Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (M _w 1.8 10⁶). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Matheson's theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.     

Finite rise time step strain modeling of nearly monodisperse polymer melts and solutions

The step shear strain experiment is one of the fundamental transient tests used to characterize the rheology of viscoelastic polymer melts and solutions. Many melts and solutions exhibit homogeneous deformation and stress relaxation; in these cases the transient dynamics can be modeled by completely ignoring momentum effects and imposing singular kinematics. Recently, however, it has been observed that there are certain classes of nearly monodisperse melts and solutions that exhibit anomalous nonhomogeneous deformation and stress relaxation (Morrison and Larson (1990), Larson, Khan, and Raju (1988), Vrentas and Graessley (1982), and Osaki and Kurata (1980)). We demonstrate that, for these classes, a finite rise time must be incorporated, some source of inhomogeneity must be present, and a small amount of added Newtonian viscosity is necessary. We examine five nonlinear and quasilinear models; the Johnson-Segalman, Phan Thien Tanner, Giesekus, White-Metzner, and Larson models. We determine which mathematical features of the models are necessary and/or sufficient to describe the observed experimental behavior.     

A slit viscometer for the measurement of the viscosity of aqueous systems at high temperatures

A slit viscometer has been constructed to measure the viscosity of aqueous systems at temperatures up to 140 °C. Liquid is forced backwards and forwards through the slit by the use of varying air pressure. The flow rate is obtained from the time for the liquid to pass conductivity probes located in liquid reservoirs either side of the slit. The pressure difference between two points on the slit wall is determined using a differential pressure transducer. By varying the slit height measurements can be made on liquids with viscosities in the range 10 to 10^–3 Pa s. Shear rates from 10 to 10⁴ s^–1 can be achieved. A simple microcomputer control system enables the shear stress to be automatically increased and decreased stepwise. Representative data on polysaccharide solutions and strach suspensions are presented. The viscometer is particularly well-suited for following temperature-dependent biopolymer transitions and the thermal depolymerisation of water soluble polymers.     

Molecular interpretation of the behaviour of polyisobutylene in different solvents

The effects of solvent environment on the behaviour of a high molecular weight polyisobutylene dissolved in kerosene and various grades of poly-1-butene solvent mixtures are investigated. The dependence of various molecular parameters such as zero-shear viscosity, intrinsic viscosity, specific viscosity, relaxation time and molecular expansion factor, on the polymer concentration, type of solvent and solvent viscosity is studied in the vicinity of dilute and semidilute regions (near the critical concentrationc ^*). The dependence of these parameters on solvent environment follows qualitatively Zimm's molecular model. The dependence on the polymer concentration deviates from this dilute solution theory. The effects of temperature on the zero-shear viscosity and the Maxwell relaxation time are also presented for two PIB solutions.     

A boundary element simulation of the unsteady motion of a sphere in a cylindrical tube containing a viscoelastic fluid

A boundary element method is used to simulate the unsteady motion of a sphere falling under gravity along the centreline of a cylindrical tube containing a viscoelastic fluid. The fluid is modelled by the upper-convected Maxwell constitutive equation. Results show that the viscoelasticity of the liquid leads to a damped oscillation in sphere velocity about its terminal value. The maximum sphere velocity, which occurs in the first overshoot, is approximately proportional to the square root of the Weissenberg number when the ratio of the sphere radius to the tube radius is sufficiently small. Particular attention is also paid to the wall effects. It is shown that a closer wall reduces the oscillatory amplitude of the sphere velocity but increases its frequency. The results suggest that the falling-ball technique, which is now widely used for viscosity measurement, might also be used for the determination of a relaxation time for a viscoelastic fluid.     

The role of short chain molecules for the rheology of polystyrene melts.

Atactic polystyrenes of narrow molar mass distribution with average molar masses larger than the critical molar massM _c were mixed with similar polystyrenes of molecular masses lower thanM _c . Linear viscoelastic melt properties of these binary blends were measured with a dynamic viscometer of the concentric cylinder type. One of the experimental findings is that the time-temperature shift factorsa _T are dependent on the composition of the samples. This can be understood, if free volume due to chain-ends is taken into account. A computer-fitted WLF-equation being modified in a proper way leads to the following results: At the glass-transition-temperature the fraction of free volume in polystyrene of infinite molar mass is only 0.015. At a temperature of 180 °C the mean value of the free volume at a chain end is 0.029 nm³ for the polystyrene investigated.     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.     

