Rheology Of Dense Suspensions Research Articles

Viscosity prediction for dense suspensions of non-spherical particles based on CFD-DEM simulations

Reliable estimation of the viscosity and rheology of dense suspensions formed from non-spherical particles is of high importance for studies of many natural and industrial processes. Still, the complexity of underlying physics makes predicting the viscosity of such suspensions a challenging task, resulting in a lack of models capable of doing so for general suspensions. In this work, we present an approach based on a combination of the computational fluid dynamics (CFD) and discrete element method (DEM) developed for arbitrarily shaped particles and use it to predict viscosity of dense suspensions of spheres, rods, and glitters. Simulation results are compared to available experimental data and commonly used engineering correlations. The developed model can reliably predict suspension viscosity in a wide range of solid volume fractions and particle shapes. The simulations with spherical particles also reveal a shear-thickening trend at increased shear rates, which corresponds to the experimentally observed non-Newtonian behavior.

Viscosity prediction for dense suspensions of non-spherical particles based on CFD-DEM simulations

Reliable estimation of the viscosity and rheology of dense suspensions formed from non-spherical particles is of high importance for studies of many natural and industrial processes. Still, the complexity of underlying physics makes predicting the viscosity of such suspensions a challenging task, resulting in a lack of models capable of doing so for general suspensions. In this work, we present an approach based on a combination of the computational fluid dynamics (CFD) and discrete element method (DEM) developed for arbitrarily shaped particles and use it to predict viscosity of dense suspensions of spheres, rods, and glitters. Simulation results are compared to available experimental data and commonly used engineering correlations. The developed model can reliably predict suspension viscosity in a wide range of solid volume fractions and particle shapes. The simulations with spherical particles also reveal a shear-thickening trend at increased shear rates, which corresponds to the experimentally observed non-Newtonian behavior.

Simulating the rheology of dense suspensions using pairwise formulation of contact, lubrication and Brownian forces

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle-based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations.

Scaling Description of Frictionless Dense Suspensions under Inhomogeneous Flow.

Predicting the rheology of dense suspensions under inhomogeneous flow is crucial in many industrial and geophysical applications, yet the conventional "μ(J)" framework is limited to homogeneous conditions in which the shear rate and solids fraction are spatially invariant. To address this shortcoming, we use particle-based simulations of frictionless dense suspensions to derive new constitutive laws that unify the rheological response under both homogeneous and inhomogeneous conditions. By defining a new dimensionless number associated with particle velocity fluctuations and combining it with the viscous number, the macroscopic friction, and the solids fraction, we obtain scaling relations that collapse data from homogeneous and inhomogeneous simulations. The relations allow prediction of the steady state velocity, stress, and volume fraction fields using only knowledge of the applied driving force.

Unifying length-scale-based rheology of dense suspensions

Unifying length-scale-based rheology of dense suspensions

Rheology of dense suspensions of ideally conductive particles in an electric field

The rheological behaviour of dense suspensions of ideally conductive particles in the presence of both electric field and shear flow is studied using large-scale numerical simulations. Under the action of an electric field, these particles are known to undergo dipolophoresis (DIP), which is the combination of two nonlinear electrokinetic phenomena: induced-charge electrophoresis (ICEP) and dielectrophoresis (DEP). For ideally conductive particles, ICEP is predominant over DEP, resulting in transient pairing dynamics. The shear viscosity and first and second normal stress differences $N_1$ and $N_2$ of such suspensions are examined over a range of volume fractions $15\,\% \leq \phi \leq 50\,\%$ as a function of Mason number $Mn$ , which measures the relative importance of viscous shear stress over electrokinetic-driven stress. For $Mn < 1$ or low shear rates, the DIP is shown to dominate the dynamics, resulting in a relatively low-viscosity state. The positive $N_1$ and negative $N_2$ are observed at $\phi < 30\,\%$ , which is similar to Brownian suspensions, while their signs are reversed at $\phi \ge 30\,\%$ . For $Mn \ge 1$ , the shear thickening starts to arise at $\phi \ge 30\,\%$ , and an almost five-fold increase in viscosity occurs at $\phi = 50\,\%$ . Both $N_1$ and $N_2$ are negative for $Mn \gg 1$ at all volume fractions considered. We illuminate the transition in rheological behaviours from DIP to shear dominance around $Mn = 1$ in connection to suspension microstructure and dynamics. Lastly, our findings reveal the potential use of nonlinear electrokinetics as a means of active rheology control for such suspensions.

