Showing papers in "Rheologica Acta in 1979"

Relation between viscoelasticity and shear-thinning behaviour in liquids

Abstract: The shear-thinning behaviour of a liquid is represented in terms of a relaxation timeλ, defined by the ratioη 0/G0 of initial viscous and elastic constants. The relationship provides a very simple basis for the evaluation ofλ andG 0 from viscosity/shear data. Results are compared with relaxation times and moduli from primary normal-stress measurement, from stress relaxation and from direct measurement of recoverable shear strain. Good agreement is found but there is experimental evidence the recoverable shear strainγ e is related to normal stressN 1 and shear stressσ byγ e = N1/3σ, which does not agree with the theoretical prediction of eitherWeissenberg orLodge.

Zur Netzwerktheorie von Polymer-Schmelzen

Abstract: Die vonLodge vorgeschlagene Theorie der „gummiartigen“ Flussigkeit stellt bei kleinen Deformationen eine korrekte Beschreibung des rheologischen Verhaltens polymerer Losungen und Schmelzen dar. Bei groseren Deformationen versagt sie jedoch zunehmend, da sie nicht in der Lage ist, strukturviskoses Verhalten, d. h. die Abnahme der Scherviskositat und der 1. Normalspannungsfunktion mit zunehmender Schergeschwindigkeit, zu erklaren. Auch bei uniaxialer Dehnung verhalten sich Polymer-Schmelzen vom Standpunkt der Lodgeschen Gleichung aus betrachtetstrukturviskos. Aus dem Vergleich des experimentell ermittelten und des fur eine gummiartige Flussigkeit vorausgesagten Spannungsverlaufs bei Relaxationsversuchen und bei Spannversuchen kann der Schlus gezogen werden, das die Struktur des temporaren Netzwerkes einer Polymer-Schmelze bei groseren Deformationen zunehmend zerstort wird. Die Zahl der das Netzwerk aufbauenden Haftstellen nimmt mit zunehmender Deformation ab. Fur den Fall der einfachen Scherung und der uniaxialen Dehnung einer wohldefinierten Polyathylen-Schmelze wird die Deformationsabhangigkeit der Haftstellenzahl angegeben und verglichen.

Shear viscosity of settling suspensions

Abstract: A new apparatus is presented which allows the determination of the viscosity of suspensions of high density particles in low viscosity media. Results obtained on suspensions of low density particles compare well with those obtained on a Weissenberg Rheogoniometer equipped with a cone-and-plate and a bob-and-cup. Also, a very interesting observation is that the Eilers equation, conveniently modified to take into account the shape of the particles by means of the intrinsic viscosity, can well correlate all the data.

A new look at the laminar flow of power law fluids through granular beds

Abstract: The paper deals with laminar flow of power law fluids through granular beds. A critical review of the assumptions concerning the capillary model of the bed, applied by various authors, led us to the conclusion that the derivation of the correlation eq. [13] given byChristopher andMiddleman was based on a too simplified model of the granular bed. Taking advantage of the approach presented in the classical works ofKozeny andCarman (which seems to be partly overlooked by some authors, including our own previous works) a modified correlation equation for power law fluids [21], a corrected formula for shear rate in the bed [29] and for Deborah number [32], as well as corrected correlation equation for fluids exhibiting memory effects [34] were presented.

Orthogonal stagnation flow, a framework for steady extensional flow experiments

Abstract: A new framework for viewing steady extensional flow is presented: Steady orthogonal stagnation flow is an ideal which one should strive to reach in an actual experiment. The kinematics and the stress boundary conditions are developed for stagnation flow in general and in two special cases: the impingement of two circular streams and of two planar sheets. Contemplating this ideal clarifies the advantages and disadvantages of current experiments, thereby pointing the way towards new experiments; a number are suggested. Axisymmetric (with\(\dot \varepsilon _x \) > 0) and planar stagnation flow within a lubricated die look particularly promising. Some preliminary experimental results are given for uniaxial extension of a polyacrylamide solution in a water lubricated die.

Elongational behaviour of polymer melts in constant elongation-rate, constant tensile stress, and constant tensile force experiments

Abstract: The extensibility of polymer melts is of great practical importance for polymer processing. On the basis of a single-integral constitutive equation with a straindepent memory functional verified for two similar well-characterized LDPE melts, predictions are made on material behaviour in uniaxial extension under constant strain-rate, tensile stress, and tensile force conditions. It is found that experiments at constant tensile force are more adequately described by assuming purely viscous response of the polymer melts than by assuming Maxwell-model type of behaviour.