Molecular weight polydispersity effects on the melt viscoelasticity of styrene-acrylonitrile random copolymers

A series of polydisperse SAN (styrene-co-acrylonitrile) random copolymers was studied by means of oscillatory rheometry in the rubbery plateau zone and in the terminal zone. The plateau modulus, the Newtonian viscosity, and the critical frequencies for the onset of non-Newtonian behavior were extracted from the experimental data. All these viscoelastic quantities consistently indicate that the tail of molecular weights below approximately M _e (the entanglement spacing) acts as a solvent for the rest of the polymer with M>M _e .     

Rheological properties of lightly crosslinked carboxy copolymers in aqueous solutions

The rheological properties of a series of lightly crosslinked carboxy copolymers in aqueous solutions have been evaluated in steady shear and dynamic oscillatory modes. Viscosity profiles and the behavior of storage modulus are related to the chemical composition of the copolymers and their crosslinking density. A maximum in viscosity and in storage modulus which depends on the type of crosslinking agent used is explained by a combination of a chain entanglement mechanism and a closely-packed spheres model. The recovery of viscosity and storage modulus after shearing is very fast and is related to the very fast rearrangement of the microgel structure as a function of time.     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. II. Comparison with experimental results

The results of the theory presented in part I are compared to already published flow birefringence data obtained with dilute up to semi-dilute solutions of polyethylene oxide which have also shown shear thickening effects. The agreement with the theory is quite good so that the reversible formation of associations in flow seems to be a process which has to be taken in account for high molecular weight flexible macromolecules solutions in relatively poor solvents.     

Linear rheology of viscoelastic emulsions with interfacial tension

Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.     

Simple linear viscoelastic models of dilute solutions of polymer molecules and emulsion droplets

The complex viscosity of microemulsions shows relaxation processes of which the largest relaxation time is about 10^–5 s or less. This time can be attributed to relaxation of stresses in the surface of emulsion droplets pertaining to interfacial tension. Superimposed on a spherical droplet surface shape fluctuations can occur due to thermal energies. Our aim is to show the influence of thermal shape fluctuations on the complex viscosity of emulsions. The method used in the derivation has also been applied to inflexible rods to demonstrate its feasibility by showing the formal rheological equivalence of in length thermally fluctuating rods and Rouse's simple model of polymers. The emulsion results have been applied to a dilution series of a non-ionic microemulsion.     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

The behaviour of polymer solutions in extension-dominated flows,with applications to Enhanced Oil Recovery

The rheometry and flow behaviour of aqueous solutions of polyacrylamide and xanthan gum are discussed, with the expectation that the results will be of use in Enhanced Oil Recovery (EOR). The rheometrical study gives particular prominence to the dramatically high values of extensional viscosity which are possible in aqueous solutions of flexible polymers such as polyacrylamide. The effect of such factors as polymer concentration, salt concentration and mechanical degradation on rheometrical properties is outlined. Reference is also made to the qualitatively-different rheometrical behaviour experienced by comparable solutions of xanthan gum.Further evidence is advanced that some dilute polymer solutions of potential use in EOR experience abnormally high resistance in flows which are dominated by extension. Since flow through a porous medium involves a substantial extensional component, it is argued that there is justification for studying the effect of this high extensional-viscosity behaviour in a number of idealized geometries of relevance to EOR conditions. The resulting experiments indicate that, at low flow rates,shear viscosity is the dominant influence, but that, after a critical set of conditions,extensional-viscosity considerations can become all important and the observed pressure losses are against any expectation based on conventional fluid mechanics.Flow visualization studies support the pressure-drop measurements in emphasising the strong influence of high extensional viscosities in flows through tortuous geometries.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

Messung der dynamischen Eigenschaften verdünnter Polymerlösungen

Zusammenfassung Ein neuartiges Rheometer zur Ermittlung der rheologischen Eigenschaften von Polymerlösungen im linear-viskoelastischen Bereich wird vorgestellt. Durch Anwendung der Laser-Doppler-Anemometrie, die eine im hydro-dynamischen Sinn störungsfreie Meßmethode darstellt, ist es möglich, niedrig-viskose bis hin zu wasserähnlichen Proben zu vermessen.Zur Bewältigung der in großer Zahl anfallenden Daten und Rechenoperationen findet ein Mikrocomputer-System Verwendung. Es erledigt im einzelnen die Aufgaben Versuchsablauf-Steuerung, Meßwerterfassung, Auswertung, Dokumentation und graphische Darstellung der Ergebnisse.Anhand von Messungen an newtonschen Flüssigkeiten werden der Funktionsnachweis erbracht und die Betriebsbereiche der Ringspaltsysteme unterschiedlichen Durchmessers ermittelt.Die viskoelastischen Eigenschaften von wäßrigen Polyethylenoxid- und Polyacrylamid-Lösungen niedriger Viskosität lassen sich über einen Frequenzbereich von 0,1 bis 100 Hz messen. Die Ergebnisse werden mit Hilfe der komplexen Viskositätsfunktion dargestellt. Daraus läßt sich als gleichwertige Darstellung das diskrete Relaxationsspektrum eines konkreten Stoffgesetzes gewinnen.

