Rheology Of Colloidal Suspensions Research Articles

Microstructure and rheology of shear thickening colloidal suspensions under transient flows

Novel measurements of the spatiotemporal microstructure of a continuous shear thickening colloidal suspension under shear cessation and reversal using small angle neutron scattering in a 1–2 shear cell are presented for moderate to high Péclet numbers. In the shear cessation experiments from high Péclet shear flow, two-step relaxation mechanism is found. Particles first readily diffuse on a characteristic timescale of single particle Brownian motion, followed by slower relaxation dynamics on a timescale of short-time self-diffusion when caging effects start dominating. In the shear reversal experiment, the unchanged scattering intensity and the quick flip in anisotropic structure around the shear thickened state suggest the persistence of hydroclusters without transitioning through the equilibrium structure, at least in a time resolution of 0.01 s. Access to the time evolution of microstructure provides valuable insights into the spatiotemporal details of interparticle interactions governing colloidal suspension rheology, such as Brownian, hydrodynamic, and nanotribological forces.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations.

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Viscoelastic and thixotropic characterization of paraffin/photopolymer composites for extrusion-based printing

Three-dimensional printing (3DP) of functional materials is increasingly important for advanced applications requiring objects with complex or custom geometries or prints with gradients or zones with different properties. A common 3DP technique is direct ink writing (DIW), in which printable inks are comprised of a fluid matrix filled with solid particles, the latter of which can serve a dual purpose of rheology modifiers to enable extrusion and functional fillers for performance-related properties. Although the relationship between filler loading and viscosity has been described for many polymeric systems, a thorough description of the rheological properties of three-dimensional (3D) printable composites is needed to expedite the creation of new materials. In this manuscript, the relationship between filler loading and printability is studied using model paraffin/photopolymer composite inks containing between 0 and 73 vol. % paraffin microbeads. The liquid photopolymer resin is a Newtonian fluid, and incorporating paraffin microbeads increases the ink viscosity and imparts shear-thinning behavior, viscoelasticity, and thixotropy, as established by parallel plate rheometry experiments. Using Einstein and Batchelor's work on colloidal suspension rheology, models were developed to describe the thixotropic behavior of inks, having good agreement with experimental results. Each of these properties contributes to the printability of highly filled (≥43 vol. % paraffin) paraffin/photopolymer composite inks. Through this work, the ability to quantify the ideal rheological properties of a DIW ink and to selectively control and predict its rheological performance will facilitate the development of 3D printed materials with tunable functionalities, thus, advancing 3DP technology beyond current capabilities.

Microrheology of colloidal suspensions via dynamic Monte Carlo simulations

Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products, such as paints, foods and inks. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by the impact of microrheology in providing information on local structure in complex systems such as colloidal glasses, active matter or biological systems, we have extended the dynamic Monte Carlo (DMC) technique to investigate active microrheology in colloidal suspensions. The original DMC theoretical framework, able to accurately describe the Brownian dynamics of colloids at equilibrium, is here reconsidered and expanded to describe the effects of an external force pulling a tracer embedded in isotropic colloidal suspensions at different densities. To this end, we studied the dynamics of a spherical tracer dragged by a constant external force through a bath of spherical and rod-like particles of comparable size. We could extract valuable details on its effective friction coefficient, being constant at small and large values of the external force, but otherwise displaying a nonlinear behaviour that indicates the occurrence of a force-thinning regime. Our DMC simulation results are in excellent quantitative agreement with past Langevin dynamics simulations and theoretical works for the bath of spherical colloids. The bath of rod-like particles is studied in the isotropic phase, and displays an example where DMC is more convenient than Brownian or Langevin dynamics, in this case, in dealing with particle rotation.

