Force transmission and the order parameter of shear thickening

Physics of Fluids, 2019

Shear thickening of particle suspensions is caused by a transition between lubricated and frictional contacts between the particles. Using three-dimensional (3D) numerical simulations, we study how the interparticle friction coefficient (μm) influences the effective macroscopic friction coefficient (μ) and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for μ in terms of distance to jamming for varying shear stresses and μm values. We find μ to be rather insensitive to interparticle friction, which is perhaps surprising but agrees with recent theory and experiments. Unifying behaviors were observed between the average coordination numbers of particles across a wide range of viscous numbers and μm values.

EPJ Web of Conferences

Dense suspensions can exhibit an abrupt change in their viscosity in response to increasing shear rate. The origin of this discontinuous shear thickening (DST) has been ascribed to the transformation of lubricated contacts to frictional, particle-on-particle contacts. Recent research on the flowing and jamming behavior of dense suspensions has explored the intersection of ideas from granular physics and Stokesian fluid dynamics to better understand this transition from lubricated to frictional rheology. DST is reminiscent of classical phase transitions, and a key question is how interactions between the microscopic constituents give rise to a macroscopic transition. In this paper, we extend a formalism that has proven to be successful in understanding shear jamming of dry grains to dense suspensions. Quantitative analysis of the collective evolution of the contactforce network accompanying the DST transition demonstrates clear changes in the distribution of microscopic variables, and leads to the identification of an "order parameter" characterizing DST.

Physical Review Letters, 2016

Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fraction elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find N1 < 0, consistent with hydrodynamic models, however at higher volume fractions and shear stresses these models break down and we instead observe dilation (N1 > 0), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity, instead this change in the sign of N1 occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model which combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fraction and shear stress.

Journal of Rheology, 2014

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article [R. Seto et al., Phys. Rev. Lett. 111, 218301 (2013)], we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including discontinuous shear thickening. We have found frictional contact forces to be essential and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: As the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition. V

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (σxy) and packing fraction (φ). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, µ = σxy/P. We find that µ decreases (i) as φ is increased and (ii) as σxy is increased. Using a new constitutive relation between µ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of µ that lead to the generic flow diagram of a DST fluid observed in experiments. Dense suspensions of frictional grains in a fluid often display an increase in viscosity η = σ xy / ˙ γ (thickening) as the confining shear stress (σ xy) or strain rate (˙ γ) are increased. At a critical density dependent shear rate ˙ γ, the viscosity increases abruptly: a phenomenon termed Dis-continuous Shear Thickening (DST). In stress-controlled protocols, η ∼ σ xy marks the DST boundary [1, 2]. Experiments have also observed interesting features in other components of the stress tensor such as the first normal stress difference, N 1 = σ xx − σ yy close to the DST regime [3]. A mean-field theory [4, 5], based on an increase in the fraction of close interactions becoming frictional (rather than lubricated) with increasing shear stress, has been extremely successful at predicting the flow curves and the DST flow diagram in the space of packing fraction, φ and shear stress or strain rate [6, 7]. The physical picture of lubricated layers between grains giving way to frictional contacts when the imposed σ xy exceeds a critical value set by a repulsive force [4] provides a consistent theory of DST [7], shear jamming fronts [8] and instabilities of the shear-thickened state [9]. Although several features relating to the flow of dense suspensions can be well explained within this mean-field theory, the nature of the microscopic correlations underlying this transition remains far from clear [6]. Conventional measures such as the pair correlation function do not exhibit pronounced changes accompanying DST. An interesting, intrinsic feature of DST is that the macro-scopic friction coefficient, µ, decreases as the fraction of frictional contacts increases: the mean normal stress grows more rapidly than the shear stress. This, and contact network visualizations from simulations [6], indicate that there are important changes in the network of fric-tional contacts that are not captured by scalar variables such as the fraction of frictional contacts. In this work, we focus on the microscopic origin of the evolution of the components of the stress tensor across DST, and construct a statistical theory for µ, the anisotropy of the stress tensor. While the changes in real space near DST can be incre-mental, and hence do not show any significant changes in pair correlations, the contact forces change dramatically and play a central role. The steady state flow of non-inertial suspensions is governed by microscopic constraints of force and torque balance, and these constraints can lead to non-trivial correlations of contact forces. Theories have focussed, up to now, on the average properties of the inter-particle forces [4]. However, fundamental questions about how interactions at the microscopic, contact level and the constraints of force balance give rise to a macroscopic transition remain [10]. In two-dimensional systems, the crucial constraint of force balance can be naturally accounted for by working in a dual space, known as a force tiling. In this representation, inter-particle forces are represented by the difference of vector height fields, { h}, defined on the voids. This representation has been shown to be particularly useful in characterizing shear jamming transitions in frictional granular materials [11]. Unlike shear jamming , where configurations and stresses are static, flowing suspensions provide an ensemble of non-equilibrium steady states that are ripe for a statistical description. We show that the non-equilibrium steady states (NESS) at a given σ xy and φ can be mapped to a statistical en

Physical Review Letters

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gearlike rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with reallife suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shearthickening materials.

2014

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article [R. Seto et al., Phys. Rev. Lett. 111, 218301 (2013)], we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including discontinuous shear thickening. We have found frictional contact forces to be essential and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: As the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition. V

Physical Review Letters, 2013

We propose a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, that links the transition from continuous to discontinuous shear-thickening in dense granular pastes to distinct lubrication regimes in the particle contacts. We identify a local Sommerfeld number that determines the transition from Newtonian to shear-thickening flows, and then show that the suspension's volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.

Nature Materials, 2010

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, that is, they shear thin. Few are reported to do the opposite, that is, shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behaviour. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.

2009

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.