Rheology Of Suspensions Research Articles

A New Concept for Interpretation of the Viscoelastic Behavior of Aqueous Sodium Carboxymethyl Cellulose Systems.

Viscoelastic behaviors of aqueous systems of commercially available sodium carboxymethyl cellulose (NaCMC) samples with the degrees of substitution (DS) of approximately 0.68 and 1.3, and the weight-average molar masses (Mw) higher than 200 kg mol-1 dissolved in pure water and aqueous sodium chloride solutions were investigated over a wide concentration (c) range of NaCMC samples. The dependencies of the specific viscosity (ηsp), the average relaxation time (τw), and the reciprocal of the steady-state compliance (Je-1) on c were discussed. The relationships ηsp ∝ c3, τw ∝ c2, and Je-1 ∝ c, characteristic of the rod particle suspensions, were clearly observed in a range lower than the c where the critical gel behavior was observed. Thus, a new concept based on the rheology of rod particle suspensions was employed to interpret the viscoelastic behaviors obtained in the c range. In this context, NaCMC polymer molecules are assumed to behave as extended rod particles with length (L) and diameter (d), including effective electrostatic repulsive distances, due to the dissociation of Na+ in aqueous systems. Thus, the number density of polymer molecules is given to be ν = c/Mw, and viscoelastic parameters such as ηsp, τw, and Je-1 are calculated using the theoretical model for rod particle suspensions proposed by Doi and Edwards. This concept reasonably described not only the viscoelastic data obtained in this study but also those from other groups using NaCMC samples with different DS and Mw values.

Effects of confinement-induced non-Newtonian lubrication forces on the rheology of a dense suspension

In this work, we propose a functionalised bi-viscous lubrication model to study the material properties of concentrated non-Brownian suspensions and explore the possible confinement-induced non-Newtonian effects of the lubricant in the rheological response of this type of suspensions. From tribological studies, it is well-known that even macroscopically Newtonian liquids under strong confinement might exhibit properties which deviate significantly from their bulk behaviour. When two surfaces separated by an extremely small gap (still large compared to the molecular size) are sheared, strong shear-thinning of the lubricant viscosity at low shear-rates is observed, in spite of its Newtonian-like bulk response. This is connected to a significant increase of the zero-shear-rate viscosity under extreme confinement. We start from an effective lubrication algorithm recently proposed and develop a new gap-size-dependent interparticle bi-viscous lubrication model, able to capture qualitatively the main phenomenology of confined lubricants. We solve the lubrication interaction between particles iteratively via a semi-implicit splitting scheme. Since the handling of lubrication is made implicitly here, the method copes efficiently with large increases of the inter-particle effective viscosities, which would otherwise lead to simulation blow-up or the use of vanishing time-steps in standard explicit schemes. We analyse the rheological response of the suspension systematically in terms of model parameters. In contrast to pure Newtonian lubrication interactions, distinct shear-thinning and shear-thickening regimes in the relative suspension viscosity are observed, which are discussed in terms of particle microstructure coupled with the complex rheology of the confined lubricant. In addition, normal-stress response is negative in both N1 and N2, which is difficult to achieve with standard contact frictional models.

Modeling the impact of the temperature profile on the sedimentation process for shear thinning suspensions in the annulus of oil well

The particle settling phenomena were broadly studied in the literature experimentally and numerically. To the best of our knowledge, previous works do not consider the temperature effect on the suspension rheology and, consequently, the influence over the settling velocity. Motivated by the problem of the sedimentation in confined drilling fluids exposed to a geothermal temperature gradient, this work proposed a continuum model for the sedimentation process of weighting agents in non-Newtonian suspensions based on the Mixture Theory. A temperature-dependent correction for the suspension consistency index was proposed and the results were discussed for different temperature profile cases, including uniform temperature profile, linear and geothermal profiles. Numerical simulations were performed, using the Finite Volume technique. Results for the solids concentration along the column for up to five years were discussed as well as the solids concentration evolution for selected points along the column. The results showed that the temperature gradient significantly impacts the settling velocity and the evolution of sedimentation regions. The main affected zones were the free settling and the sediment zones, which can alter directly parameters of interest for applications in oil wells, such as the height of sediment.