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A novel rheometer for determining the elastic characteristics of polymeric solutions in the linear-viscoelastic region is described. Laser-Doppler anemometry, which does not introduce hydrodynamic disturbances, is used to enable low viscosity liquids including water-like samples to be measured.A microcomputer system is utilized to control the experiments, store and analyse the measured data, and provide graphical representations of the results. Measurements on Newtonian liquids verified the validity of the method and allowed the operational regions of the annulus systems with different diameters to be determined.The elastic characteristics of low viscosity aqueous solutions of polyethyleneoxide and polyacrylamide can be measured at frequencies from 0.1 to 100 Hz. The results are presented using the complex viscosity function. As a result the discrete relaxation spectrum of a special material law can be obtained as an equivalent representation.

     

A new eccentric-cylinder rheometer

A new eccentric-cylinder rheometer with guard-ring equipment was constructed as an auxiliary set-up to a Rheometrics Mechanical Spectrometer, type 7200, which enables measurements with the eccentric disk technique. Experimental tests with Newtonian fluids and polymer solutions of relatively low viscosity show that this instrument yields reliable plots of shear viscosity and first normal-stress coefficient over several decades of the effective average shear rate. These coincide very well with plots from a commercial cone-and-plate rheometer even for higher relative eccentricities (up to 0.75). However, no systematic effects of eccentricity, to be expected for higher shear rates, could be observed with these fluids, so that supplementary tests applying fluids with more pronounced viscoelastic properties are to be carried out.     

Velocity profiles in rectangular channel flow of liquid crystalline polymer solutions

The motion of aqueous solutions of hydroxypropylcellulose in a shallow channel was visualized by means of an electrochemical technique. Isotropic and anisotropic solutions of approximately the same viscosity were used. The velocity profiles of the liquid crystalline solution were found to be qualitatively very different from those of the isotropic one. In particular, anomalous maxima in the velocity near the side walls were observed.     

Linear viscoelastic behavior of narrow molecular weight distribution 1,4 polybutadiene: Comparison with Doi-Edwards theory of reptation

Linear viscoelastic behavior of narrow molecular weight distribution 1,4 polybutadiene samples with molecular weights between 42500 and 779000 has been correlated with molecular structure using a simple modification of the Doi-Edwards theory of reptation. The entire GPC curve is required for the calculations of viscoelastic behavior.The plateau modulus obtained from the experimental data is comparable to literature values, while the equilibrium compliance (which is indicative of polydispersity) is greater than values reported in the literature for nearly monodisperse polybutadienes. Reasonable agreement between theory and experiment is obtained over the entire molecular weight range. The agreement between theory and experiment using the GPC curve is better than that obtained by assuming the polymer to be monodisperse or by using the Doi fluctuation model. The model appears to break down for a more polydisperse sample . This study indicates that it may be possible to use the Doi-Edwards theory to explain the viscoelastic behavior of narrow MWD polybutadienes without introducing any new concepts into the theory (fluctuations, constraints release, etc.).     

Primary normal-stress coefficient prediction at high shear rates

On the basis of a brief analysis of well known normal-stress calculation methods, the necessity of improved models of prediction is elaborated. A modified form of the so-called mirror relation which meets these requirements is presented. In combination with the Carreau viscosity equation, an analytical solution is given which leads to a Carreau normal-stress coefficient equation and, thus, to a simple method of calculation. The comparison between measured normal stresses and those determined by experiments shows that the values calculated in accordance with the presented method agree well with the measured values, especially within the range of high shear rates. The parameters andK to be selected for this purpose are determined in dependence on the slope of the viscosity function ₁ at high shear rates for each polymer individually, using empirical relations so that the global selection of parameters, which is common practice with other methods, is obviated. In an appendix a method for deriving the relations between material functions on the basis of operator calculation is given.Extended version of a paper read at the 2^nd Symposium on Rheology of the GDR in Tabarz/Thuringia, December 7–11, 1987