Viscous properties of calcium carbonate filled polymer melts

Abstract: The viscous properties of calcium carbonate filled polyethylene and polystyrene melts were examined. The relative vircosityηr defined in the previous paper gave an asymtptotic value(ηr)l in the range of the shear stress below 105 dyne/cm2.(ηr)l of the calcium carbonate filled system was higher than that of the glass beads or glass balloons filled system at the same volume fraction of the fillerφ. Maron-Pierce equation withφ0 = 0.44 was able to approximate the(ηr)l — φ relationship. However, it was deduced here that the high value of(ηr)l of calcium carbonyl filled system was due to the apparent increase ofφ and this increase was attributed to the fixed polymer layer formed on the powder particle. By assuming the particle as a sphere with a diameter of 2 µm, the thickness of the fixed polymer layer was estimated as about 0.17 µm. The yield stress estimated from the Casson's plots increased exponentially withφ.

Das anomale Fließverhalten von Polyäthylen hoher Dichte

Abstract: Das anomale Stromungsverhalten von Polyathylen hoher Dichte (HDPE) wird mit Hilfe eines Kapillar-Rheometers am Beispiel der Stromung durch Dusen mit Kreisquerschnitt untersucht. Die Ergebnisse der Untersuchung werden in Form „scheinbarer Flieskurven“ dargestellt. Es wird der Einflus der Temperatur, der Oberflachenbeschaffenheit der Duse, der Duseneinlauf-Geometrie, des Druckniveaus und der Zugabe von Zusatzstoffen (Stabilisator, Holzmehl) auf den Verlauf der „scheinbaren Flieskurve“ untersucht. Es kann gezeigt werden, das die bei diesem Material besonders ausgepragt auftretenden Fliesanomalien nicht wie bei anderen Polymertypen (wie z. B. LDPE, PS, PP) auf Vorgange im Duseneinlauf beruhen, sondern auf eine Anderung der Flieseigenschaften der Kunststoffschmelze im Bereich der Dusenwand zuruckzufuhren sind. Diese Anderung der Flieseigenschaften fuhrt in der Duse zu einem Gleiten bzw. zu Haft-Gleierscheinungen. Visuelle Untersuchungen, bei denen die Lage- und Gestaltanderungen farbig markierter Proben beobachtet werden, bestatigen diese Ergebnisse.

Das viskoelastische Verhalten von Polyamid-6-Schmelzen

Abstract: Das rheologische Verhalten von Polyamid-6-Schmelzen mit verschiedenen Molekulargewichten wurde mit Hilfe von Kapillarviskosimetern, einem modifizierten Weissenberg-Rheogoniometer, einem Parallelplatten-Kriechrheometer und einem Schwingungsviskosimeter untersucht. An Mesbeispielen wird der Einflus der Feuchte und der Meszeit auf das Stabilitatsverhalten der Schmelze diskutiert. Auf Grund ihrer gleichartigen Schulz-Flory-Molekulargewichtsverteilungen last sich fur die Viskositatsfunktionen bei einer Normierung der Viskositats- und Schergeschwindigkeits-Skala mit der Nullviskositat eine Masterkurve konstruieren, die nicht nur temperaturinvariant, sondern auch vom Molekulargewicht unabhangig ist. Die Strangaufweitungen und Einlaufdruckverluste bei Dusenstromung konnen als Funktionen der Schubspannung an der Dusenwand ebenfalls temperatur- und molekulargewichtsinvariant dargestellt werden. Die aus dynamischen Messungen, aus Messungen der reversiblen Scherung und der 1. Normalspannungs-differenz im linearen Fliesbereich ermittelten Gleichgewichts-Nachgiebigkeiten stimmen uberein. Als Folge des konstanten Verhaltnisses von $$\bar M_w /\bar M_n = 2$$ ist die Gleichgewichts-Nachgiebigkeit unabhangig vom Molekulargewicht. Die Temperaturabhangigkeit der Nullviskositat folgt einer Arrhenius-Beziehung mit einer vom Molekulargewicht unabhangigen Aktivierungsenergie vonE 0 = 60 kJ/Mol.

