Viscous behavior of concentrated emulsions of two immiscible Newtonian fluids with interfacial tension

A new equation for the relative viscosity of infinitely dilute emulsions of noncolloidal droplets is proposed using the analogy between shear modulus and shear viscosity. In the limit of capillary number -->0, the proposed equation reduces to the well-known Taylor viscosity law for infinitely dilute emulsions. Starting from the proposed equation for an infinitely dilute emulsion, new viscosity equations for concentrated emulsions are then developed using a differential scheme. The proposed equations for concentrated emulsions are evaluated in light of a large body of published experimental data on the viscosity of emulsions.     

Study of Shear Properties of Nanoparticle Suspensions

Low-frequency complex shear modulus of the colloidal suspensions of nanoparticles Nd:YAG in ethylene glycol was measured for the first time by using acoustic a resonance method with piezoquartz vibrator. Dependence of viscoelastic properties of the colloidal suspensions on nanoparticles sizes and their concentrations has been carried out.     

Effects of the degree of surface modification on the rheological responses of precipitated silica suspensions in benzyl alcohol

Two types of precipitated silica powders modified by poly (dimethylsiloxane) (PDMS) were suspended in benzyl alcohol and their rheological properties were investigated as a function of silica volume fraction, φ. The suspensions were classified into sol, pre-gel, and gel states based on the increase in φ. An increase in the degree of surface modification by PDMS caused gelation at higher φ. Plots of apparent shear viscosity against shear rate in the sol and pre-gel states of highly modified silica suspensions showed weak shear thickening behavior, while the same plots for silica suspensions with a low modification level exhibited shear thinning behavior. The dynamic moduli of hydrophobic suspensions in the pre-gel and gel states were dependent on the surface modification: the storage modulus G′ was larger than the loss modulus G″ in the linear region and these moduli increased with increasing φ, irrespective of the silica powder. The linear region of the φ range for the precipitated silica suspensions was wider than that for the fumed silica powders modified by PDMS suspended in benzyl alcohol, while the G′ value in the linear region for the precipitated silica suspensions was less than those for the fumed silica suspensions.     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.     

Rheology and UV protection properties of suspensions of fine titanium dioxides in a silicone oil

Ultrafine particles of titanium dioxide (TiO2) are very attractive as a UV protection ingredient in cosmetic products. The UV-scattering behavior of TiO2 suspensions in a silicone oil are studied in relation to rheological properties. To control the dispersion stability of suspensions, two types of polyether-modified silicones are used as dispersants. When the suspensions are prepared with branch-type dispersants in which the polyether groups are incorporated as side chains along the backbone, the flow is shear-thinning even at low shear rates. The appearance of plateaus in the frequency-dependence curves of storage modulus implies the solidlike responses. On the other hand, the suspensions prepared with linear conformation dispersants, in which the silicone group and polyether group are alternately repeated in one long chain, are Newtonian at low shear rates. The suspensions are regarded as liquids, because the storage modulus decreases rapidly in the low-frequency region. The suspension rheology is strongly associated with flocculated structures that are primarily controlled by the interparticle attractions. The differences in rheological behavior can be explained by the differences in the adsorbed conformation of dispersant silicones. From optical measurements, it is confirmed that UV scattering increases with decreasing flocculation degree. Therefore, good agreement is established between rheological properties and UV protection ability.     

Rheology of concentrated carbon nanotube suspensions

The rheological properties of non-Brownian carbon nanotube suspensions are measured over a range of nanotube volume fractions spanning the transition from semidilute to concentrated. The polymer-stabilized nanotubes are "sticky" and form a quiescent elastic network with a well-defined shear modulus and yield stress that both depend strongly on nanotube volume fraction with different but related critical exponents. We compare controlled-strain-rate and controlled-stress measurements of yielding in shear flow, and we study the effect of slow periodic stress reversal on yielding and the arrest of flow. Our measurements support a universal scaling of both the linear viscoelastic and steady-shear viscometric response. The former allows us to extract the elastic shear modulus of semidilute nanotube networks for values that are near or below the resolution limit of the rheometers used, while the latter provides a similar extrapolation of the yield stress. A simple scaling argument is used to model the dependence of yield stress and elastic modulus on concentration.     

