Showing papers in "Rheologica Acta in 1968"

Constitutive equations from molecular network theories for polymer solutions

Abstract: In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by alternative assumptions concerning the creation and loss of network segments, and the theory is extended to non-Gaussian networks.Kayes theory is extended to allow for the presence of entanglement junctions of different complexities.

Nicht-lineare Effekte beim Strömen viskoelastischer Flüssigkeiten durch Schlitz- und Lochdüsen

Abstract: Nach einem kurzen Uberblick uber die bisher durchgefuhrten theoretischen Untersuchungen betreffend das Einstromen viskoelastischer Flussigkeiten in Schlitzund Lochdusen, sowie uber die in solchen Anordnungen mit Polymerschmelzen gewonnenen experimentellen Ergebnisse werden entsprechende Versuche mit verdunnten Polymerlosungen beschrieben. Besonderes Interesse findet dabei die Abhangigkeit der Effekte von der Gestalt der Dusen. Stationare Zirkularstromungen und elastische Turbulenz (verbunden mit Schwankungen im austretenden Strahl), sowie verschiedene Ubergangsformen zwischen diesen beiden Erscheinungen (periodische Instabilitaten, unsymmetrische stationare Einstromungen) werden beobachtet. In Lochdusen findet oberhalb eines kritischen Durchsatzes ein Wechsel der Strahlform statt: Die ubliche „Zwiebel“ geht momentan in einen schwach divergierenden Kegel uber. Aus den Beobachtungsergebnissen werden einige Folgerungen bezuglich der theoretischen Behandlung der Ubergangsphanomene — als eines „rheodynamischen Stabilitatsproblems“ — abgeleitet.

Shear thickening phenomena in poly(vinyl)alcohol-borate complexes

Abstract: Bizarre rheological properties of shear thickening complexes of poly(vinyl) alcohol and sodium borate have been investigated in Couette flow experiments. At least three distinct types of shear rate induced rheological transitions have been discovered. The type of shear thickening which results when a threshold shear rate is exceeded is reversible, and the threshold shear rate depends upon the composition. Typical rheological behaviorbelow andabove the threshold shear rate are as follows: Type I: shear thinning-shear thickening, Type II: shear thickening-erratic, Type III: Newtonian (low viscosity)-Newtonian (high viscosity). Normal stress effects and time dependent shear thickening have also been observed. The results are interpreted in the light of mechanisms advanced to explain gradient and time dependent shear thickening phenomena. Included is a concise literature survey of shear thickening phenomena.

Dynamic modulus of polyisobutylene solutions in superposed steady shear flow

Abstract: Measurements are reported for the first time of the effect on the dynamic modulus of a viscoelastic liquid of the superposition of a steady shearing orthogonal to the oscillatory shearing. The author believes that the study of this flow, together with the case of parallel superposition of a steady and an oscillatory shearing, will clarify the importance of the second invariant of the rate of deformation tensor used in a number of rheological equations of state for viscoelastic liquids. 8.54, 6.86 and 5.39% solutions of polyisobutylene in cetane were studied using a recently developed electromagnetic transducer over the frequency range 0.3 to 150 c.p.s. Preliminary experiments on the orthogonal superposition of two oscillatory shear flows are also reported.

Some basic viscous flows in micropolar fluids

Abstract: This paper analyzes some basic viscous flows of micropolar fluids. The problems ofCouette andPoiseuille flows between two parallel plates and a rotating fluid with a free surface, are solved using the theory of micropolar fluids. The results are presented graphically and compared with the classical ones, and the differences are discussed.

On the use of a rheogoniometer: Part III. Oscillatory shear between parallel-plates

Abstract: Further consideration is given to the usefulness of theWeissenberg Rheogoniometer in the characterization of elastico-viscous liquids. The theory for free and forced oscillation experiments in the parallel-plate system is developed. The advantages of the parallel-plate geometry in the case of forced oscillation experiments is stressed, and the limited value offree oscillation experiments is indicated.