Hidden hierarchy in the rheology of dense suspensions

Hidden hierarchy in the rheology of dense 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.

Dynamic-bond-induced sticky friction tailors non-Newtonian rheology.

Frictional network formation has become a new paradigm for understanding the non-Newtonian shear-thickening behavior of dense suspensions. Recent studies have exclusively focused on interparticle friction that instantaneously vanishes when applied shear is ceased. Herein, we investigate a friction that emerges from dynamic chemical bridging of functionalized particle surfaces sheared into close proximity. This enables tailoring of both friction magnitude and the time release of the frictional coupling. The experiments use dense suspensions of thiol-functionalized particles suspended in ditopic polymers endcapped with benzalcyanoacetamide Michael-acceptors. The subsequent room temperature, catalyst-free dynamic thia-Michael reactions can form bridging interactions between the particles with dynamic covalent bonds that linger after formation and release in the absence of shear. This chemical friction mimics physical friction but is stickier, leading to tunable rheopexy. The effect of sticky friction on dense suspension rheology is explored by varying the electronic nature of the benzalcyanoacetamide moiety, the molecular weight of the ditopic polymers, the amount of a competitive bonding compound, and temperature. These results demonstrate how dynamic-bond-induced sticky friction can be used to systematically control the time dependence of the non-Newtonian suspension rheology.

Shear thickening in dense suspensions driven by particle interlocking

The processing of dense suspensions is a crucial step in many industries including mining; the production of ceramics; and the manufacture of pharmaceuticals. It is widely reported that these suspensions exhibit nonlinear behaviours such as shear thinning and thickening, with particle surface contacts recently being accepted as a primary culprit in the latter. In light of this, the modelling community have started to explore the role of particle surface tribology, predominantly by incorporating Coulombic friction models borrowed from the field of dry granular matter. Full details of the interactions between particle surfaces remain unclear, however, and it is suggested that physical interlocking of particle asperities may be key. Here, we use particle-based simulations to explore explicitly the effect of interlocking on the rheology of dense suspensions of micron-sized solids in a Newtonian fluid. Our simplified model recovers shear thinning, thickening and jamming phenomena commonly seen in experiments.

Stress-activated constraints in dense suspension rheology

Dispersing small particles in a liquid can produce surprising behaviors when the solids fraction becomes large: rapid shearing drives these systems out of equilibrium and can lead to dramatic increases in viscosity (shear-thickening) or even solidification (shear jamming). These phenomena occur above a characteristic onset stress when particles are forced into frictional contact. Here we show via simulations how this can be understood within a framework that abstracts details of the forces acting at particle-particle contacts into general stress-activated constraints on relative particle movement. We find that focusing on just two constraints, affecting sliding and rolling at contact, can reproduce the experimentally observed shear thickening behavior quantitatively, despite widely different particle properties, surface chemistries, and suspending fluids. Within this framework parameters such as coefficients of sliding and rolling friction can each be viewed as a proxy for one or more forces of different physical or chemical origin, while the parameter magnitudes indicate the relative importance of the associated constraint. In this way, a new link is established that connects features observable in macroscale rheological measurements to classes of constraints arising from micro- or nano-scale properties.

A fast and efficient tool to study the rheology of dense suspensions

A cutting-edge software that adopts an optimized searching algorithm is presented to tackle the Newton–Euler equations governing the dynamics of dense suspensions in Newtonian fluids. In particular, we propose an implementation of a fixed-radius near neighbors search based on an efficient counting sort algorithm with an improved symmetric search. The adopted search method drastically reduces the computational cost and allows an efficient parallelization even on a single node through the multi-threading paradigm. Emphasis is also given to the memory efficiency of the code since the history of the contacts among particles has to be traced to model the frictional contributions, when dealing with dense suspensions of rheological interest that consider non-smooth interacting particles. An effective procedure based on an estimate of the maximum number of the smallest particles surrounding the largest one (given the radii distribution) and a sort applied only to the surrounding particles only is implemented, allowing us to effectively tackle the rheology of non-monodispersed particles with a high size-ratio in large domains. Finally, we present validations and verification of the numerical procedure, by comparing with previous simulations and experiments, and present new software capabilities.