Viscoelastic properties of high molecular weight polymers in the molten state: II. Influence of the molecular weight distribution on linear viscoelastic properties

Abstract: SummaryThe effect of the molecular-weight distribution on linear viscoelastic properties is studied in the case of atactic polystyrene. First, the prediction of the linear behavior is made from an analytical expression of the complex complianceJ* (ω), in a broad frequency range (8 decades). We then deduct the properties of binary blends, using a blending law on the complex modulusG* (ω). We extend at last this blending law to the case of a continuous distribution of molecular weights. The agreement with experimental data was found satisfactory, provided the molecular-weight distribution is known with a good precision, and the low-molecularweight tail (M < Mc) is negligible.ZusammenfassungBei ataktischem Polystyrol wird die Wirkung der Molekulargewichtsverteilung auf die linear-viskoelastischen Eigenschaften untersucht. Zuerst wird das lineare Verhalten mittels eines analytischen Ausdrucks für die komplexe KomplianzJ* (ω) über einem Frequenzbereich von 8 Dekaden vorausgesagt. Damit werden die Eigenschaften binärer Mischungen abgeleitet, wobei ein Mischungsgesetz für den komplexen ModulG* (ω) angewandt wird. Schließlich wird dieses Gesetz auf kontinuierliche Molekulargewichtsverteilungen verallgemeinert. Die Übereinstimmung mit den experimentellen Ergebnissen ist zufriedenstellend, wenn die Molekulargewichtsverteilung hinreichend genau bekannt ist und der niedermolekulare Anteil (M < Mc) vernachlässigt werden kann.

Estimation of zero-shear viscosity of polymer solutions from falling sphere data

Abstract: Extrapolation methods for the determination of zero-shear viscosity from falling sphere tests are compared with each other and in particular with dicrect viscometric measurements of this parameter. It is found that all methods of extrapolation overestimate the true zero-shear viscosity and that the discrepancy depends on the degree of shear thinning encountered by the falling spheres. Falling sphere tests only yield the true zero-shear viscosity when the spheres fall in the lower Newtonian region of fluid behaviour. In most instances a suitable combination of sphere properties to achieve this can only be found in the case of very viscous fluids which can in any case also be characterized by direct viscometric measurements in this region. If sphere fall data must be extrapolated, methods based on shear rate rather than shear stress appear preferable since they generally yield lower values of zero-shear viscosity, which are therefore nearer to the true value.

A mechanical model for rubbers containing entanglements

Abstract: A simple model of macromolecular networks containing both chemical crosslinks and entanglements is developed by assuming that in the entanglements the chains may slide so as to equilibrate their tension. The resulting constitutive equation shows small but significant departures from the classical statistical theory, which are generally in qualitative agreement with the mechanical behaviour of rubbers.

Injection moulding of plastics

Abstract: In continuation of a previous investigation a simple analytical expression is derived in closed form for the thickness distribution of the “freeze-off” layer which is vitrified at the (flat) wall of an oblong rectangular cavity. As has been pointed out previously, this layer is marked for amorphous polymers by the molecular orientation (birefringence pattern) in the moulded sample. One can show that a more detailed study with the aid of the coupled equations of energy and of motion will not furnish essential improvements. Problems of polymer physics like glass transition or crystallization kinetics at extreme rates of cooling and shearing must be solved first.

The flow field of Newtonian fluids in cone and plate viscometers with small gap angles

Abstract: The flow of a Newtonian fluid in cone-plate viscometers is determined by solving the Navier-Stokes equations. It is shown in an order-of-magnitude analysis that the governing equations can be simplified and that the flow field can be split into two parts, if the angle between cone and plate is small. A closedform solution for the inner flow field is established through an iteration procedure. The zeroth-order solution in which the convective terms are neglected is inserted into the governing equations which then can be integrated again. The outer flow field is also described analytically. The solution satisfies the boundary condition of the vanishing radial velocity component at the free surface. The flow is described throughout the whole gap. Velocity components, pressure distributions, torque and normal force due to inertia are calculated. Pressure distributions and the maximum radial velocity are measured. The free surface boundary condition is experimentally examined.

Wall effects in polymer flow on inclined plane

Abstract: It has been observed that polymeric fluids exhibit frequently anomalous wall effects in rate-dependent laminar flow. In this work, we propose a new technique to obtain quantitative effects of anomalies observed in the gravity flow of six aqueous polymeric solutions on inclined plane surfaces. Wall effects are determined from departures of the experimental flow rates from the theoretical predictions, assuming Ellis behaviour for the non-Newtonian fluids. In all cases, the experimental flow rates exceed the predicted values, by a factor of four in some cases. The deviations are interpreted in the light of the “separation” phenomenon, ascribable to the formation of a layer of dilute polymer solution at the wall. From determination of the viscosity of the wall, it is shown that the polymer concentration is from 10 to 56% less of that of the bulk fluid.