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.     

Investigation of shear thinning behavior and microstructures of MWCNT/epoxy and CNF/epoxy suspensions under steady shear conditions

This report investigates the steady-state viscosities of multiwall carbon nanotube (MWCNT)/epoxy and carbon nanofiber (CNF)/epoxy suspensions with varying filler concentrations under different shear rates at various temperatures. In situ observation of filler networks suggests the build-up of shear induced MWCNT and CNF agglomerates at low shear rates, which correlates with the measured shear thinning behavior. The agglomeration process in MWCNT/epoxy suspensions is enhanced at lower shear rates in the case of higher temperatures, whereas, at high shear rates, both nano-fillers show good dispersion. Shear thinning behavior is observed for both types of fillers, and shear thinning exponential parameters are evaluated as a function of filler content. The shear thinning exponent increases in conjunction with increase in filler content, but it is found to saturate at a specific value, independently of filler material. Finally, the micromechanical elasticity-based analogy model is applied to the prediction of steady state shear viscosity of suspensions at higher shear rates with the assumption of complete dispersion and alignment of individual nano-fillers in suspensions. The predicted viscosities and the experimental data at higher shear rates are compared. The results conclude that fairly good agreement can be seen for the cases of CNF/epoxy suspensions at lower temperatures, whereas MWCNT/epoxy suspensions and CNF/epoxy suspensions at higher temperatures show discrepancy between the prediction and the experimental data.     

Equilibrium properties of reversibly flocculated dispersions

The structure of sonic flocculated dispersions can be changed reversibly by means of shearing. Often the changes are not instantaneous. The resulting shear-history effect gives rise to a complex but interesting rheological behaviour. Using non-aqueous suspensions of fumed silica, the rheological equilibrium properties of such systems are investigated. To change the floc structure, the water content of the particles is altered. As well as the steady-state shear viscosity, the equilibrium modulus and the yield stress are measured. Various techniques are compared. The effect of concentration on the equilibrium properties is used to test some structural models. The concentration dependence is best described by a power-law relation, the power being identical for modulus and yield stress. These results compare well with some theoretical predictions. Contrary to the assumptions used in the modelling, the yield stress is often dominated by kinetic phenomena. This shortcoming also shows up in the predictions for the critical strain.     

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.     

Structural network theory for a filled polymer melt in large amplitude oscillatory shear

The large amplitude oscillatory shear (LAOS) behavior of a high density polyethylene (HDPE) pipe resin containing 2% carbon black has been measured with a sliding plate rheometer incorporating a shear stress transducer. We have evaluated a structural network theory recently proposed by De Kee and Chan Man Fong for suspensions, in LAOS. This model provides for the creation of junctions due to an imposed flow field, and has been proposed as a generalization of the Liu kinetic rate equation, to model the complex behavior of suspensions. A new model, also based on the transient network concept, is proposed for filled polymer melts, and has the desirable feature of separating the effects of the filler material from the entanglement kinetics of the pure polymer. Both models are able to fit the steady shear viscosity data measured for this material. We find that both models are capable of predicting the LAOS behavior of this material, except for severe conditions.     

Synthesis and characterization of cubic cobalt oxide nanocomposite fluids

Narrow size distribution cubic Co₃O₄ nanoparticles were synthesized and rheological properties of suspensions of the cubes in oligomeric polyethylene glycol (PEG) were explored over a range of particle volume fractions and rotational shear flow conditions. At low and high particle volume fractions, the relative viscosity of the suspensions is described by a Krieger–Dougherty formula with an intrinsic viscosity consistent with expectations for suspensions of ideal cuboids. At intermediate to high particle loadings, the suspensions manifest complex rheological behavior, including shear thinning and shear-thickening features. These observations are discussed in terms of the charge carried by the cubes and the shear rate/volume fraction dependency of the transition from shear thinning to shear thickening.     

