Showing papers in "Rheologica Acta in 1982"

Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities

Abstract: On the basis of some very plausible assumptions about the response of physical systems to stimuli, such as Boltzmann's superposition principle and the causality principle, Spence showed that the following characteristics obtain for the modulus and compliance functions: (i) They are analytic in the lower half of the complex frequency plane, (ii) they are limited if the frequency tends to infinity, and (iii) the real and imaginary parts are even and odd functions, respectively, of the frequencyω. It can generally be demonstrated that the real and imaginary parts of every function satisfying these three requirements and (iv) without singularities on the real frequency axis, are interrelated by Kramers-Kronig transforms. Similar relations hold between the logarithm of the modulus and the argument of the function.

The measurement of the yield stress of liquids

Abstract: An analysis has been made of different methods of measuring the yield stress of liquids. In the experimental program, a comparison is made of measurements of the yield stress using an Instron 3250 Rheometer in several geometries (cone-plate, parallel plate and eccentric disk) in shear flow and stress relaxation, a laboratory vane and a cone penetrometer. Good agreement has been obtained between the shear flow data and the laboratory vane, while stress relaxation appears to underestimate the yield stress.

A unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration-dependent molecular mobility *)

Abstract: The concept of a configuration-dependent tensorial drag (or mobility) coefficient developed some sixteen years ago is presented in a more generalized manner. In particular, the special case of a one-mode model is discussed. This is shown to be equivalent to the one-mode Leonov model as well as to a recently published model of Dashner and VanArsdale.

Shear induced phase transitions in highly dilute aqueous detergent solutions

Abstract: Aqueous solutions of some cationic detergents show rheopectic behaviour at very low concentrations. Rheological measurements and the electrical anisotropy of the streaming solutions indicate that the rheopectic behaviour of the solutions is due to a shear induced phase transition.

Long wavelength approximation to peristaltic motion of a power law fluid.

Abstract: Peristaltic motion of a power law fluid in a two-dimensional channel is studied. Assuming that the wavelength of the peristaltic wave is large in comparison to the mean half-width of the channel, a solution for the stream function is obtained as an asymptotic expansion in terms of slope parameter. Expressions for axial pressure gradient and shear stress are derived. The effect of flow behaviour indexn on the streamline pattern and shear stress is studied and the phenomenon of trapping is discussed.

Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids

Abstract: The equations of linear viscoelasticity with a bounded memory kernel have been shown to propagate singularities in a similar way as hyperbolic equations. In this paper, we investigate a model problem for a certain class of unbounded memory kernels. It is shown thatC∞-solutions are obtained, although there is a discontinuity in the boundary conditions.

Effect of alkali metal ions on the viscoelasticity of concentrated kappa-carrageenan and agarose gels

Abstract: The effect of the addition of the monovalent cations Li+, Na+, K+, and Cs+ on the gelation of agarose and kappa-carrageenan aqueous gels has been studied by the measurement of longitudinal vibration. The dynamic Youngs's modulusE′ of 2% w/w agarose and 0.4–6% w/w kappa-carrageenan gels containing the alkali metal salt LiCl, NaCl, KCl or CsCl of various concentrations from 0 to 4.5 mol/l has been measured at various temperatures. By the addition of the alkali metal salt, the value ofE′ for agarose gels is influenced only slightly, while for kappa-carrageenanE′ is increased substantially. Kappa-carrageenan has many sulphate groups. The addition of the alkali metal ions screens the electrostatic repulsion between these groups. As a result of this, the helical structure of kappa-carrageenan is stabilised and the helices may form densely packed aggregates, so increasingE′. In contrast, agarose has a naturally stable molecular structure and therefore, the structure and henceE′ is not sensitive to added ions. The K+ and Cs+ ions increaseE′ more than Li+ and Na+ for kappa-carrageenan gels. This is interpreted on the basis that these ions are either structure ordering or structure disordering ions for water.

Viscoelastic flow of dilute polymer solutions in regularly packed beds

Abstract: It is well known that dilute polymer solutions may exhibit strong viscoelastic flow effects when exposed to elongational flow fields with elongation rates that exceed certain “Onset”-conditions. Such flow fields occur in the converging-diverging flow passages of a porous matrix but also in regularly packed beds of spheres.