Transition from steady shear to oscillatory shear rheology of dense suspensions.

Recent studies have highlighted that oscillatory and time-dependent shear flows might help increase the flowability of dense suspensions. While most focus has been on cross-flows we here study a simple two-dimensional suspensions where we apply simultaneously oscillatory and stationary shear along the same direction. We first show that the dissipative viscosities in this set-up significantly decrease with an increasing shear-rate magnitude of the oscillations and given that the oscillatory strain is small, in a similar fashion as found previously for cross-flow oscillations. As for cross-flow oscillations, the decrease can be attributed to the large decrease in the number of contacts and an altered microstructure as one transitions from a steady shear to an oscillatory shear dominated rheology. As subresults we find both an extension to the μ(J) rheology, a constitutive relationship between the shear stresses and the shear rate, valid for oscillatory shear flows and that shear-jamming of frictional particles at oscillatory shear dominated flows occurs at higher packing fractions compared to steady shear dominated flows.

Particle Surface Roughness as a Design Tool for Colloidal Systems.

Control over the surface roughness of colloidal particles offers exciting opportunities to tailor the properties and the processing of a broad range of soft matter systems. Moreover, identifying surface roughness as a design parameter reveals the possibility to connect seemingly distinct phenomena and materials via the role played by roughness effects. In this feature article, we concisely review some approaches to synthesize and characterize rough colloidal particles, with a focus on model spherical colloids. We then discuss the impact that surface roughness has on both the high-shear rheology of dense suspensions and the stabilization of Pickering emulsions. Commenting on developments of our own research, we aim to offer an original perspective for a property-oriented development of colloidal particles that transcends classical divisions between materials and processes toward innovative solutions.

A constitutive model for sheared dense suspensions of rough particles

In a concentrated suspension, particles come into contact due to the presence of asperities on their surfaces. As a result, the contact forces and interparticle friction become one of the important factors governing the rheology of rigid particle suspensions at high concentrations. We show that a load-dependent friction model can be used to reproduce the experimentally observed shear thickening [ST—continuous and discontinuous (DST)] behavior with an increase in the asperity size. Increasing the particle surface roughness size leads to a decrease in the critical shear rate above which shear-thickening takes place, a reduction in the critical volume fraction for DST and an increase in the viscosity jump across non-shear-thickened to shear-thickened regime. In this paper, we propose a constitutive model to quantify the effect of increasing the roughness size on the rheology of dense ST suspensions as well as on the critical shear rate for ST and the critical volume fraction for DST. We fit this model to our simulation data for stress controlled shear flow of dense rough particle suspensions. Once the fitting is complete, these equations are used to predict exact volume fractions and shear stress values for transitions between three regimes on the shear stress-shear rate flow state diagram for different roughness values. The results of this study can be used to tune the particle surface roughness for manipulating the dense suspension rheology according to different applications.

Development of Test Procedures Based on Chaotic Advection for Assessing Polymer Performance in High-Solids Tailings Applications

Post-thickener polymer addition to initiate rapid tailings dewatering has gained considerable interest for tailings storage facility (TSF) management. However, the highly viscous and non-Newtonian rheology of dense suspensions presents unique challenges for mixing with polymer solutions. Such mixing is highly inefficient, often resulting in polymer overdosing and wide variations in deposited tailings characteristics, with the potential to significantly compromise TSF performance. In this study, a new type of mixer based on the principles of chaotic advection was used for treating kaolin suspensions with high molecular weight (MW) anionic copolymer solutions. Chaotic advection imparts efficient mixing by gently stretching and folding flows in a controlled manner, as opposed to random, high-shear flows associated with turbulent mixing, and this lower shear stress allows for the controlled formation of larger aggregate structures with vastly improved dewatering characteristics. A pre-conditioning pipe reactor prior to this mixer can also be advantageous in terms of providing a short burst of high shear for initial polymer distribution. Seven acrylamide/acrylate copolymers of a fixed anionic charge density (30%) spanning a distinct MW range, as characterized by intrinsic viscosity, were applied at elevated dosages to high-solids (20–30 wt %) kaolin suspensions in continuous flow through the chaotic mixer described above. Medium-to-high MW polymers were generally preferred, with further increases in MW resulting in significantly diminished dewatering outcomes. Direct analysis of polymer solution properties through oscillatory rheology gave a better indication of a polymer’s potential performance compared with intrinsic viscosity, offering a more robust basis for polymer selection. This represented the first systematic study into the effects of polymer properties on deposition behavior after dosing at high solids, which was only possible through the ability to apply controlled shear across the entire suspension during sample preparation.

