspension exhibits an unusual rheological behavior: the minimum viscosity does not occur as expected at [Formula: see text], but instead decreases with further increase of [Formula: see text] to [Formula: see text]. The second normal stress difference [Formula: see text] acts similarly. This behavior is caused by particles ordering into a layered structure, as is also reflected by the zero slope with respect to time of the mean-square displacement in the velocity gradient direction. The relative viscosity [Formula: see text] of bidisperse rate-dependent suspensions can be predicted by a power law linking it to [Formula: see text], [Formula: see text] in both low and high shear stress regimes. The agreement between the power law and experimental data from literature demonstrates that the model captures well the effect of particle size distribution, showing that viscosity roughly collapses onto a single master curve when plotted against the reduced volume fraction [Formula: see text]. 
    more » « less
  5. Abstract Complex fluids exhibit a variety of exotic flow behaviours under high stresses, such as shear thickening and shear jamming. Rheology is a powerful tool to characterise these flow behaviours over the bulk of the fluid. However, this technique is limited in its ability to probe fluid behaviour in a spatially resolved way. Here, we utilise high-speed imaging and the free-surface geometry in drop impact to study the flow of colloidal suspensions. Here, we report observations of coexisting solid and liquid phases due to shear jamming caused by impact. In addition to observing Newtonian-like spreading and bulk shear jamming, we observe the transition between these regimes in the form of localised patches of jammed suspension in the spreading drop. We capture shear jamming as it occurs via a solidification front travelling from the impact point, and show that the speed of this front is set by how far the impact conditions are beyond the shear thickening transition. 
    more » « less