Linearized dynamics for step jumps of velocity and displacement of shearing flows of a simple fluid

Abstract: We consider linearized dynamics associated with step jumps in the velocity or displacement of the boundary of a fluid in a shearing motion. The discontinuity will propagate into the interior with a speed\(C = \sqrt {{{G\left( 0 \right)} \mathord{\left/ {\vphantom {{G\left( 0 \right)} \rho }} \right. \kern- ulldelimiterspace} \rho }} \) (ρ is the density) if the initial valuesG(0) andG′(0) of the fading memory kernels are bounded, 0

Laminar and turbulent flows of dilute polymer solutions: a physical model

Abstract: It is well known that diluted high-molecular polymer solutions give rise to drastic flow effects; for example, in laminar flow through porous media, a pressure drop increase of up to thirty times the value of the flow of the pure solvent is observed, whereas in turbulent wall bounded flow, a pressure drop decrease or drag reduction of up to 80% or five times lower than the Newtonian value is measured. Although both these dramatic influences on the flow are caused by the same polymers, dissolved in the same solvent and employed in the same concentration range, the effects are usually interpreted by different models in the literature. The reason for this is the apparent contrariety of the observed polymer effects in laminar and turbulent flows.

Rheological properties of disperse systems at low shear stresses

Abstract: Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions. Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity. At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent. These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.

A comparative study of the thermotropic mesomorphic tendencies and rheological characteristics of three cellulose derivates: Ethylene and propylene oxide ethers and an acetate butyrate ester

Abstract: Samples of cellulose acetate butyrate (CAB) hydroxypropyl cellulose (HPC) and ethyl cellulose (EC) are contrasted with commercial (atactic) polystyrene (PS) and isotactic polypropylene (PP) in studies of (i) differential scanning calorimetry, (ii) quiescent polarized light microscopy (iii) optical retardation variation following an imposed stress field. It is concluced that HPC and EC are thermotropic liquid crystals, while CAB behaves in a manner similar to a vitrifying isotropic melt such as PS. Studies of the shear viscosity and dynamic viscosity indicate HPC and EC exhibit yield values while CAB shows a zero shear viscosity and Vinogradov-Malkin reduced viscosity curve identical to PS. The normal stress and extrudate swell behavior of CAB are also similar to PS. The HPC and EC exhibit substantially reduced extrudate swell. Measurement of the principal normal stress difference behavior of the HPC melt is troubled by the existence of yield values.

Viscosity of concentrated protein solutions

Abstract: The viscosity of solutions of four proteins (Bovine Serum Albumin, Ovalbumin, α s -1 Casein, Lysozyme), brought to the random coil conformation, has been measured over a large concentration range extending into the entanglement region. A master curve is obtained in the dilute and semi-dilute regions with the reduced variables \( \tilde \eta = {\eta _{sp}}/\left[ \eta \right]c \) and \( \tilde c = c/y \) of Simha and Utracki.

Rheological determination of polymer-filler affinity

Abstract: An experimental method to quantify the affinity of polymers for certain fillers is presented. In this method, the relative viscosity of filled and unfilled polymer systems as determined by capillary rheometry is taken as a measure of the thickness of the adsorbed layer of polymeric material on the filler surface and hence of the affinity of the polymer for the filler. A styrene-butadienestyrene block copolymer is thus found to have a higher affinity for talc than do polypropylene and an ethylene-propylene-diene terpolymer.

On some contraction flows for Boger fluids

Abstract: The contents of this lecture are a part of a general research programme which seeks to investigate flows for which elastico-viscous effects are a dominating influence. The basic experimental work is supported by attempts to simulate numerically the observed flow characteristics using finite-difference techniques (see, for example, Cochrane, Walters and Webster [1] Walters and Webster [2]).

