Microscopic Origin of Frictional Rheology in Dense Suspensions: Correlations in Force Space

Scalability of a graph neural network in accurate prediction of frictional contact networks in suspensions

Dense suspensions often exhibit shear thickening, characterized by a dramatic increase in viscosity under large external forcing. This behavior has recently been linked to the formation of a system-spanning frictional contact network (FCN), which contributes to increased resistance during deformation. However, identifying these frictional contacts poses experimental challenges and is computationally expensive. This study introduces a graph neural network (GNN) model designed to accurately predict FCNs by two dimensional simulations of dense shear thickening suspensions. The results demonstrate the robustness and scalability of the GNN model across various stress levels (σ), packing fractions (ϕ), system sizes, particle size ratios (Δ), and amounts of smaller particles. The model is further able to predict both the occurrence and structure of a FCN. The presented model is accurate and interpolates and extrapolates to conditions far from its control parameters. This machine learning approach provides an accurate, lower cost, and faster predictions of suspension properties compared to conventional methods, while it is trained using only small systems. Ultimately, the findings in this study pave the way for predicting frictional contact networks in real-life large-scale polydisperse suspensions, for which theoretical models are largely limited owing to computational challenges.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order-disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order-disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order-disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Dense bidisperse suspensions under non-homogeneous shear

We study the rheological behaviour of bidisperse suspensions in three dimensions under a non-uniform shear flow, made by the superimposition of a linear shear and a sinusoidal disturbance. Our results show that (i) only a streamwise disturbance in the shear-plane alters the suspension dynamics by substantially reducing the relative viscosity, (ii) with the amplitude of the disturbance determining a threshold value for the effect to kick-in and its wavenumber controlling the amount of reduction and which of the two phases is affected. We show that, (iii) the rheological changes are caused by the effective separation of the two phases, with the large or small particles layering in separate regions. We provide a physical explanation of the phase separation process and of the conditions necessary to trigger it. We test the results in the whole flow curve, and we show that the mechanism remains substantially unaltered, with the only difference being the nature of the interactions between particles modified by the phase separation.

Structure and Dynamics of Force Clusters and Networks in Shear Thickening Suspensions

Dense suspensions can exhibit shear thickening in response to large deformation. A consensus has emerged over the past few years on the formation of force networks, that span the entire system size, that lead to increased resistance to motion. Nonetheless, the characteristics of these networks are to a large extent poorly understood. Here, force networks formed in continuous and discontinuous shear thickening dense suspensions (CST and DST, respectively) are studied. We first show the evolution of the network formation and its topological heterogeneities as the applied stress increases. Subsequently, we identify force communities and coarse grain the suspension into a cluster network, and show that cluster-level dynamics are responsible for stark differences between the CST and DST behavior. Our results suggest that the force clusters formed in the DST regime are considerably more constrained in their motion, while CST clusters are loosely connected to their surrounding clusters.

Microstructure of continuous shear thickening colloidal suspensions determined by rheo-VSANS and rheo-USANS

Research on shear thickening colloidal suspensions demonstrates that measurements of the microstructure can elucidate the source of the rheological material properties in the shear thickened state as well as critically test simulations and theory based on a variety of mechanisms such as enhanced lubrication hydrodynamics, elastohydrodynamics, and contact friction. Prior work on continuous shear thickening dispersions with a well-defined shear thickened state identified the formation of hydroclusters as characteristic of this state, determined the anisotropy in the nearest neighbor distribution, and used this information to test prevailing theories and simulations. However, important questions remain about the mesoscale (i.e., particle cluster scale) microstructure of the shear thickened state. Here we employ neutron scattering methods applied to shearing colloidal dispersions of spherical particles with two extremes of friction and lubrication surface properties to resolve the longer-length scale microstructure in the shear thickened state. Hydroclusters are shown to be highly localized, in agreement with prior neutron scattering and direct optical measurements, but in disagreement with the most recent simulations that predict a longer-range structure formation. These results combined with prior measurements provide experimental evidence about the length scale of microstructure formation in continuous shear thickening suspensions necessary to improve our understanding of the phenomenon as well as guide theoretical investigations that quantitatively link nanoscale forces to macroscopic properties in the shear thickened state.

Jamming Distance Dictates Colloidal Shear Thickening

We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength β scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional rotational constraints, require an average of 1.5-2 fewer particle contacts as compared to smooth colloids, in order to generate the same β. This is because the surface roughness enhances geometric friction in such a way that the rough colloids do not experience a large change in the free volume near the jamming point. The available free volume for colloids of different roughness is related to the deficiency from the maximum number of nearest neighbors at jamming under shear. Our results further suggest that the force per contact is different for particles with different morphologies.

Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear

In this study, we numerically investigated the mechanical responses and trajectories of frictional granular particles under oscillatory shear in the reversible phase where particle trajectories form closed loops below the yielding point. When the friction coefficient is small, the storage modulus exhibits softening, and the loss modulus remains finite in the quasi-static limit. As the friction coefficient increases, the softening and residual loss modulus are suppressed. The storage and loss moduli satisfy scaling laws if they are plotted as functions of the areas of the loop trajectories divided by the strain amplitude and diameter of grains, at least for small values of the areas.

Spongelike Rigid Structures in Frictional Granular Packings

We show how rigidity emerges in experiments on sheared two-dimensional frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a critical contact number z_{c}=2.4±0.1, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a spongelike morphology. While the pressure within rigid structures always exceeds the pressure outside the rigid structures, they are not identified with the force chains of shear jamming. These findings highlight the need to focus on mechanical stability arising through arch structures and hinges at the mesoscale.

Contact criterion for suspensions of smooth and rough colloids

We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, φ_J. The jammed suspensions are subsequently diluted with known volumes of solvent to φ < φ_J. Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to φ_J to determine the mean contact number at jamming, 〈z〉_J. Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈z〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions (φ > 0.50) due to an increased number of nearest neighbors in the first coordination shell.

Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear

We numerically study the linear response of two-dimensional frictional granular materials under oscillatory shear. The storage modulus G^{'} and the loss modulus G^{''} in the zero strain rate limit depend on the initial strain amplitude of the oscillatory shear before measurement. The shear jammed state (satisfying G^{'}>0) can be observed at an amplitude greater than a critical initial strain amplitude. The fragile state is defined by the emergence of liquid-like and solid-like states depending on the form of the initial shear. In this state, the observed G^{'} after the reduction of the strain amplitude depends on the phase of the external shear strain. The loss modulus G^{''} exhibits a discontinuous jump corresponding to discontinuous shear thickening in the fragile state.

Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: shear jammed and fragile states

Dense non-Brownian suspensions, including both hydrodynamic interactions and frictional contacts between particles, are numerically studied under simple and oscillatory shears in terms of the lattice Boltzmann method. We successfully reproduce the discontinuous shear thickening (DST) under a simple shear for bulk three-dimensional systems. For our simulation of an oscillatory shear in a quasi-two-dimensional system, we measure the mechanical response after the reduction of the strain amplitude from the initial oscillations. Here, we find the existence of a shear-jammed state under this protocol in which the storage modulus G' is only finite for high initial strain amplitude γI0. We also find the existence of a fragile state in which both fluid-like and solid-like responses can be detected for an identical area fraction and an initial strain amplitude γI0 depending on the initial phase Θ (or the asymmetricity of the applied strain) of the oscillatory shear. We also observe a DST-like behavior under the oscillatory shear in the fragile state. Moreover, we find that the stress anisotropy becomes large in the fragile state. Finally, we confirm that a stress formula based on the angular distribution of the contact force recovers the contact contributions to the stress tensors for both simple and oscillatory shears with large strains.

Testing the Wyart-Cates model for non-Brownian shear thickening using bidisperse suspensions

There is a growing consensus that shear thickening of concentrated dispersions is driven by the formation of stress-induced frictional contacts. The Wyart-Cates (WC) model of this phenomenon, in which the microphysics of the contacts enters solely via the fraction f of contacts that are frictional, can successfully fit flow curves for suspensions of weakly polydisperse spheres. However, its validity for "real-life", polydisperse suspensions has yet to be seriously tested. By performing systematic simulations on bidisperse mixtures of spheres, we show that the WC model applies only in the monodisperse limit and fails when substantial bidispersity is introduced. We trace the failure of the model to its inability to distinguish large-large, large-small and small-small frictional contacts. By fitting our data using a polydisperse analogue of f that depends separately on the fraction of each of these contact types, we show that the WC picture of shear thickening is incomplete. Systematic experiments on model shear-thickening suspensions corroborate our findings, but highlight important challenges in rigorously testing the WC model with real systems. Our results prompt new questions about the microphysics of thickening for both monodisperse and polydisperse systems.

Using Acoustic Perturbations to Dynamically Tune Shear Thickening in Colloidal Suspensions

Colloidal suspensions in industrial processes often exhibit shear thickening that is difficult to control actively. Here, we use piezoelectric transducers to apply acoustic perturbations to dynamically tune the suspension viscosity in the shear-thickening regime. We attribute the mechanism of dethickening to the disruption of shear-induced force chains via perturbations that are large relative to the particle roughness scale. The ease with which this technique can be adapted to various flow geometries makes it a powerful tool for actively controlling suspension flow properties and investigating system dynamics.