Shear flow of non-Brownian rod-sphere mixtures near jamming.

We use the discrete element method, taking particle contact and hydrodynamic lubrication into account, to unveil the shear rheology of suspensions of frictionless non-Brownian rods in the dense packing fraction regime. We find that, analogously to the random close packing volume fraction, the shear-driven jamming point of this system varies in a nonmonotonic fashion as a function of the rod aspect ratio. The latter strongly influences how the addition of rodlike particles affects the rheological response of a suspension of frictionless non-Brownian spheres to an external shear flow. At fixed values of the total (rods plus spheres) packing fraction, the viscosity of the suspension is reduced by the addition of "short"(≤2) rods but is instead increased by the addition of "long"(≥2) rods. A mechanistic interpretation is provided in terms of packing and excluded-volume arguments.

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.

English translation of Giesekus's famous article on flows with constant velocity gradient and the motion of particles suspended therein. Part I. Spatial flows

Within the framework of a statistical rheology of suspensions, emulsions, and solutions, it is important to obtain an overview of the total set of flows with a constant velocity gradient. Therefore, the solutions of the differential equations of such flows are given and discussed especially with respect to the influence of the deformation and rotation parts of the velocity gradient. Subsequently, the motion of rigid particles in these flows is analyzed. Both the flow types themselves and the types of motion of the suspended particles can be divided into two broad classes. Among those with predominant deformation influence, we have hyperbolic–parabolic flows as well as a setting of the particles in fixed directions. Among those with predominant rotational influence, we have elliptical–spiral flows as well as a non-uniform orbital motion of the particles. The change from one place of motion to the other depends not only on the shape of the flow but also on the shape of the particles. Deformation becomes stronger as the form anisotropy of the particles increase.

Rheology of dilute bubble suspensions in unsteady shear flows

The viscoelasticity of a dilute bubble suspension is theoretically derived from the constitutive equation originally for a dilute emulsion proposed by Frankel & Acrivos (J. Fluid Mech., vol. 44, issue 1, 1970, pp. 65–78). Non-dimensionalization of the original tensor equation indicates that the viscoelasticity is systematized for a given void fraction by the capillary number $Ca$ and dynamic capillary number $Cd$ , representing the bubble deformability and unsteadiness of bubble deformation. Comprehensive evaluation of the viscoelasticity according to the volume fraction, $Ca$ and $Cd$ reveals that whether the viscosity increases or decreases depends on whether $Ca$ or $Cd$ exceeds a common critical value. In addition, it is indicated that the bubble suspension has the most prominent viscoelasticity when the time scale of the shear deformation is the same as the relaxation time of the suspended bubble and when the bubbles keep a spherical shape, that is, $Ca \ll 1$ and $Cd = 1$ . The applicability of this theory in flow prediction was examined in a Taylor–Couette system, and experimentally good agreement was confirmed.

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.

Maximal submergence in dense granular suspensions

How far can a person sink downwards in quicksand? Experience would seem to suggest that there is low risk of submerging completely, but it is not easy to demonstrate this because of the complex rheology of granular suspensions. We study several mathematical models for the sinking of a vertical cylinder downwards into quicksand, finding that an approach with a buoyancy equation modified by drag force gives an unphysical answer. We instead argue that our proposed conclusion is supported by considering the dynamics of vibration-induced compactification of liquid-saturated granular suspensions. We compare quicksand with other non-Newtonian fluids, emphasising that in this case the same model does not apply and that the risk of drowning could be much more significant. We finish by suggesting some relevant experiments that can be performed in a classroom setting.

Viscosimetric squeeze flow of suspensions.

The rheology of particle suspensions has been extensively explored in the case of a simple shear flow, but less in other flow configurations which are also important in practice. Here we investigate the behavior of a suspension in a squeeze flow, which we revisit using local pressure measurements to deduce the effective viscosity. The flow is generated by approaching a moving disk to a fixed wall at constant velocity in the low Reynolds number limit. We measure the evolution of the pressure field at the wall and deduce the effective viscosity from the radial pressure drop. After validation of our device using a Newtonian fluid, we measure the effective viscosity of a suspension for different squeezing speeds and volume fractions of particles. We find results in agreement with the Maron-Pierce law, an empirical expression for the viscosity of suspensions that was established for simple shear flows. We prove that this method to determine viscosity remains valid in the limit of large gap width. This makes it possible to study the rheology of suspensions within this limit and therefore suspensions composed of large particles, in contrast to Couette flow cells which require small gaps.