Superposed shear and compression of strong colloidal gels

Although the rheology of strong colloidal gels is predominantly concerned with either pure shear or pure compressive deformation, the vast majority of practical applications involves an arbitrary combination of shear and compressive stresses and strains. This situation demands a tensorial rheology of colloidal suspensions, where the multidimensional response of these complex materials to arbitrary superposed stress states needs to be characterized and constitutive models developed. In this study, we use 2D discrete element modelling simulations in the absence of hydrodynamic interactions to probe the behavior of a model strong colloidal gel under combined shear and compressive deformation. We consider the deformation and failure of these gels under strain-controlled conditions that range from pure compression to shear-dominated consolidation. Particle-scale observations uncover how shear stresses act to stimulate nonaffine buckling and rupture of force chains during consolidation, leading to augmented failure and collapse of the particle network. At the macroscopic level, we find that the energy required to consolidate a colloidal suspension from the gel point to close packing passes through a minimum that corresponds to weak shear strain, indicating that small amounts of shear play a critical role in destabilizing the colloidal network. These results represent an important step toward a complete understanding of the tensorial rheology of strong colloidal gels.

Colloidal processing and characterization of TiO2–MnO‐doped alumina/alumina slurries and tapes

AbstractAqueous slurries of alumina doped with manganese and titanium oxides were developed. The powders and tapes were investigated by scanning electron (SEM) microscopy, X‐ray diffractometry (XRD), and thermal analyses (TG/DSC). The stability and rheology of colloidal suspensions of undoped and doped alumina suspensions were investigated. At neutral pH of 7, pure alumina and MnO–TiO2 dopant particles present positive and negative surface charges and are prone to heterocoagulation. Optimized colloidal processing through proper adjustment of parameters was achieved to reach particle stabilization. The surface charge of the oxide particles was negative, and the suspensions did not agglomerate at a pH of 7 and higher. Tapes were cast, dried, and burned out. The thermal analyses revealed the release of residual water and decomposition of short‐chain organics at temperatures under 215°C and of long‐chain additives over 300°C.

Microstructure and rheology of shear-thickening colloidal suspensions with varying interparticle friction: Comparison of experiment with theory and simulation models

Two colloidal suspensions of paucidisperse, spherical silica particles with different surface chemistries leading to extreme limits of surface contact friction are studied to identify experimental differences in shear rheology and microstructure and quantitatively test theory and simulation models. The nonequilibrium microstructure in the plane of shear is measured by flow-small angle neutron scattering for steady shear states spanning the shear thinning and shear thickening regimes. The shear rheology and microstructure are compared against predictions from theory for Brownian hard sphere suspensions and state-of-the-art simulation methods that incorporate either contact friction or enhanced lubrication hydrodynamics. The first normal stress differences are confirmed to distinguish between these micromechanical mechanisms for stress enhancement in the shear thickened regime. The nonequilibrium microstructure in the plane of shear shows more anisotropy for the suspension with higher interparticle friction. A significant fourfold symmetry is confirmed and found to be amplified with increasing surface contact friction in the shear thickened state. The differences in shear-induced microstructures between suspensions with varying contact friction demonstrate that the nonequilibrium microstructure can distinguish between nanotribological interactions in the shear thickened state. Statistical comparison of experiments with simulations indicates that better resolution of microstructures in simulation models is required to be validated by the experimental data presented. Implications for the development of theories for colloidal suspension rheology are discussed.

Computation and experiment in non- colloidal suspension rheology

This paper presents a current view of non-Brownian (non-colloidal) suspension rheology; experimental and computational works are compared where possible. The matrix fluids are either Newtonian or viscoelastic; the rigid particles are compact and close to spherical. Volume fractions of 0.5 and below are considered. It is important to move beyond steady simple shearing, so unsteady shearing and uniaxial extensional flows are discussed. Steady shearing is fairly well understood but the extensional flows are not prominent in the literature. In steady shearing with Newtonian matrices the role of friction and the estimation of the average friction coefficient, which reduces as the macroscopic shear stress (or shear rate) increases, is discussed. The ratio of the two normal stress differences to the shear stress is modelled well provided a reasonable value for the average friction coefficient is assumed. With viscoelastic matrices agreement between experiment and theory is less satisfactory. Unsteady and oscillatory flows are surveyed briefly; the prominent hysteresis in oscillatory flows appears to be a frictional effect. While progress has occurred it appears that satisfying agreement between computation and experiment is rare. More attention to rheological and frictional modelling is needed, and improved computational methods may need to be developed.

Contact Networks Enhance Shear Thickening in Attractive Colloid-Polymer Mixtures.