Model analysis of nonlinear viscoelastic behaviour by use of a single integral constitutive equation: Stresses and birefringence of a polystyrene melt in intermittent shear flows

Abstract: A single integral constitutive equation with strain dependent and factorized memory function is applied to describe the time dependence of the shear stress, the primary normal-stress difference, and, by using the stress-optical law, also the extinction angle and flow birefringence of a polystyrene melt in intermittent shear flows. The theoretical predictions are compared with measurements. The nonlinearity of the viscoelastic behaviour which is represented by the so called damping function, is approximated by a single exponential function with one parametern. The damping constantn as well as a discrete relaxation time spectrum of the melt can be determined from the frequency dependence of the loss and storage moduli.

Streaming birefringence in extensional flow of polymer solutions

Abstract: The stress and birefringence in liquid filaments undergoing an extensional flow were measured in an isothermal filament-spinning apparatus. In conjunction with these measurements, an experimental arrangement is described which, as subsequent analyses show, overcomes the difficulties associated with the measurement of birefringence in this geometry. The fluids studied were 1 1/2% and 2 1/2% solutions of two polyacrylamides (Separan AP 30 and Separan AP 273) in a 1 : 1 water/glycerol mixture and a 5% solution of polystyrene (Styron 686) in Aroclor 1254. For all solutions studied, the measured birefringence exhibited a non-linear relation to the principal stress difference. In addition, for the polystyrene/Aroclor solution, the birefringence measured in extension was nearly two orders of magnitude higher than the birefringence in shear at comparable deformation rates. These observations imply a greater degree of molecular orientation is produced by the extensional flow than the shear flow and suggest that birefringence data obtained in shear and extension are useful complements to depict a wider range of stress-optical behavior.

Etude rhéologique en régime transitoire de quelques échantillons de sangs humains artificiellement modifiés

Abstract: Une methode tres sensible d'etude in vitro des proprietes rheologiques du sang en regime d'ecoulement transitoire a faible vitesse de cisaillement developpee recemment permet de mettre en evidence avec precision la viscoelasticite et la thixotropie du sang a partir de l'enregistrement de quatre rheogrammes obtenus en quelques minutes, dans des conditions mecaniques differentes et selon un protocole experimental standard bien defini, sur un meme echantillon de sang de quelques cm3. On peut ainsi caracteriser un sang donne au moyen d'un petit nombre de parametres mecaniques.

Rheological characterization of thixotropic fluids

Abstract: The paper presents a phenomenological method of rheological characterization of inelastic thixotropic fluid in viscometric flow. The fluid was regarded as a material of the rate type and a structural parameterκ was defined as one of the variables describing the fluid state. A definition of positive and negative thixotropy was also given. A procedure leading to the construction of a model of thixotropic fluid in the form of an equation of state and a rate equation was proposed. Using the simplest dependence of power law, the model was constructed in an explicite form. It was proved that the experiment of the type “step-change of the shear rate” enables the determination of the five rheological parameters occurring in this model.

The spike-strain test for polymeric liquids and its relevance for irreversible destruction of network connectivity by deformation

Abstract: The basic assumptions ofLodge's rubberlike-liquid constitutive equation for polymer melts and concentrated solutions are summarized. By two additional assumptions — (i) the network disentanglement assumption and (ii) the irreversibility assumption — a modified rubberlike-liquid constitutive equation is obtained, which has been shown to be a valid description of material behaviour in shear and elongational flow. In this paper a novel test — the spikestrain test — is proposed. On the basis of this experiment the assumption of irreversible destruction of network connectivity by deformation can be examined. The significance of the spike-strain test for a larger class of constitutive equations is discussed.

The motion of a slightly deformed sphere in a viscoelastic fluid

Abstract: To study the motion of an arbitrary near sphere immersed in a homogeneous shear flow of an incompressible viscoelastic fluid we impose the restriction that the flow is dynamically and rheologically slow. This allows us to derive an expression for the hydrodynamic force and couple, respectively, which are exerted upon the particle. With the exception of elongational flows marked differences to the behavior in a newtonian fluid show up: sedimentation in a quiescent fluid is accompanied by a rotation until a stable terminal orientation is attained. For prolate spheroids the symmetry axis thus ends up parallel to the direction of the external force and perpendicular to it if the spheroid is oblate. In simple shear the difference between prolate and oblate spheroids manifests itself in the direction in which the rotating symmetry axis drifts (orbit-drift): prolate spheroids drift towards the orbitC = 0 while for oblate ones the drift is towardsC = 0. For deviations from the spheroidal shape (but still fore-aft symmetry) another orbitC * comes into play. Some particles drift towardsC * while others towardsC = 0 if initiallyC < C * and towardsC = ∞ if initiallyC > C *. If no longer matters whether the particle is slender or not. Although this is perhaps the most interesting result obtained one should also mention the behavior of an ovoid in simple shear. If the symmetry axis is parallel to the vorticity vector the resulting translational slip velocity causes the particle to migrate out of the flow-shear plane in the direction of its pointed end.

