Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

Solutions of xanthan gum/guar gum mixtures: shear rheology,porous media flow,and solids transport in annular flow

Mixtures of xanthan and guar gum in aqueous solution were studied in two flow situations: simple shear and porous media. In addition, solids transport in vertical annular flow of sand suspensions was explored. The zero shear rate viscosity of the solutions displayed a pronounced synergy: the viscosity of the mixture is higher than that of the polymer solutions in a wide range of relative concentrations of the two polymers, in agreement with previous literature. However, at relatively high shear rates, the viscosity approaches the value of the more viscous xanthan gum solutions at mass fractions of xanthan gum between 0.1 and 0.15, and the degree of synergy substantially decreases. Stress relaxation experiments in simple shear indicate that the polymer mixtures exhibit a well-defined yield stress after relaxation that is absent in solutions of pure polymers. In porous media flow experiments, a synergistic behavior mimicking the shear flow results was obtained for the polymer mixtures at low shear rates. However, at a critical shear rate, the apparent viscosity in porous media flows exceeds the shear viscosity due to the elongational nature of flow in the pores. The solids transport capacity in annular flows is well-represented by trends in shear viscosity and stress relaxation behavior. However, the lack of viscosity synergy at high shear rates limits the applicability of the mixtures as a way to improve solids suspension capacity in annular flows.     

Fibre suspension rheology: effect of concentration, aspect ratio and fibre size.

Viscosity data for fibre suspensions are produced using cone-and-plate geometry of enhanced dimensions for the reduced influence of fibre-wall interactions. Semi-concentrated suspensions of monodisperse polyamide fibres in silicone oil, with a variety of fibre concentrations (2, 5 and 8%), lengths and diameters, were studied. The suspension viscosity was measured in a range of shear stress in order to study the stress dependence. The study here focuses on the nature of the forces and interactions that contribute to the suspension viscosity. The results show that at sufficiently high stress levels, the suspension viscosity tends to reach a steady-state. At very low stress levels the suspension viscosity increases over time, most likely due to structures formed by adhesive forces. At higher concentrations, the viscosity depends on the absolute size of the fibres, again indicating the presence of non-hydrodynamic interactions.     

Rheological characterization of highly branched poly(ethyleneterephthalate)

Linear and highly branched poly(ethyleneterephthalate) samples were synthesized and characterized in terms of intrinsic viscosity, molecular weight and melt viscosity over a wide range of shear rates at several temperatures, in the range from 265° to 295 °C. Linear samples exhibited Newtonian behavior over a wide range of shear rates, while the branched ones became shear thinning at relatively low shear rates. Our experimental data, as well as data previously reported, were found to be described by a proposed correlation between the melt viscosity ratio and a branching index. Moreover, the activation energy for melt flow was found for the highly branched samples to be a little higher than that of the linear samples.     

Rheology of coal suspensions

Proper design of operations encountered in preparation, transport and employment of suspensions like coal slurries and coal-oil mixtures require an accurate knowledge of their rheological behaviour.Such concentrated suspensions generally exhibit non-Newtonian behaviour (shearthinning) which is more pronounced at higher coal concentrations. The nature of the dispersing medium influences the aggregation state of the disperse phase and, consequently, affects the stability and the rheology of the systems. In the present paper coal suspensions prepared with different dispersing media and covering a wide range in solid phase concentration are studied, by using a rotational coaxial cylinders viscometer.Different models have been taken into consideration for correlating experimental data. In particular, in order to describe the dependence of viscosity on shear rate and solid phase concentration, the suitability of the model suggested by Smith and Bruce is evaluated. Accordingly, the aggregation state of the disperse phase as well as its dependence on shear rate and dispersing medium can be estimated.     

An experimental study of food melt rheology

The shear viscosity of commercial maize grits, potato powder and a low density polyethylene has been measured under a range of extrusion processing conditions using an extruder-fed slit die viscometer and a capillary rheometer. The results show the strong dependence of the viscosity of food melts on the processing history undergone during extrusion. To this end, the shear viscosity data for the food materials have been fitted to relationships including the effects of temperature, shear rate and moisture. The effect of the shear processing history on the viscosity has been represented by a power-law relationship with extruder screw speed.     