Increased shear thinning arising due to strong attractive interactions between colloidal particles is thought to obscure shear thickening. Here, we demonstrate how moderate attractions, induced by adding a nonadsorbing polymer, can instead enhance shear thickening. We measure the rheology of colloidal suspensions at a constant particle volume fraction of ϕ=0.40 with dilute to weakly semidilute concentrations of three polyacrylamide depletants of different molecular weights. Suspensions containing large polymer exhibit increased shear thickening and positive first normal stress differences at high shear stress, and increased heterogeneous fluctuations in the boundary stress. These results are consistent with a friction-based model for shear thickening, suggesting that the presence of large, extended polymers induces the formation of near-spanning networks of interparticle contacts.

Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory.

We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

Quartz crystal microbalance as a device to measure the yield stress of colloidal suspensions

The application of quartz crystal microbalance (QCM) as a device to measure the rheology of colloidal suspensions has been studied. Using a commercial dip-probe QCM, the yield stress of magnesium hydroxide suspensions has been correlated to the resonance properties of a 5 MHz AT-cut quartz sensor. A stable resonance baseline was first established in air before submerging the sensor into the colloidal suspension. The response of the sensor resistance was shown to correlate to changes in the suspension yield stress, while the frequency response was found to result from more complex contact mechanics and suspension viscoelasticity contributions. Since the QCM is a relatively simple technique with no mechanically moving parts, this approach offers the potential for rapid in situ rheology assessment.

Understanding the surface properties and rheology of a silica suspension mediated by a comb-type poly(acrylic acid)/poly(ethylene oxide) (PAA/PEO) copolymer: effect of salinity.

Understanding the surface properties and rheology of colloidal suspensions in the presence of polymer additives with high salinity are of great importance in formulating construction materials and optimizing process conditions in the mining and petroleum industry. In this work, the surface properties and rheology of a model spherical silica aqueous suspension mediated by a comb-type poly(acrylic acid)/poly(ethylene oxide) (PAA/PEO) copolymer at various salt concentrations have been investigated. Adsorption measurements using a Quartz Crystal Microbalance with Dissipation monitoring (QCM-D) align well with zeta potential tests and show that polymer adsorption on silica surfaces is enhanced at high salinity (i.e., 3 M NaCl) than at low salinity (i.e., 1 mM NaCl) due to the suppression of the electrical double layer. Surface Forces Apparatus (SFA) measurements reveal that for interactions between two mica surfaces (the basal plane of which has a similar structure as silica) at a high polymer concentration (e.g., 2 wt%), steric repulsion dominates in 1 mM NaCl while bridging attraction is observed in 3 M NaCl. Surface force measurements agree with rheological results on silica suspensions with 0.5 to 2 wt% of PAA/PEO addition, which shows a significant decrease in yield stress in 1 mM NaCl due to steric repulsion but an insignificant variation in yield stress in 3 M NaCl due to attractive bridging interactions. This work provides useful information regarding the surface properties and rheological properties of comb-type polymer-mediated silica suspensions under different salinity conditions, with implications on designing and processing complex colloidal suspensions with polymer additives for various applications.