Rheology of polymer blends

Abstract: Rheological properties of blends of amorphous and crystalline polymers were studied for a broad range of compositions and temperatures. It was established that below the melting pointTm the viscoelastic properties of blends of crystalline polymers are similar to those of polymers filled with mineral fillers. In both cases these properties are influenced by the existence, in such systems, of a temporary structural network formed by mineral or polymeric particles and its subsequent breakdown under the action of shear stresses. It was found that an anomalous decrease in the melt viscosity of the main component on addition of a small amount of a second polymer depended on deformation conditions. The comparison of data on viscoelastic properties and thermodynamic interaction between the components in the melt, estimated from the parameterχ23 of a new Flory theory, shows that the sharp drop of viscosity takes place in the region of microphase separation due to the appearance of an excess free volume in the interphase region. Calculation of the relaxation spectra for various blends also revealed marked changes when various amounts of a second component were added to the main polymer.

Run-up and spin-up in a viscoelastic fluid. III

Abstract: The problem is discussed of run-up in an incompressible viscoelastic fluid contained between infinite parallel rigid plates which are simultaneously given equal parallel velocities. The problem is analyzed in terms of the disturbances which spread from the boundaries into the fluid and are reflected back and forth at the boundaries.

Die Charakterisierung viskoelastischer Fluide mit Hilfe ihrer Strömungseigenschaften in Kugelschüttungen

Abstract: Das viskoelastische Verhalten verdunnter makromolekularer Losungen wird anhand von Stromungen durch Zufallsschuttungen mit einheitlichem Kugeldurchmesser untersucht. Zur Beschreibung der experimentell beobachteten Polymereffekte wird das Konzept einer reprasentativen Deborahzahl angewandt, die sich fur die Porenstromung als Produkt aus der Relaxationszeit der Polymerflussigkeit und der effektiven Dehnrate im Porenraum ergibt. Zur Modellierung der polymeren Flussigkeit und zur Ableitung von Dehnviskositatsgleichungen werden Modellvorstellungen herangezogen, die auf der kinetischen Theorie verdunnter Hantelsuspensionen basieren. Fur endlich dehnbare, nichtlinear-elastische Hanteln als Modellmolekule erhalt man fur die Modellflussigkeit ein Zweiparametersystem (b, τH), welches unmittelbar in die viskoelastischen Kenngrosen einer reinen Dehnstromung eingeht. Die Porenstromung wird als eine solche Dehnstromung modelliert. Experimentelle Ergebnisse aus Porenstromungen zeigen, das der Einflus aller masgebenden stromungsmechanischen und physikalisch-chemischen Parameter, die das viskoelastische Verhalten von verdunnten Polymerlosungen bestimmen, von den theoretisch abgeleiteten Endbeziehungen korrekt beschrieben wird.

Influence of drag reducing additives on the structure of turbulence in a mixing layer

Abstract: The structure of a free turbulent mixing layer in Newtonian and drag reducing fluids is discussed using results from visualization and LDA-techniques. Particular emphasis is placed on results for the turbulent shear stress and the time correlation function.

Some aspects of linear and nonlinear viscoelastic behaviour of polymer melts in shear

Abstract: In linear viscoelastic investigations the frequency dependence of the phase shift between stress and strain appears to be very characteristic of the molecular structure of the material. This function is also a good approximation of the slope of the double logarithmic plot of the absolute value of the shear modulus G d vs. the angular frequency ω. The product (G d /π) sin 2δ comes very close to the relaxation spectrum H(τ), with τ = 1/ω, in all physical states of the material.

Rheograms for asphalt from single viscosity measurement

Abstract: Asphalt materials are used in a variety of applications such as road paving, waterproofing, roofing membranes, adhesive binders, rust proofing and water resistant coatings. There are available in a number of grades distinguished in terms of their softening point and flow resistance. The selection of the proper grade of asphalt for a particular application is governed by the desired flow behaviour. A knowledge of the complete flow curve depicting the variation of melt viscosity with shear rate at the relevant temperatures is necessary not only for proper grade selection, but also for specifying processing conditions for aggregate mixing and spraying. The rheological data are also useful in assessing end use performance. The scientific techniques for generating the rheological data involve the use of expensive, sophisticated instruments. Generation of the necessary flow data using these instruments is beyond the financial and technical means of most processors of asphalt materials. The engineering techniques involving the use of inexpensive vacuum viscometers are relatively easy, but provide a single point viscosity measurement at low shear rate. In the present work, a method is proposed for unifying the viscosity versus shear rate a data at various temperatures for a number of asphalt grades. A master curve has been generated that is independent of the grade of asphalt and the temperature of viscosity measurement. The master curve can be used to generate rheograms at desired temperatures for the asphalt grade of interest, knowing its zero-shear viscosity at that temperature.

