Scaling Analysis of Shear Thickening Suspensions

Abstract

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 FR, 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 ∼ FRa−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 N2 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.

Rheology of a crowd: from faster-is-slower to shear thickening

“…A recent study 62 proposed a universal scaling for shear thickening transitions. In this work and other 63 , the authors employed the scaling in equilibrium phase transition framework 64 rather than fitting data to functional forms. The scaling framework allows for collapsing data over a broad range of multiple control parameters, resulting in a tool extremely useful in systems such as the current one where both density and stress vary with the parameter of control v 0 .…”

“…where the function g is more general than the function f(p), expanding the transition dependence to density besides the stress 62,63 . The scaling analysis…”

Spreading ceramic stereolithography pastes: Insights from shear- and orthogonal-rheology

“…While the above-mentioned scenario is usually observed experimentally at low and intermediate shear rates, a nonmonotonic evolution of the viscosity, corresponding to shearthickening mechanisms, is often observed when the shear rate is further increased. Generally speaking, one can define the shear-thickening onset as the transition from lubricated to frictional flow [28][29][30] in non-Brownian suspensions, essentially corresponding to the formation of transient (hydro)clusters [30][31][32][33] capable of holding a large amount of stress by breaking and reforming under the bulk shearing motion 34,35 . Importantly, clustering is promoted by particles roughness and shape anisotropy that involve sliding and rolling friction as well as interlocking hindrance, which limit particles motion 34,36 .…”