Stress jumps on weakly flocculated dispersions: steady state and transient results

Weakly flocculated, thixotropic suspensions have been investigated by means of fast stress jump experiments. With a suitable procedure, reliable stress relaxation data could be collected starting 20 ms after cessation of flow. This technique has been used to determine the elastic and hydrodynamic contributions to the shear stress. Steady state as well as transient flows have been studied for suspensions containing either fumed silica or carbon black particles in a Newtonian medium. In both systems, the elastic stress totally dominates the response at low shear rates and consequently also the apparent yield stress. This stress contribution becomes negligibly small at high shear rates. The hydrodynamic contribution to the viscosity has finite limits at both the low and high shear rate ends. The data are relevant for testing rheological models. As an illustration, it is shown that the data agree qualitatively with the model proposed by Potanin et al. (J. Chem. Phys. 102 (14) (1995) 5845-5853).     

Effects of bending and torsion rigidity on deformation and breakage of flexible fibers: a direct simulation study

To understand the various mechanisms of fiber deformation of flexible fiber suspensions, we carry out a direct simulation study to analyze the effect of fiber rigidity on fiber motion in simple shear flow. Such a study may be used to investigate the critical parameters controlling the breakage of flexible fibers during processing. We model the fiber as a series of rigid spheres connected by stiff springs. The stretching, bending, and torsional rigidities are determined by Young's modulus and shear modulus to realistically model the fiber rigidity. The model correctly predicts the orbit period of fiber rotation, T ?γ, as well as the trend of critical flow strength, η ?γ/E, versus fiber aspect ratio, r(p), at which breakage occurs in simple shear flow.     

Size effect on the rheological behavior of nanoparticle suspensions in associating polymer solutions

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups and tend to create bonds between chains by reversible associating interactions. The effects of associating polymer on the steady-shear viscosity and dynamic viscoelasticity are studied for suspensions of silica nanoparticles with diameters of 8, 18, and 25 nm. The silica particles of 8 nm are entrapped in the transient network of associating polymer by reversible adsorption. The enhancement of network results in the high viscosity with a Newtonian flow profile in the limit of zero shear rate. In suspensions of 25 nm silica, the hydrophobes extending from the chains adsorbed onto different particles can form a micelle by association interactions. The multichain bridging gave rise to the shear-thinning flow and high storage modulus at low frequencies. The suspensions of 25 nm silica are characterized as flocculated systems. Because of intermediate curvature, the flexible bridges are formed between silica particles of 18 nm. When the flexible bridges are highly extended within the lifetime in shear fields, the suspensions show shear-thickening flow. The shear-thickening flow can be attributed to the elastic effect of flexible bridges.     

Shear field modification of strongly flocculated suspensions — Aggregate morphology

Rheological and microscopical studies have been made to elucidate the effects of shear fields on the morphology of concentrated, aggregated model colloids. The models employed are well-characterised, predominantly chargestabilised polymer latices, coagulated by the addition of excess electrolyte. Continuous shear rheological and viscoelastic measurements indicate a very significant decrease in shear yield stress, apparent viscosity and shear modulus following prolonged shearing.Electron microscopy reveals the source of these changes. Freshly coagulated suspensions form networks that are porous, strong and qualitatively similar to simulated structures for diffusion limited aggregation. Following protracted shearing, the network structure is rearranged to yield discrete, tightly packed aggregates with a characteristic size, which is principally a function of the primary particle size.     