Beeinflussung der Turbulenzstruktur in der ebenen Mischungsschicht zweier Ströme durch Polymerzusätze

Abstract: Ausgehend von der Frage, ob beim Phanomen der Widerstandsverminderung (Toms-Effekt) die Wirkung der Polymeren nur auf die Stromung in den wandnahen Bereichen beschrankt ist oder eine solche auch in wandferneren Gebieten gefunden werden kann, hat die vorliegende Untersuchung zum Ziel, den Einflus derartiger Zusatze in der sog. „Freien Turbulenz“ zu analysieren, bei denen also keine Wechselwirkungen mit festen Wanden vorhanden sind. Als besonders einfaches Beispiel einer solchen Stromung wurde diejenige in einer ebenen turbulenten Mischungsschicht ausgewahlt, die sich zwischen zwei mit verschiedener Geschwindigkeit bewegten Parallelstromen ausbildet. In derartigen Stromungen existiert eine charakteristische Wirbelstruktur, die von einer turbulenten Mikrostruktur uberlagert wird, und es sollte untersucht werden, wie diese Strukturen sich bei Zugabe von widerstandsvermindernden Polymeren andern. Als Untersuchungsmethode wurde die raum-zeitliche Korrelationsanalyse mittels Laser-Doppler-Anemometern verwendet. Da aber die bekannten Systeme hierfur nur bedingt einsetzbar sind, wurde eine fur diesen Zweck besser geeignete optische Anordnung neu entwickelt. Als wichtigstes Ergebnis wurde gefunden, das durch den Polymerzusatz die Intensitat und die Koharenzlange der turbulenten Makrostrukturen erheblich anwachsen, wohingegen die turbulenten Mikrostrukturen weitgehend unterdruckt werden. Grose und Abstand der Wirbel werden zwar verkleinert, doch wird ihre Aufeinanderfolge vergleichmasigt, und ihre Lebensdauer nimmt entsprechend zu. Weiter wurde nachgewiesen, das die mit der Polymerzugabe verbundene Viskositatserhohung nicht die Hauptursache fur diese Effekte sein kann, da solche bei newtonschen Flussigkeiten mit vergleichbarer Viskositat langst nicht in so ausgepragter Weise auftreten. Das ebenfalls beobachtete verringerte Dickenwachstum vor allem im Anfangsbereich der Mischungsschicht in Verbindung mit einer Verstarkung der Intensitat der langsameren turbulenten Langsschwankungen legt die Deutung nahe, das durch die Hauptstromung infolge Entknauelung und Orientierung der Polymermolekeln eine Fliesanisotropie erzeugt wird. Dagegen last sich die Verlangsamung des Wirbelwachstums und die Unterdruckung der Mikroturbulenz am ehesten durch die Behinderung lokaler Dehnstromungen infolge einer stark erhohten Dehnviskositat erklaren. Die Vorstellung, das bei den Austauschvorgangen in einer freien turbulenten Mischungsschicht die Flussigkeitseigenschaften keine Rolle spielen, ist somit durch diese Untersuchung als zumindest fur viskoelastische Flussigkeiten nicht zutreffend nachgewiesen worden.

The dynamic performance of the Weissenberg Rheogoniometer

Abstract: The dynamic performance of a standard Model R18 Weissenberg Rheogoniometer has been studied in detail. The Rheogoniometer was carefully calibrated and used to measure accurately the rheological behaviour of a highly nonlinear viscoelastic polymer solution (1% polyacrylamide in 50% glycerol/water).