Nonlinear rheology of colloidal suspensions probed by oscillatory shear

The nonlinear stress and microstructural response of a colloidal hard sphere suspension undergoing medium and large amplitude oscillatory simple shear have been studied using Accelerated Stokesian dynamics. The goal is to understand how nonlinearity arises and to link the structural effects to the resulting suspension stress. The imposed shear is given by the time-dependent rate γ̇(t)=γ̇0eiαt. Most results are shown for a hard-sphere suspension at a particle volume fraction ϕ=0.4. These are freely flowing conditions far from either glassy or jammed conditions, but the concept of the particle cage from glass dynamics is used. The cage is defined here in a statistical manner as the surface of elevated nearest neighbor probability, a sphere at contact for equilibrium. The cage concept is used in interpreting the microstructural deformation: For sufficiently small strain amplitude γ0, the cage deforms negligibly due to flow and the suspension remains in the linear response regime, but this is found to require γ0<0.01 at ϕ=0.4, as shown by a spectral decomposition of the microstructure in time, which discriminates rigorously between linear and nonlinear deformation. At larger γ0, termed medium amplitude and large amplitude in other studies, the material response is nonlinear. To preface the large amplitude oscillatory shear analysis, we use linear viscoelasticity theory to compare stress fluctuations at equilibrium to results obtained at finite Péclet number Pe and small γ0, as well as available experimental data and theoretical predictions; Pe=6πηγ̇0a3/kT is the ratio of hydrodynamic to Brownian forces, where η is the viscosity of the suspending liquid, γ̇0 is the shear rate amplitude, a is the particle radius, k is the Boltzmann constant, and T is the absolute temperature. The shear stress σxy and the normal stress differences N1 and N2 are analyzed under oscillatory shear at amplitudes 0.01≤γ0≤3.6 for a range of Pe. (The frequency α is related to Pe through γ̇0=αγ0 and the nondimensional frequency is given by the Deborah number De=Pe/γ0=6πηαa3/kT.) Pipkin diagrams are shown for σxy, N1 and N2. When hydrodynamic forces dominate the flow of the suspension, the complex viscosity |η*| has a nonmonotonic dependence on γ0, and Fourier-transform rheology shows the nonlinearity of the stress response to be maximized at an intermediate strain amplitude that depends on Pe. The elastic and viscous behavior of the suspension, as determined by a Chebyshev polynomial decomposition, is distinctly different for small and large Pe. The influence of the microstructure on the normal stress differences is discussed, noting that N1 is significant only when angular distortion of the microstructure is present, whereas N2 is formed with an accumulation of pair correlation at contact even at low oscillation amplitude.

Constant Stress and Pressure Rheology of Colloidal Suspensions.

We study the constant stress and pressure rheology of dense hard-sphere colloidal suspensions using Brownian dynamics simulation. Expressing the flow behavior in terms of the friction coefficient-the ratio of shear to normal stress-reveals a shear arrest point from the collapse of the rheological data in the non-Brownian limit. The flow curves agree quantitatively (when scaled) with the experiments of Boyer et al. [Phys. Rev. Lett. 107, 188301 (2011)]. Near suspension arrest, both the shear and the incremental normal viscosities display a universal power law divergence. This work shows the important role of jamming on the arrest of colloidal suspensions and illustrates the care needed when conducting and analyzing experiments and simulations near the flow-arrest transition.

Microstructure and rheology relationships for shear thickening colloidal dispersions

The non-Newtonian shear rheology of colloidal dispersions is the result of the competition and balance between hydrodynamic (dissipative) and thermodynamic (conservative) forces that lead to a non-equilibrium microstructure under flow. We present the first experimental measurements of the shear-induced microstructure of a concentrated near-hard-sphere colloidal dispersion through the shear thickening transition using small-angle neutron scattering (SANS) measurements made in three orthogonal planes during steady shear. New instrumentation coupled with theoretical derivations of the stress-SANS rule enable rigorous testing of the relationship between this non-equilibrium microstructure and the observed macroscopic shear rheology. The thermodynamic and hydrodynamic components of the stress that drive shear thinning, shear thickening and first normal stress differences are separately defined via stress-SANS rules and compared to the rheological behaviour of the dispersion during steady shear. Observations of shear-induced hydrocluster formation is in good agreement with Stokesian dynamics simulation results by Foss & Brady (J. Fluid Mech., vol. 407, 2000, pp. 167–200). This unique set of measurements of shear rheology and non-equilibrium microstructure of a model system provides new insights into suspension mechanics as well as a method to rigorously test constitutive equations for colloidal suspension rheology.

Simulating the Rheology of Suspensions Using Dissipative Particle Dynamics

A new mesoscopic simulation method, dissipative particle dynamics (DPD), is applied to model suspensions. DPD is a coarse-graining technology, in which several atoms are united into a single simulation particle so that simulation is realized in a larger length scale and time scale. Now this method has been widely used in simulating the rheology of colloidal suspensions, and mainly focused on the equilibrium dynamics and the steady-state shear rheological behaviors for a range of suspensions volume fractions. It is shown that the diffusion coefficient of dispersion decreased, but the viscosity of suspension increased at a given shear rate with the increase of volume fractions of suspension particles; the viscosity decreased with the increase of shear rate at the same volume fractions of suspensions.

Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations.