Entropie im Nichtgleichgewicht

Abstract: In der Kontinuumsphysik ist der Entropiebegriff nur fur den Fall des thermodynamischen Gleichgewichtes entwickelt. Am Beispiel elektrischer Netzwerke wird auseinandergesetzt, das bei Vorgangen eine Entropie nicht eindeutig definiert werden kann. Es wird jedoch gezeigt, das die Gesetze der Kontinuumsphysik auch ohne den Entropiebegriff entwickelt werden konnen. Dies gelingt mittels der sogenannten fundamentalen Ungleichung, welche in Parallele zur Passivitatseigenschaft elektrischer Netzwerke steht und welche mit dem zweiten Hauptsatz begrundet werden kann. Bei kleinen Abweichungen von einem festen Bezugszustand gewinnt man leicht detaillierte Ergebnisse. Schlieslich werden einige Moglichkeiten zur Definition einer Entropie bei Vorgangen diskutiert; sie zeigen deutlich, das die Entropie bei Vorgangen vom Beobachter und den ihm zugestandenen Mes- (d. h. Informations-) moglichkeiten abhangt.

The measurement of normal-stress differences using a cone- and-plate total thrust apparatus

Abstract: The proposal ofJackson andKaye (1966) for evaluating both differences of normal stress in a viscometric flow by using only total thrust measurements in a cone- and-plate viscometer is extended. An analytic relation valid for all values of the separation between cone and plate is obtained, which is shown to include as special cases the well-known cone- and-plate formula, the parallel-plate formula ofKotaka et al. (1959) andJackson andKaye's.

The static drag on bodies in Bingham plastics

Abstract: A good indication of the static drag force experienced by a body immersed in a Bingham plastic can be obtained by summing the static yield stress over the cross-sectional area of the body normal to the direction of movement of the plastic and multiplying the result by 16.7. The actual drag may be slightly higher in the case of a disc or a sphere than for a cylinder or a rectangular plate, and an additional factor may be required if the length of the body parallel to the flow exceeds its width. The mechanism of transmission of the force from the Bingham plastic to the immersed body is not understood at present.

Das Fließen ebener Schichten inkompressibler viskoelastischer Flüssigkeiten mit einer in Ablaufrichtung infinitesimal gestörten freien Oberfläche

Abstract: Die rheostatische Aufgabe des isothermen Ablaufens und Verlaufens von nicht fluchtigen, chemisch bestandigen und physikalisch homogenen dunnen Schichten (beispielsweise Anstrichschichten) aus inkompressiblen viskoelastischen (Rivlin-Ericksen-) Flussigkeiten mit einer freien, in Ablaufrichtung infinitesimal gestorten Oberflache und einer an einem beliebig geneigten, ebenen, nicht saugfahigen Festkorper haftenden Sohle unter dem Einflus von Schwere und Kapillaritat, aber unter Ausschlus von Massentragheit wird in einer linearen Theorie behandelt.

Les contraintes normales et les spectres de relaxation dans les systèmes polymères

Abstract: Ce memoire considere les relations entre les contraintes normales qui naissent au cours des deformations de cisaillement des systemes polymeres fluides (effetWeissenberg) et leurs spectres de relaxation. Les auteurs montrent que la croissance des contraintes tangentielles et leur relaxation evoluent plus rapidement que celles des contraintes normales. Une formule qui a ete etablie de determiner le spectre de relaxation en fonction des variations des contraintes normales en regime transitoire de de deformation. Il a ete demontre que le coefficient des contraintes normales dans le domaine lineaire est identique a la deformabilite (compliance) d'equilibre. Cette conclusion est confirmee par plusieurs resultats experimentaux. Il decoule de la l'applicabilite de la formule deLodge qui donne une relation entre les contraintes et les deformations elastiques dans le domaine lineaire de comportement mechanique des systemes visco-elastiques. Les auteurs examinent les relations entre les contraintes et la vitesse de cisaillement et entre le module dynamique et la frequence aussi bien dans les domaines lineaire et non lineaire.

A torsional creep apparatus

Abstract: This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10−8 m2/N, in the time range between 1 and 105 seconds. Within five minutes and with an accuracy of 1 ‡C, the temperature of the specimen can be adjusted to any value between −175 and –200 ‡C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10−3.