New measurements of the flow-curves for Carbopol dispersions without slip artefacts

The thickening properties of many commercial thickeners are difficult to measure because of wall slip artefacts. Here we report a series of experiments on a typical thickener where these artefacts have been successfully eliminated. As a result, complete, steady-state flow-curves of aqueous Carbopol 980 (the toxicologically preferred version of the older and more well-known Carbopol 940) dispersions are reported for a range of concentrations of 0.045–1.0 wt%. The vane-and-basket flow geometry was used to avoid slip problems at low shear stress, with the geometry housed in a TA AR1000-N controlled-stress rheometer, whilst a Haake RV2 viscometer with an SV2P and MV2P concentric-cylinder geometries were used at higher shear rates. The flow-curves obtained show a smooth but steep transition from a very high Newtonian viscosity at low shear stress to a much lower viscosity at high shear stress. No real yield stresses were detected, but the higher shear rate results can be fitted to the Herschel-Bulkley model, which assumes an apparent yield stress. The various model parameters are displayed as a function of Carbopol concentration. Received: 29 November 2000/Accepted: 26 February 2001     

Shear flow rheological properties of vinylon- and glass-fiber reinforced polyethylene melts

Shear viscosity, shear stress and first normal-stress difference have been investigated for glass- and vinylon-fiber filled polyethylene melts over a wide range of shear rate by means of three kinds of instruments. The influence of fiber content and fiber properties on the rheological properties is discussed. The viscosity increases with increasing aspect ratio and fiber content, and the influence of these parameters on the flow properties is evident at low shear rates. The first normalstress difference increases more rapidly with increasing glass fiber content, especially at low shear stresses. The influence of vinylon fibers on the first normal stress-difference vs. shear-stress relationship is different from that of glass fibers.     

Influence of surfactant addition on the rheological properties of aqueous Welan matrices

In the present work the effects produced by the presence of two different surfactants (Abil B 8842 and Triton N 101) on the rheological properties of aqueous welan matrices are studied, both in steady and in oscillatory shear conditions. Welan is an acidic microbial polysaccharide having high thermal, pH, and salt stability. At sufficiently low concentrations it forms aqueous weak gel matrices which can be profitably used to regulate the rheological properties of disperse systems and improve their stability. Different systems are examined, having the same polysaccharide concentration (0.25 wt%) and different surfactant concentrations (up to 40 wt%, far beyond the range of practical interest for emulsion preparation). All the systems exhibit marked shear-thinning properties which can be described quite satisfactorily by the Cross equation. The concentration dependence of the zero-shear-rate viscosity as well as the mechanical spectra confirm that, in the concentration range considered, the aqueous welan systems are typically weakly structured fluids. The influence of both surfactants is examined in detail by comparing the behavior of the different classes of systems. Both surfactants reduce the polymer contribution at low shear, whereas an opposite action is exerted at high concentration and shear. These contrasting effects are ascribed to the different structural features of the polymer matrix under low stresses and high shear conditions, respectively. Received: 6 February 2000 Accepted: 1 November 2000     

Uniaxial elongational flow effects and morphology development in LDPE/phosphate glass hybrids

Shear and elongational viscosity measurements were performed on low-density polyethylene/phosphate glass (LDPE/Pglass) hybrid materials in the liquid state. Under shear deformation, the hybrids with low concentrations of Pglass showed a Newtonian region at low frequencies, followed by shear-thinning behavior at high frequencies. High Pglass concentrations displayed shear-thinning behavior over the whole range of frequencies studied. Deviations from the log-additivity rule for viscosity were found to be compositionally dependent and generally indicated an immiscible mixture. The elongational viscosity of the hybrids increased at very low Pglass concentrations (1–2 vol.% Pglass) and then was drastically reduced at higher concentrations (i.e., >10 vol.% Pglass). In addition, elongational flow was found to induce the formation of Pglass fibrils in hybrids containing at least 10 vol.% Pglass. This was correlated to the elongational capillary number; the critical elongational capillary number was estimated to be 0.22. The elongational deformation was also found to greatly increase the overall crystallinity of the system due to molecular orientation of the LDPE polymer chains as confirmed by wide angle X-ray diffraction. A critical composition of 5 vol.% Pglass was found to be the point at which LDPE hybrid rheological properties, molecular orientation, and morphology changed drastically.     