We discuss pressure-driven channel flow for a model of shear-thinning glass-forming fluids, employing a modified lattice-Boltzmann (LB) simulation scheme. The model is motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions and captures a nonvanishing dynamical yield stress and the appearance of normal-stress differences and a flow-induced pressure contribution. The standard LB algorithm is extended to deal with tensorial, nonlinear constitutive equations of this class. The new LB scheme is tested in 2D pressure-driven channel flow and reproduces the analytical steady-state solution. The transient dynamics after startup and removal of the pressure gradient reproduce a finite stopping time for the cessation flow of yield-stress fluids in agreement with previous analytical estimates.

Effect of repulsive interactions on structure and rheology of sheared colloidal dispersions

A previously developed Smoluchowski theory for concentrated hard-sphere suspensions in shear flow is extended to study structure and rheology of colloidal suspensions with soft repulsive interactions. Accelerated Stokesian Dynamics simulations are carried out to provide insight and to enable direct comparison with theoretical predictions. The effect of extended range repulsive interactions is studied by considering repulsive interactions with different steepness, using identical potentials in simulation and theory, for varying shear rates characterized in dimensionless form as 0.1 ≤ Pe ≤ 100; here, Pe = 6πηa3/kbT is the ratio of hydrodynamic to Brownian forces and η is the fluid viscosity, is the shear rate, a is the particle radius and kbT is the thermal energy. Examples of predicted microstructures and the equivalent simulated results for hard-sphere suspensions at ϕ = 0.40 are also presented for comparison. The predicted pair distribution function is in good agreement with simulations before the onset of a shear-induced ordering transition in simulations of the soft colloids. The calculations of shear viscosity based on the predicted microstructure were also in general agreement with simulation results. The role of hydrodynamic interactions on flow-induced structures is discussed in the context of the proposed theory.

Non-Newtonian Stress in an Electrolyte

Analogies are drawn between the dynamics of electrolyte solutions and those of dilute suspensions of charged colloidal particles. The viscosity of both electrolytes and suspensions is a function of the ionic concentration c and of the Peclet number Pe characterizing the ratio of applied shear rate that tends to deform the ionic charge clouds, to diffusion that allows them to relax back to equilibrium. In particular, previously published results on the rheology of colloidal suspensions ( Lever , D. A. J. Fluid Mech. 1979 , 92 , 421 - 433 ) imply not only that the Falkenhagen O(c(1/2)) electrical contribution to viscosity is shear thinning, as shown by H. Wada ( J. Stat. Mech.: Theory Exp. 2005 , P01001 ), but also that this contribution to the stress is elastic, with normal stress differences appearing at O(Pe(2)). In practice, the shear rates required for substantial departure from a Newtonian rheology are large, typically 10(9) s(-1).

Macroscopic dynamics of flocculated colloidal suspensions

The macroscopic dynamics of strongly flocculated colloidal suspensions are of both fundamental interest and practical significance across a range of applications from soil mechanics to solid–liquid separation. Over 30 years ago, Buscall and White [ Buscall, R., White, L.R., 1987. The consolidation of concentrated suspensions. Part 1. The theory of sedimentation, Journal of the Chemical Society: Faraday Transactions I 83 (3), 873–891] proposed a one-dimensional (1D) theory of sedimentation and consolidation of such suspensions, which spawned suspension characterization tools and process modeling techniques to successfully predict 1D separation behavior. However, many applications such as continuous thickening or cross-flow filtration are multidimensional in practice, involving suspension transport, deformation and separation, and so cannot be described by the 1D BW theory. Multidimensional suspension mechanics has received a little attention over the past 30 years, requiring development of a tensorial rheology of suspensions, capable of describing arbitrary loadings and simultaneous shear and compression. In this paper, we develop a multidimensional theory of the macroscopic mechanics of strongly flocculated colloidal suspensions to describe suspension transport, deformation and separation in terms of the bulk suspension velocity field and local average solids volume fraction alone. This is achieved by consistent extension of the fundamentals of BW theory to multiple dimensions, with constitutive models justified and expressed in terms of experimentally measurable material functions. Constitutive aspects which are outstanding due to lack of empirical evidence are clearly identified, pointing to potential research directions regarding the tensorial rheology of colloidal suspensions. Utility of the theory is demonstrated in an example comparison between 1D and 2D continuous gravity thickener operation.