Dispersion in non-Newtonian fluids: Effects of chemical reaction

Abstract: The dispersion of a solute in non-Newtonian fluids flowing through channels and pipes has been studied by taking into account the homogeneous first-order chemical reaction. It is shown that for the same mean velocity of the flow the equivalent dispersion coefficient decreases as the rate of the chemical reaction increases. This decrease is enhanced due to non-Newtonian nature of the fluid.

Determination of viscometric data from the Brookfield R.V.T. viscometer

Abstract: A computer program has been written which converts torque-speed data obtained from the five “disk-like” spindles of the Brookfield RVT viscometer into shear stress — shear rate data Experimental results obtained on the same samples from the Brookfield viscometer and commercial rheogoniometers are used to demonstrate the utility of the program

Visual observation of flow irregularities in polymer solutions at theta-conditions

Abstract: Polystyrene/decalin solutions exhibit flow irregularities in a cone-and-plate rheometer at theta-conditions. The onset of flow irregularities was found at low shear rates. The elastic component (normal stress) is shown to be responsible for the anomalous flow. The onset of flow irregularities has been predicted from measurements of recoverable strain as a function of shear stress. We suggest that this analysis should be suitable to find the best coating fluid leading to the highest possible speed without exhibiting flow irregularities.

Testing of a constitutive equation with free volume dependent relaxation spectrum

Abstract: A model of non-linear viscoelasticity with relaxation times dependent upon free volume is here proposed. The free volume is related to the isotropic part of the stress tensor by means of a simple differential equation. The model predictions are compared with a large amount of experimental results taken on polymeric melts or concentrated solutions and reported in the literature. The single parameter of the model is determined, within each set of data, by fitting of the viscosity curve. A satisfactory agreement is obtained with data taken under both elongation and shear for which also the relaxation behavior after single and double strain steps is considered.

Some anomalous rheological responses of thermotropic liquid crystals

Abstract: The rheological properties of smectic, nematic and cholesteric thermotropic liquid crystals have been investigated with the Rheometrics Mechanical Spectrometer. Steady flow, relaxation after cessation of steady flow, sinusoidal deformation and step strain modes have been employed. Highly non-linear responses for the smectic systems have been observed which can possibly lead to new areas of applications some of which are briefly discussed.

Dynamic-mechanical properties of a bitumen-silica composite: I. Relation with filler content and bitumen-silica interfacial area

Abstract: SummaryDynamic-mechanical properties of bitumen-silica composite materials, measured at room temperature, do not vary with the volume ratio (φ) in a simple manner as do usual bituminous concretes. However,E′ is a linear function of the interfacial area (φψ) between the filler and the binder per unit volume. ThusE′ = E0′ +a(φψ), wherea is a constant related to the storage modulus, in the absence of voids and with a void ratio factor. The loss moduli, plotted against (φψ) go through a maximum in a similar way as when plotted versus decreasing temperatures.RésuméLes propriétés mécaniques dynamiques, mesurées à la température ambiante, d'un système composite bitume-silice, n'évoluent pas simplement avec la fraction volumique de charges comme dans le cas des enrobés usuels. En effet, le module de conservationE′ varie linéairement avec l'aire de l'interface liant-charge par unité de volume (φψ). Ainsi la relation suivante a pu être mise en évidence:E′ = E0′ +a(φψ), la constantea étant fonction d'un module indépendant du taux de vide et d'un terme relié à ce dernier. Siφψ augmente, les modules de perte passent par une valeur maximale. Ces variations sont semblables à celles que l'on aurait si l'on portait ces modules en fonction de la température.ZusammenfassungDie bei Zimmertemperatur gemessenen dynamischmechanischen Eigenschaften von Bitumen, welches mit Siliziumdioxid gefüllt worden ist, ändern sich nicht in einer so einfachen Weise mit dem Volumenanteilφ des Füllstoffs, wie es bei gewöhnlichen Asphaltbetonen der Fall ist. Dagegen ergibt sich der SpeichermodulE′ als eine lineare Funktion der Grenzflächeφψ zwischen Bindemittel und Füllstoff pro Volumeneinheit:E′ = E0′ +a(φψ), wobeia eine Konstante bedeutet, die zum einen von dem Speichermodul bei Abwesenheit von Hohlräumen und zum andern von einem durch solche Hohlräume bedingten Faktor abhängt. Der Verlustmodul als Funktion vonφψ zeigt ein Maximum ähnlich wie bei der Auftragung gegen die Temperatur.