Temperature-responsive interdrop association of condensed attractive nanoemulsions

This study introduces a temperature-responsive attractive nanoemulsion (ANE) system, which is characterized by the polymer chain conformation-driven dipolar interaction across different oil droplets in an aqueous medium. To achieve this, highly stable ANEs were produced by co-assembly of amphiphilic triblock copolymers (ATCs), poly(ethylene oxide)-b-poly(ε-caprolactone)-b-poly(ethylene oxide) (PEO-b-PCL-b-PEO), with lecithin at the oil-water interface. The dipolar attraction of the methoxy terminated-PEO (mPEO) of ATCs on one drop surface with the lecithin head located on the other drop surface led to the drop-to-drop association. We showed that the efficiency of this interdrop association was dominantly influenced by the chain conformation of mPEO blocks. From dense suspension rheology studies, it was demonstrated that the ANEs formed a gel-like phase below the lower critical solution temperature (LCST) of the mPEO, but transformed to a liquid-like phase above the LCST, which occurred reversibly, thus enabling the development of temperature-responsive emulsion fluids.

Unifying viscous and inertial regimes of discontinuous shear thickening suspensions

The rheology of dense suspensions in the viscous regime can be characterized by the viscous number J and granular flows by the inertia number I, both relating the shear rate γ ˙ to the confining pressure P. Furthermore, several works have shown that the rheology of suspensions and granular flows can be unified, and this unification is used to characterize suspensions with non-negligible particle inertia from the viscous to the inertial regime (i.e., granular flows). There have also been recent works that apply this unification to suspensions where the number of frictional contacts increases upon the shear rate with constant packing fraction, a model that has successfully described discontinuous shear thickening in suspension flows. We and other researchers have previously shown that the fraction of frictional contacts χ f is a key control parameter for friction-driven shear thickening in the viscous regime. It is, however, difficult to control and study the effect of the number of frictional contacts on the rheology of dense suspensions at constant packing fraction as this quantity increases sharply around a threshold shear rate. In this work, we extend our previous work and use numerical simulations to study particle flows in both the viscous and inertial regimes as well as for suspensions in the crossover between these regimes with varying χ f. By having pressure-controlled simulations, we are able to keep χ f at values between 0 and 1, hence critically testing the validity of a unification at intermediate values. With the help of a binary model composed of nonfrictional and frictional particles, where χ f is well-controlled, we manage to obtain expressions for constitutive laws in both limits. For the critical load model, we find a simple relationship between χ f and the pressure-rescaled threshold force f ^ applicable for both the viscous and inertial regimes. Combining these expressions, we then show that suspensions in the crossover between these regimes can be characterized by four dimensionless numbers, f ^, K, K μ, and K z, where the last three are simple combinations of J and I and verified against numerical simulations. These expressions can be further simplified by approximating K μ = K, which we show is a good approximation close to shear jamming or at low Stokes numbers. In the end, we construct a dimensionless parameter encoding various shear protocols and show predictions of behaviors of suspensions under different shear conditions. Having derived constitutive relations from constant pressure simulations, we finally test our relations under constant volume assumption which indeed well captures the various discontinuous shear thickening behaviors seen at different Stokes numbers. Finally, we discuss the role of having a varying microscopic friction coefficient μ p as a function of the normal force.

Stress Controlled Rheology of Dense Suspensions Using Transient Flows.

Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we can track how a dense suspension approaches its shear-jammed state dynamically and quantitatively map out the onset stress for solidification in a state diagram.

From Yielding to Shear Jamming in a Cohesive Frictional Suspension.

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, with an intermediate region of stress in which the material is flowable.