Droplet deformation of a strongly shear thinning dense suspension of polymeric micelles

We investigated the deformation of a strong shear thinning droplet undergoing simple shear flow in a Newtonian liquid. The droplet was an aqueous solution of poly(ethylene oxide) end capped with an alkyl group that forms spherical micelles in aqueous solution. At high concentrations and below a critical temperature, the jammed micelles showed strong shear thinning behaviour, and neither a yield stress nor a Newtonian viscosity was observed. At small shear rates, the droplet rotated and aligned in the flow, but did not deform or only very weakly. At high shear rates, the droplet deformation increased with increasing shear rate. The deformed droplet did not relax after the shear was stopped except for a modest rounding of the edges. For each shear rate, an apparent viscosity, η _ad, of the equivalent Newtonian droplet was calculated assuming affine deformation. η _ad showed a power law dependence on the capillary number Ca with an exponent of − 1.8 and was larger than the shear viscosity of the micelle suspension at the same shear rates. The results were explained by the existence of a strong gradient of the viscosity inside the droplet leading to a very low viscosity fluid layer near the droplet/matrix interface.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

The steady shear viscosity of filled polymeric liquids described by a linear superposition of two relaxation mechanisms

Filled polymeric liquids often exhibit apparent yielding and shear thinning in steady shear flow. Yielding results from non-hydrodynamic particle—particle interactions, while shear thinning results from the non-Newtonian behavior of the polymer melt. A simple equation, based on the linear superposition of two relaxation mechanisms, is proposed to describe the viscosity of filled polymer melts over a wide range of shear rates and filler volume fraction.The viscosity is written as the sum of two generalized Newtonian liquid models. The resulting equation can describe a wide range of shear-thinning viscosity curves, and a hierarchy of equations is obtained by simplifying the general case. Some of the parameters in the equation can be related to the properties of the unfilled liquid and the solid volume fraction. One adjustable parameter, a yield stress, is necessary to describe the viscosity at low rates where non-hydrodynamic particle—particle interaction dominate. At high shear rates, where particle—particle interactions are dominated by interparticle hydrodynamics, no adjustable parameters are necessary. A single equation describes both the high and low shear rate regimes. Predictions of the equation closely fit published viscosity data of filled polymer melts. n power-law index - n ₁,n ₂ power-law index of first (second) term - shear rate - steady shear viscosity - ₀ zero-shear rate viscosity - _{0, 1}, _{0, 2} zero-shear rate viscosity of first (second) term - time constant - ₁, ₂ time constant of first (second) term - µ _r relative viscosity of filled Newtonian liquid - ₀ yield stress - ø solid volume fraction - ø _m maximum solid volume fraction     

Überlegungen zur Scherviskosität von Suspensionen aufgrund einer Dimensionsanalyse

Dimensional analysis of the motion of solid particles suspended in a fluid phase shows that the macroscopic relative shear viscosity of suspensions generally depends not only on the volume concentration and particle shape but also on two Reynolds numbers and a dimensionless sedimentation number. These dimensionless numbers are formed using parameters characterizing the structure and motion of the suspension at the microscopic level. The analysis was based on the assumptions that the dispersed particles are rigid and sufficiently large that Brownian motion may be neglected, that the continuous fluid phase is Newtonian and that the interactions between particles and between particles and fluid phase are only hydrodynamic. The Reynolds numbers describe the influence of the inertial forces at the microscopic level, and the sedimentation number the influence of gravity. The dimensionless numbers can be neglected if their values are much smaller than one. For each of the dimensionless numbers both the shear rate and the particle size influence the shear viscosity. Thus sedimentation number is large for low shear rates, whereas the Reynolds numbers are large for high shear rates. The viscosity function for one suspension can be transformed into the viscosity function for another suspension with geometrically similar particles but of a different size. The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. The influence of non-hydrodynamic effects at the microscopic level on the shear viscosity can be detected by deviations from the derived scale-up rules.     

Influence of degree of sulfation on the rheology of cellulose nanocrystal suspensions

The rheology and microstructure of two different cellulose nanocrystals (CNC) samples possessing different degrees of sulfation are studied over a broad concentration range of 1 to 15 wt%. CNC suspensions are isotropic at low concentration and experience two different transitions as concentration increases. First, they form chiral nematic liquid crystals above a first critical concentration where the samples exhibit a fingerprint texture and the viscosity profile shows a three-region behavior, typical of liquid crystals. By further increasing the concentration, CNC suspensions form gels above a second critical concentration, where the viscosity profile shows a single shear-thinning behavior over the whole range of shear rates investigated. It has been found that the degree of sulfation of CNC particles has a significant effect on the critical concentrations at which transitions from isotropic to liquid crystal and liquid crystal to gel occur. Rheological properties and microstructure of these suspensions have been studied using polarized optical microscopy combined with rheometry.     