Evaluation of calculated entanglement spacings for undiluted linear amorphous polymers

Abstract: In reality, entanglements based on rheological measurements have been essentially defined operationally as a kinetic or time delay effect present in concentrated polymer systems. This is where intuitively molecular loops or overlap and entanglements of polymer chains are most likely to occur. The evaluation in fig. 2 suggests that the theory of rubber elasticity, even discounting the inherent imprecision of measurements, gives anM e which is not relatable to polymer composition 1and chain structure. Conversely reliable and internally consistent values ofM c can come from the molecular weight dependence of: 1.Newtonian viscosities, 2.NMR relaxation times, and 3 the shear dependence of viscosities, see fig. 1. However, entanglement spacings calculated in this way lack adequate theoretical substantiation particularly as to the mechanism of flow. Nonetheless, the correlation ofM c with composition and structure is convincing and provides a sound empirical correlation and the basis for a renaissance in theoretical interpretation of viscoelastic behavior of linear amorphous polymers. Further theory must rationalize the fact that the shear compliance, which is proportional toM e , depends on a combination of molecular weight averages involvingZ andZ+1. Yet the break in viscosity-molecular weight curves yieldingM c has been generally confirmed to depend on only weight average molecular weight. The values ofM c appear worthy of further experimental and theoretical evaluation. The values ofM e appear to be based on experimental techniques that at present do not provide sufficient precision to warrant citation of such values molekular weight distribution is thought to have an important yet ill-defined influence on calculated values of M e .

Die Strömung viskoelastischer Flüssigkeiten in einem konvergenten Kanal

Abstract: Ausgehend von einer Entwicklungsschreibweise des rheologischen Zustandsgesetzes fur viskoelastische Flussigkeiten wird das Stromlinienfeld in einem konvergenten Kanal bestimmt. Die Stromfunktionψ sowie die Geschwindigkeitv sind hierbei regulare Funktionen des DurchsatzesQ, als dessen Potenzreihe alsoψ undv erscheinen. Der Koeffizient vor jeder PotenzQv wird aus der Entwicklung des Theologischen Zustandsgesetzes bis zurv-ten Ordnung bestimmt.

Laminar velocity profile development in straight pipes of circular cross section

Abstract: Velocity profile development has been studied experimentally in Newtonian and some non-Newtonian fluids. The entry length for the development of 99% of the terminal axial velocity from an initially flat profile has been found to be given byZe = 1.1–0.112N(Re) for laminar flow Reynolds numbers between 1 and 1500 with Newtonian fluids. There were substantial increases in this length for weakly visco-elastic aqueous solutions of polyethylene oxide and polyacrylamide in the Reynolds number range (between 1 and 10) where these have been studied.

Plastifiziermodelle für die Verarbeitung benetzender und nichtbenetzender Thermoplaste auf Einschnecken-Extrudern

Abstract: Die Untersuchungen mit verschiedenen PVC hart-Ansatzen haben gezeigt, das das Plastifizierungsmodell vonMaddock undStreet nur auf mittel- und niedrigviskose, benetzende Thermoplaste anzuwenden ist und fur hochviskose nicht benetzende Thermoplaste keine Gultigkeit hat.

The Correlation of non-newtonian turbulent pipe-flow data

Abstract: Several formulae have been proposed for treating non-newtonian pipe flow friction data, and with one exception they rely in some way on laminar data for predicting turbulent data. Perhaps the most widely accepted and quoted of these formulae is that due toDodge andMetzner (2) which is also stated to be rigorous. Some consideration is given to theDodge-Metzner equation which seems to show that far from being rigorous it is not valid for real fluids. Moreover the formula ofBowen (1), which is the exceptional case not requiring laminar flow data, gives superior correlations and is, therefore, to be preferred. Using a diameter independence hypothesis andBowen's, formula it is possible to find an expression for the turbulent velocity profile. This is checked indirectly by comparing the theoretical and experimental friction factors. In a number of cases (but not all) the comparison is favourable.

Neue Ergebnisse zum Einfluß der Elastizität bei der Kapillarströmung von konzentrierten Polymerlösungen unter hohem Schergefälle

Abstract: An konzentrierten Losungen von Polyisobutylen in Toluol und Polyathylenglykol in Wasser wurden Messungen des Fliesverhaltens im Hochdruckkapillarviskosimeter durchgefuhrt, wobei die Dimensionen der Kapillaren im Rahmen der Langen/Radien-Verhaltnisse von 200 bis 4000 variiert wurden, Dabei ergaben sich deutlich kapillarabhangige Flieskurven.