Polymer-Assisted 3D Printing of Inductor Cores.

Poly(glycerol monomethacrylate) (PGMA) prepared by reversible addition-fragmentation chain transfer polymerization was investigated as an additive for high-loading iron oxide nanoparticle (IOP) 3D printable inks. The effect of adjusting the molar mass and loading of PGMA on the rheology of IOP suspensions was investigated, and an optimized ink formulation containing 70% w/w IOPs and 0.25% w/w PGMA98 at pH 10 was developed. This ink was successfully 3D printed onto various substrates and into several structures, including rectangles, high aspect ratio cylinders, letters, spiral- and comb-shaped structures, and thin- and thick-walled toroids. The effect of sintering on the mechanical properties of printed artifacts was investigated via four-point flexural and compressive testing, with higher sintering temperatures resulting in improved mechanical properties due to changes in the particle size and microstructure. The printed toroids were fabricated into inductors, and their electrical performance was assessed via impedance spectroscopy at a working frequency range of 0.001-13 MHz. There was a clear trade-off between electrical properties and sintering temperature due to a phase change between γ-Fe2O3 and α-Fe2O3 upon heating. Nevertheless, the optimized devices had a Q factor of ∼40 at 10 MHz, representing a superior performance compared to that of other inductors with iron oxide cores previously reported. Thus, this report represents a significant step toward the development of low-cost, fully aqueous, high loading, and 3D printable ceramic inks for high-performance inductors and functional devices.

Unifying length-scale-based rheology of dense suspensions

Unifying length-scale-based rheology of dense suspensions

On the rheology of thixotropic and rheopexic suspensions: accounting of the trimers formation

Semi-empirical equations are derived that describe the dependence of shear stress on shear rate during the flow of a one-component suspension. The suspension is considered as consisting of three fractions: single grains of the solid phase, their dimers and trimers, between which reversible dimerization and trimerization reactions occur. In this case, dimerization and trimerization are considered as reactions with invariable rate constants, and dissociation of dimers and trimers as reverse reactions with rate constants that increase linearly with shear rate. The derived equations are based on the Krieger-Doherty formula generalized to the case of a multicomponent suspension. The equations describe well pseudoplasticity, dilatancy, thixotropy and rheopexy, as well as suspensions with variable behaviour (when pseudoplastic behaviour is replaced by dilatant behaviour, and thixotropic behaviour is replaced by rheopexic one and vice versa).

Unraveling the Rheology of Nanocellulose Aqueous Suspensions: A Comprehensive Study on Biomass-Derived Nanofibrillated Cellulose

Unraveling the Rheology of Nanocellulose Aqueous Suspensions: A Comprehensive Study on Biomass-Derived Nanofibrillated Cellulose

Granular aqueous suspensions with controlled interparticular friction and adhesion.

We present a simple route to obtain large quantities of suspensions of non-Brownian particles with stimuli-responsive surface properties to study the relation between their flow and interparticle interactions. We perform an alkaline hydrolysis reaction on poly(methyl methacrylate) (PMMA) particles to obtain poly(sodium methacrylate) (PMAA-Na) particles. We characterize the quasi-static macroscopic frictional response of their aqueous suspensions using a rotating drum. The suspensions are frictionless when the particles are dispersed in pure water. We relate this state to the presence of electrosteric repulsion between the charged surfaces of the ionized PMAA-Na particles in water. Then we add monovalent and multivalent ions (Na+, Ca2+, La3+) and we observe that the suspensions become frictional whatever the valency. For divalent and trivalent ions, the quasi-static avalanche angle θc at large ionic strength is greater than that of frictional PMMA particles in water, suggesting the presence of adhesion. Finally, a decrease in the pH of the suspending solution leads to a transition between a frictionless plateau and a frictional one. We perform atomic force microscopy (AFM) to relate our macroscopic observations to the surface features of the particles. In particular, we show that the increase in friction in the presence of multivalent ions or under acidic conditions is driven by a nanoscopic phase separation and the bundling of polyelectrolyte chains at the surface of the particle. Our results highlight the importance of surface interactions in the rheology of granular suspensions. Our particles provide a simple, yet flexible platform to study frictional suspension flows.