The dynamic performance of the Weissenberg Rheogoniometer: II. Large amplitude oscillatory shearing — Fundamental response

Abstract: A standard model R18 Weissenberg Rheogoniometer was used to study the nonlinear dynamic rheological behaviour of 1% polyacrylamide in 50% glycerol/water over the frequency range 5 × 10−3 ⩽f ⩽ 50 Hz. Both cone and plate (CP) and parallel plates (PP) geometries were used and fundamental strain amplitudes in the ranges 0.092 ⩽γCP0 ⩽ 4.05 and 0.250 ⩽γPP0 ⩽ 27.0 were covered. The Oscillation Input and Torsion Head displacement transducer signals were processed using a Digital Transfer Function Analyser.In the absence of fluid inertia effects the shearing deformation may be defined completely in terms of the Oscillation Input and Torsion Head motions. For the cone and plate geometry the fundamental nonlinear dynamic propertiesη′(ω, γ0) andG′(ω, γ0) may be evaluated using the well known linear (small amplitude) oscillatory shearing formulae. For the parallel plates geometry new formulae are derived herein. Good agreement was obtained between the results obtained from both geometries.Fluid inertia effects were found to be negligible if the modified Reynolds number,Reθc2 orRe(H/R)2, had a value less than about 0.1. They may be reduced or eliminated by descreasing the gap angle/width. Not only is the parallel plates geometry better suited to this purpose but also its use greatly increases the range of strain amplitudes available.

Flocculation and rheology of kaolinite/quartz suspensions

Abstract: Rheological properties of suspensions of Na-kaolinite and colloidal quartz (Min-U-Sil) at constant overall volume concentration of 2% are determined with a Weissenberg Rheogoniometer using a combined Couette and cone-and-plate geometry. The results are interpreted in terms of the flocculation behaviour of the constituent particles in the presence of high salt concentrations (0.1–0.75m NaCl) at pH 6, 7 and 8. In these chemical environments these suspensions are pseudoplastic for much of the range of mixture compositions becoming Newtonian for suspensions containing only quartz. These properties reflect the dominant influence of interactions between kaolinite particles on the flocculation behaviour of the mixture.

Elastic properties of polyethylene melts at high shear rates with respect to extrusion

Abstract: At high shear rates a steady state of shear flow with constant shear rate, constant shear stress, and constant recoverable shear strain is observed in the short-time sandwich rheometer after some few shear units already. The melt exhibits rather high elastic shear deformations and the recovery occurs at much higher speed than it is observed in the newtonian range. The ratio of first normal stress difference and twice the shear stress, being equal to the recoverable strain in the second-order fluid limit, significantly underestimates the true elastic shear strains at high shear rates. The observed shear rate dependence of shear stress and first normal stress difference as well as of the (constrained) elastic shear strain is correctly described on the basis of a discrete relaxation time spectrum. In simple shear a stick-slip transition at the metal walls is found. Necessary for the onset of slip is a critical value of shear stress and a certain amount of elastic shear deformation or orientation of the melt.

Stresses in polymer melts at the beginning of flow instabilities (melt fracture) in cylindrical capillaries

Abstract: The flow of fluid polymers is often accompanied by flow instabilities. This phenomenon can be observed at the outlet of capillaries and is a characteristic phenomenon of polymer melts [1, 2]. In plastic processing this effect is called melt fracture. Because of the low Reynolds numbers at which melt fracture starts, it is assumed that these instabilities are caused by the viscoelastic properties of those melts. Up to now these assumptions could not be proved, because in most cases the elastic properties of the polymers are unknown at shear rates K where melt fracture begins.

Das rheologische Verhalten von Polymerlösungen: Strömungsverfestigung in Scher- und Dehnströmungen

Abstract: Um das Dehnverhalten auch relativ niedrigviskoser viskoelastischer Fluide praktisch ohne den Einflus von Vorbeanspruchungen messen zu konnen, wird ein neuartiges Dehnrheometer eingesetzt. Das Mesverfahren stellt eine Weiterentwicklung der Methode des rohrlosen Hebers (tubeless-syphon) dar, bei dem durch eine rechnergesteuerte Abzugswalze das Material unter definierten Bedingungen entgegen der Wirkung der Schwerkraft nach oben gezogen wird.