Viscoelasticity of Shear Thickening Fluid Based on Silica Nanoparticles Dispersing in 1-butyl-3-methylimidizolium Tetrafluoroborate

The viscoelasticity of shear thickening fluid (STF), a crucial property in the protective composite applications, with different silica nanoparticle concentrations in ionic liquid, 1-butyl-3-methylimidizolium tetrafluoroborate ([C₄min]BF₄), was studied at different temperatures and with shear frequencies through oscillatory shear, respectively. All STFs present strain thickening behavior. With increasing silica nanoparticle concentration, the critical shear strain for the onset of strain thickening decreased, while the complex viscosity, storage modulus, and loss modulus increased significantly. The critical shear strain increased with an increase of temperature, while the complex viscosity, storage modulus, and loss modulus decreased notably. The critical shear strain was constant with increasing the frequency of strain, while the complex viscosity decreases slightly. The storage modulus and loss modulus were independent with frequency in the strain thickening region. Nanoparticle clusters leading to strain thickening were demonstrated. The viscoelastic response of STFs to varying silica nanoparticle content, temperature, and frequency investigated here will help to design the specific application of STFs in soft protective composites and damping devices.     

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology

We apply the quiescent and mechanically driven versions of nonlinear Langevin equation theory to study how particle softness influences the shear modulus, the connection between shear elasticity and activated relaxation, and nonlinear rheology of the repulsive Hertzian contact model of dense soft sphere fluids. Below the soft jamming threshold, the shear modulus follows a power law dependence on volume fraction over a narrow interval with an apparent exponent that grows with particle stiffness. To a first approximation, the elastic modulus and transient localization length are controlled by a single coupling constant determined by local fluid structure. In contrast to the behavior of hard spheres, an approximately linear relation between the shear modulus and activation barrier is predicted. This connection has recently been observed for microgel suspensions and provides a microscopic realization of the elastic shoving model. Yielding, shear and stress thinning of the alpha relaxation time and viscosity, and flow curves are also studied. Yield strains are relatively weakly dependent on volume fraction and particle stiffness. Shear thinning commences at values of the effective Peclet number far less than unity, a signature of stress-assisted activated relaxation when barriers are high. Apparent power law reduction of the viscosity with shear rate is predicted with a thinning exponent less than unity. In the vicinity of the soft jamming threshold, a power law flow curve occurs over an intermediate reduced shear rate range with an apparent exponent that decreases as fluid volume fraction and/or repulsion strength increase.     

Linear Viscoelastic Behavior of Multiphase Dispersions

The linear viscoelastic behavior of polymer-thickened oil-in-water emulsions, polymer-thickened solids-in-liquid suspensions, and their blends is investigated using a controlled-stress rheometer. The emulsions exhibit a predominantly viscous behaviour at low values of oil concentration in that the loss modulus (G") exceeds the storage modulus (G') over most of the frequency range. At high values of oil concentration, the emulsions exhibit a predominantly elastic behavior. The ratio of storage modulus to loss modulus (G'/G") increases with the increase in oil concentration. Emulsions follow the theoretical model of J. F. Palierne (1990, Rheol. Acta 29, 204) only at low values of oil volume fraction (/=G' over most of the frequency range. The ratio G'/G" varies only slightly with the increase in solids volume fraction. The Palierne model describes the linear viscoelastic properties of suspensions accurately only at low values of solids volume fraction. At high values of solids concentration, the Parlierne model underpredicts the linear viscoelastic properties of suspensions and the deviation increases with the increase in solids concentration. The blends of emulsions and suspensions exhibit strong synergistic effects at low to moderate values of frequencies; the plots of blend modulus versus emulsion content exhibit a minimum. However, at high values of frequency, the blend modulus generally falls between the moduli of pure suspension and pure emulsion. The high-frequency modulus data of blends of emulsions and suspensions are successfully correlated in terms of the modulus ratio versus volume fraction of solids, where modulus ratio is defined as the ratio of blend modulus to pure emulsion modulus at the same frequency. Copyright 2000 Academic Press.