Rheological characterization of commercial highly viscous alginate solutions in shear and extensional flows

The rheological properties of sodium alginate in salt-free solutions were studied by steady shear, dynamic oscillatory and extensional measurements. This biopolymer consists of mannuronic and guluronic acid residues that give a polyelectrolyte character. We applied the scaling theories and checked their accordance with polyelectrolyte behaviour for low concentrations with a shift to neutral polymer behaviour at larger concentrations. This nature was supported by the effect of the concentration on the specific viscosity, the relaxation times from steady shear and the longest relaxation times from small amplitude oscillatory shear (SAOS) measurements. To analyze the extensional behaviour of the samples, we conducted a study of dimensionless numbers and time scales where filament thinning driven by viscous, capillary or elastic forces is at play. We conclude that an exponential filament thinning followed by breakup results in the best regimes that describe the experimental data. Besides, the data pointed out that alginate in salt-free concentrated solutions shows strain thinning of the extensional viscosity and chain rigidity, behaviours that cannot be inferred from the shear rheometry.     

Viscosity of suspensions in polymeric solutions

Viscosities of suspended particles in polymeric solutions depend upon dissolved polymer concentration, volume fraction of particles and shear rate. In this analysis of viscosity data, relative viscosity was defined as the ratio of suspension viscosity to solution viscosity at the same shear stress rather than shear rate. These relative viscosities reached asymptotic values at high shear stress for all concentrations of dissolved polymer and for all particle loadings. At a given particle loading, the asymptotic values of relative viscosity were nearly independent of the concentration of dissolved polymer. Realtive viscosities were correlated with volume fraction by the one-constant equation of Maron and Pierce.     

Flow properties of oven-curing high solids white enamels

For the characterization of the rheological behaviour of a white, high solids, oven-curing enamel for household equipment with regard to its industrial application, attention was focused on the flow aspects involved in laying down process and film formation phenomena, i.e. viscosity at very high and very low shear rate, structural build-up in rest conditions, presence and magnitude of elastic components. Hence, investigations were aimed at (1) the determination of the equilibrium flow curve; the application of the Shangraw-Grim-Mattocks model led to the evaluation of parameters to describe infinite shear-rate viscosity and yield stress; (2) obtaining information about particle aggregation state in shear conditions. Quemada model gave indication that, even at very high shear, particle aggregates are stable; (3) the determination of time-dependent behaviour: elastic components were found to be almost negligible; the Trapeznikov-Fedotova procedure allowed thixotropic build-up in rest conditions to be evaluated, as concerns both amount and kinetics. Remarkable flow features found were: differences in the temperature dependence of viscosity at low shear rate and of yield value for enamels formulated with different pigment volume concentrations and the strong effect of the pigment volume concentration on the initial rate of thixotropic build-up in rest conditions.     

Steady and dynamic shear properties of non-aqueous drag-reducing polymer solutions

The steady and dynamic shear properties of two non-aqueous drag-reducers (a medium molecular weight polyisobutylene and a commercial organic drag-reducer) in kerosene solutions over a wide range of temperature and concentration were presented. The intrinsic and zero-shear viscosity results were used to identify the concentrate regimes of these solutions. A characteristic time constant λ₀, which was based on the spring-bead model for dilute solutions, was employed as the scaling parameter for both steady-shear and dynamic data over a wide range of concentration and temperature. The inadequacy of the Graessley reduced-variable method in the dilute region was illustrated. The shear-thinning behaviour of these polymer solutions could be described by the Carreau model. The dynamic data followed the Zimm and Rouse-like behaviour in the low and high frequency limits. The Cox-Merz rule was obeyed in the low shear rate and frequency regions. The Carreau and the zero-frequency Maxwell time constants appeared to be related to λ₀ by a constant factor over a wide range of polymer concentrations. The finding provides a method for extrapolating viscoelastic information into the drag reduction regime, and could be useful for interpretation of drag reduction results.