Rheology of bi-disperse dense fiber suspensions.

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

Rheology of amino-functionalized graphene oxide suspensions in hydrogels

This work investigates the effects of amino-functionalized graphene oxide (AFGO) suspensions on the rheological behavior of Carbopol® hydrogels at pHs 5, 7, and 9. The AFGO concentration and media pH were evaluated and related to the suspension's microstructure and rheology. Graphene oxide (GO) nanosheets were synthesized using the modified Hummers method and functionalized with triethylenetetramine via microwave-assisted reaction to produce AFGO. The nanosheets were characterized by different techniques, such as scanning electron microscopy (SEM), thermogravimetric analysis, Raman spectroscopy, and x-ray photoelectron spectroscopy. The suspensions were characterized by rheological tests through steady-state and dynamic flow, zeta potential, and cryo-SEM for microstructure analysis. All samples presented a viscoplastic behavior and were modeled by the Herschel–Bulkley equation. Concerning the base hydrogels, the sample prepared at pH 9 showed lower viscosity, yield stress, and elastic modulus. At all pHs, the increase in the nanosheet concentration promotes a drop in the yield stress, viscosity, storage, and loss moduli. The cryomicrographs showed the impact of pH on the base hydrogel structure. It was also possible to observe that increasing nanoadditive concentration affects the Carbopol microgel swelling and weakens the suspension microstructure.

Pinching dynamics and extensional rheology of dense colloidal suspensions with depletion attractions

We study the extensional flow properties by characterizing the capillarity-driven pinching dynamics of dense colloidal suspensions at a constant volume fraction ϕ=0.40 with polymer-induced depletion interactions using a dripping-onto-substrate (DoS) protocol. Methacrylate copolymer particles with dimethylacrylamide copolymer brushes are suspended in a refractive-index- and density-matched mixture of 80 (w/w)% glycerol in water with NaCl added to screen the electrostatic repulsions. Depletion attractions between the colloids are introduced by adding polyacrylamide polymers of weight and dispersity. The addition of polymer delays and modifies the pinch-off dynamics of the dense suspensions, depending on the size and dispersity of the polymer. The extensional relaxation time λE of suspensions collapses as a function of the normalized free volume polymer concentration c/c∗ with the corresponding polymer solutions, indicating that the elastic properties of the polymer solutions control the extensional time scale. Following the results of our previous study [Soetrisno et al., Macromolecules 56, 4919–4928 (2023)], the polymer size determines the scaling exponent of λE for colloid-polymer mixtures in the dilute regime and high dispersity shifts the concentration where the scaling of λE transitions from power-law to linear. The filament lifespans tf of colloid-polymer mixtures and of polymer solutions collapse onto a master curve as a function of c/c∗ when normalized by the filament lifespan of the corresponding fluid without polymer tf,0. These results provide insight into the role of the polymer size in dictating the pinching dynamics and extensional rheology of colloid-polymer mixtures and further suggest that the shear and extensional responses of these mixtures can be separately tuned through the concentrations of the two constituents.

Characterization of the Starch Extracted from an Ancestral Andean Meal: Chuño

AbstractThe ancestral method of preparing chuño (freeze‐dried potato) involves three steps: freezing, soaking, and drying. The objective of this study is to identify the changes in microstructure, in physicochemical properties, and rheology of gels and suspensions of Andean potato starches caused by the procedure used to obtain chuño. A laboratory simulation of the procedure is performed using the potato variety “Rosadita” (Solanum tuberosum ssp. Andigenum). From the tests carried out on the starches extracted from the chuño obtained in the field and in the laboratory, differences phosphate content and gelatinization temperature are found. Marked differences are observed with respect to the control starch in the soluble amylose content, RVA profiles, textural attributes, and dynamic and viscous rheological properties. The chuño starches present greater resistance to granular breakdown. These observations suggest a different hydration, swelling, and gelation mechanism for the Rosadita and chuño starch samples compared to conventional potato starch and at the same time a modification due to the effect of freezing, which is more noticeable in the chuño obtained at −5 °C.

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.