Constitutive Model for Time-Dependent Flows of Shear-Thickening Suspensions

Rheology of Dense Suspensions under Shear Rotation

Dense non-Brownian suspensions exhibit a spectacular and abrupt drop in viscosity under change of shear direction, as revealed by shear inversions (reversals) or orthogonal superposition. Here, we introduce an experimental setup to systematically explore their response to shear rotations, where one suddenly rotates the principal axes of shear by an angle θ, and measure the shear stresses with a biaxial force sensor. Our measurements confirm the genericness of the transient decrease of the resistance to shear under unsteady conditions. Moreover, the orthogonal shear stress, which vanishes in steady state, takes non-negligible values with a rich θ dependence, changing qualitatively with solid volume fraction ϕ and resulting in a force that tends to reduce or enhance the direction of flow for small or large ϕ. These experimental findings are confirmed and rationalized by particle-based numerical simulations and a recently proposed constitutive model. We show that the rotation angle dependence of the orthogonal stress results from a ϕ-dependent interplay between hydrodynamic and contact stresses.

Rheology of particulate suspensions with non-Newtonian fluids in capillaries

Particulate suspensions occur in situations from blood flow to slurries in drilling applications. Existing investigations of these suspensions generally concentrate on the impact of particle volume fraction for suspensions in Newtonian fluids under free-flow conditions. Recently, particulate-polymer composites have been used in additive manufacturing (AM). Here, the polymer becomes a shear-thinning non-Newtonian fluid during extrusion, creating a particulate suspension. Motivated by the challenges in AM of particulate composites, this study investigates the rheology of suspensions of micrometre-sized particles in shear-thinning silicone while extruded through AM-scaled nozzles (millimetre-scale diameters). The suspensions were observed to follow a power-law behaviour and their rheology was investigated through the measured flow consistency (K) and behaviour (n) indices. The impact of the particle volume fraction (ϕ) and the ratio (ω) of the capillary inside diameter to the particle diameter on both indices were measured. n was found to be only impacted by the suspension fluid type and ϕ. K was found to be constant at large ω, but decreased and then increased to infinity with ω decreasing. Based on its behaviour, K was categorized into two conditions and analysed separately with semi-empirical models. The impact of particle size distribution was also investigated.

Dynamics of microstructure anisotropy and rheology of soft jammed suspensions

We explore the rheology predicted by a recently proposed constitutive model for jammed suspensions of soft elastic particles derived from particle-level dynamics [Cuny et al., Phys. Rev. Lett., 2021, 127, 218003]. Our model predicts that the orientation of the anisotropy of the microstructure, governed by an interplay between advection and contact elasticity, plays a key role at yielding and in flow. It generates normal stress differences contributing significantly to the yield criterion and Trouton ratio. It gives rise to non-trivial transients such as stress overshoots in step increases of shear rate, residual stresses after flow cessation and power-law decay of the shear rate in creep. Finally, it explains the collapse of storage modulus as measured in parallel superposition for a yielded suspension.

Shear Jamming and Fragility of Suspensions in a Continuum Model with Elastic Constraints

Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of the viscosity.

A Rheological Model for Evaluating the Behavior of Shear Thickening of Highly Flowable Mortar

Neither the modified Bingham model nor the Herschel–Bulkley model can be used to characterize and calculate the performance of shear thickening of highly flowable mortar because of their incalculability of the rheological parameters. A new exponential rheological model was established to solve the characterization and calculation of shear thickening of the lubrication layer (highly flowable mortar) during the pumping of concrete in this paper. This new exponential rheological model has three rheological parameters, namely, yield stress, consistency coefficient, and consistency exponent. They can quantitatively describe the yield stress, differential viscosity, and shear thickening degree of highly flowable mortar. The calculating results of the rheological parameters of the newly established model for the mortars with different compositions showed that the consistency exponent of mortar decreased with the increase of its sand-binder ratio or the dosage of fly ash in the binder. This indicates that the shear thickening degree of mortar decreases. The consistency exponent of mortar initially decreases and subsequently increases with the increase in silica fume content or the dosage of the superplasticizer. It illustrates that the degree of the shear thickening of mortar initially decreased and subsequently increased. These varying patterns were confirmed by the rheological experiment of mortars.

Consititutive modeling of time-dependent flows in frictional suspensions

This paper summarizes recent joint work towards a constitutive modelling framework for dense granular suspensions. The aim is to create a time-dependent, tensorial theory that can implement the physics described in steady state by the Wyart-Cates model. This model of shear thickening suspensions supposes that lubrication films break above a characteristic normal force so that frictional contact forces come into play: the resulting non-sliding constraints can be enough to rigidify a system that would flow freely at lower stresses [1]. Implementing this idea for time-dependent flows requires the introduction of new concepts including a configuration-dependent ‘jamming coordinate’, alongside a decomposition of the velocity gradient tensor into compressive and extensional components which then enter the evolution equation for particle contacts in distinct ways. The resulting approach [2, 3] is qualitatively successful in addressing (i) the collapse of stress during flow reversal in shear flow, and (ii) the ability of transverse oscillatory flows to unjam the system. However there is much work required to refine this approach towards quantitative accuracy, by incorporating more of the physics of contact evolution under flow as determined by close interrogation of particle-based simulations.

Modeling the Microstructure and Stress in Dense Suspensions under Inhomogeneous Flow

Under inhomogeneous flow, dense suspensions exhibit behavior that violates the conventional homogeneous rheology. Specifically, one finds flowing regions with a macroscopic friction coefficient below the yielding criterion, and volume fraction above the jamming criterion. We demonstrate the underlying physics by incorporating shear rate fluctuations into a recently proposed tensor model for the microstructure and stress, and applying the model to an inhomogeneous flow problem. The model predictions agree qualitatively with particle-based simulations.