A simple extension apparatus for dilute gelatin gels

Abstract: An apparatus has been designed and constructed which allows the rupture properties of dilute gelatin gels to be studied Breaking stresses in the range 17×104 to 1×106 dyne cm−2 have been determined; extension at break varied between 46 and 155%

Zum zeitlichen Verlauf des Kriechens von Zementstein und Beton

Abstract: Es wird eine Kriechfunktion abgeleitet, die die bekannten, empirisch bestimmten Kriechfunktionen als Spezialfalle enthalt. Fur die relative Endkriechverformung ergibt sich sowohl aus der exakten Losung als auch aus den Naherungen der Wert 2σ/E. Fur die Halbwertszeit, nach der die Halfte des Endkriechmases erreicht wird, bekommt mann = 2l RZ′ α, E.

On the stability of elastico-viscous flows

Abstract: The stability ofCouette flow and planePoiseuille flow of an elastico-viscous liquid is analyzed. It is found that in both cases the flow is less stable than that of Newtonian liquids. The critical wave number is also changed due to the elasticity of the liquid. These changes depend on the type of flow under consideration.

Effect of concentration and polydispersity on flow birefringence of polystyrene

Abstract: Normal stresses were estimated from viscosity and flow birefringence measurements on solutions and melts of substantially two samples of polystyrene. A large range of concentration and temperatures was covered. The interpretation of results was tried along lines originally handled for dilute solutions only. In meeting the requirements of this method, a well-known reduction scheme with respect to concentration (and temperature) was rediscussed and applied. For the sample with a narrow molecular weight distribution this procedure was very satisfactory. For the polydisperse sample, however, the reduction with respect to concentration was only partly successful. For this latter sample it could be shown that results on very dilute solutions corresponded with those on the bulk polymer. This is in favour of the current concept for molten bulk polymers and, in particular, of the interpretation given to polydispersity effects. Deviations at intermediate concentrations are qualitatively interpreted in terms of an inhomogeneous dispersion of solvent between high and low molecular weight species.

Secondary flows induced by the rotation of a sphere or coaxial cones in micropolar fluids

Abstract: The micropolar fluids like Newtonian and Non-Newtonian fluids cannot sustain a simple shearing motion, wherein only one component of velocity is present. They exhibit both primary and secondary motions when the boundaries are subject to slow rotations. The primary motion, as in Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., resembles that of Newtonian fluid for slow steady rotation. We further notice that the micro-rotation becomes identically equal to the vorticity present in the fluid and the condition b) of "Wall vorticity" can alone be satisfied at the boundaries. As regards, the secondary motion, we notice that it can be determined by the above procedure for a special class of fluids, namely that for which j0(n2-n3)=4 n3/l2. Moreover for this class of fluids, the micro-rotation is identical with the vorticity of the fluid everywhere. Also the stream function for the secondary flow is identical with that for the Newtonian fluid with a suitable definition of the Reynolds number. In contrast with the Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., this class of micropolar fluids does not show separation. This is in conformity with the statement of Condiff and Dahler (3) that in any steady flow, internal spin matches the vorticity everywhere provided that (i) spin boundary conditions are satisfied, (ii) body torques and non-conservative body forces are absent, and (iii) inertial and spin-inertial terms are either negligible or vanish identically.

A capillary rheometer for dilute polymer solutions

Abstract: A capillary rheometer developed by TNO enables, in principle, a reliable determination of the viscosity of dilute polymer solutions in the range of shear rates, where also measurements of the flow birefringence can be performed. For Newtonian liquids, agreement with the results ofUbbelohde measurements was found. For moderately concentrated solutions, however, a difference with the results ofUbbelohde measurements was observed, which may point to the presence of an elastic entrance effect in the latter measurements.

Kurzer Beitrag zur Berechnung des Relaxationsspektrums: Generalisierter Iterationsprozeß zur Berechnung des Relaxationsspektrums Roesler — Twyman für den veränderlichen Iterationsparanieter

Abstract: Mittels des oben beschriebenen Rechnungsverfahrens stabilisiert die gewonnene Funktion des Relaxationsspektrums ihre Grundform fur die positiven Werte des Spektrums ebenso schnell wie die Funktionen, welche mittels der ursprunglichen MethodeRoesler-Twyman(2) gewonnen werden.