Showing papers in "Rheologica Acta in 1976"
TL;DR: In this article, nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods and a theoretical description is given to explain the kinetic transition of fluid polymer media into high elasticity state at temperatures above the flow temperature.
Abstract: Nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.
509 citations
TL;DR: In this paper, a single integral constitutive equation is presented, which gives a reasonable description of the non-linear shear and elongational behavior of a low-density branched polyethylene melt at constant strain rate observed by Meissner.
Abstract: A single integral constitutive equation is presented, which gives a reasonable description of the non-linear shear and elongational behavior of a low-density branched polyethylene melt at constant strain rate observed byMeissner. The memory function of this integral equation is a product of the memory function of Lodge's rubber like-liquid theory and a damping functionh = exp [ —n\(h = \exp [ - n\sqrt {I_2 - 3} ]\)], whereI2 is the second invariant of the Finger tensor. Stress- and normal stress overshoot are described as well as shear rate dependence of the transient shear viscosity and the first normal stress coefficient. Tensil stress overshoot and a finite, rate-dependent steady-state elongational viscosity is predicted in simple elongational flow.
336 citations
TL;DR: In this article, an approximate closed form analytical solution has been obtained for the motion of a solid sphere in powerlaw fluids and this solution was verified experimentally using boundary layer theory; the results were used to separate form and skin friction.
Abstract: This is essentially an engineering study undertaken with a view to providing drag coefficient correlations for the motion of a solid sphere in inelastic and viscoelastic fluids over a wide range of Reynolds numbers. An approximate closed form analytical solution has been obtained for the motion of a solid sphere in powerlaw fluids and this solution has been verified experimentally. The high Reynolds number flow was analysed theoretically using boundary layer theory; the results were used to separate form and skin friction. Viscoelastic fluids showed “drag reduction” at high Reynolds number. About 300 experimental data points were used to obtain drag coefficient correlations over a wide range of material and flow parameters.
129 citations
TL;DR: In this article, two different apparatuses for measuring the elongational behavior of polymer melts at constant tensile stress and constant elongational strain rate are described, and the recoverable strain increases with growing deformation and reaches a constant value in the steady-state.
Abstract: Two different apparatuses for measuring the elongational behaviour of polymer melts at constant tensile stress and constant elongational strain rate are described. Measurements on a low density polyethylene were carried out up to stretching ratios of 400. The homogeneity of sample deformation in both test methods was sufficient to reach a steady-state of elongational flow where the tensile stress and the strain rate as functions of time are constant. By unloading the molten rod the recoverable strain can be determined at any state of deformation. The recoverable strain increases with growing deformation and reaches a constant value in the steady-state. The elongational viscosity calculated from the rate of viscous flow agrees with the Trouton viscosity in the case of very small deformations only. With growing deformation the elongational viscosity increases up to a constant value in the steady-state which is greater than the Trouton viscosity by about a factor of six at measured strain rates of 0.03 s−1 and 0.1 s−1, respectively. The elongational viscosity and the recoverable strain in the steady-state measured with the two different test methods under the same experimental conditions are in good agreement.
117 citations
TL;DR: In this paper, a rheologic theory has been compared to results of different shear experiments in the region of moderate elastic strains using a polymer solution as an example using the Weissenberg Rheogoniometer.
Abstract: In the present paper a rheologic theory (1) has been compared to results of different shear experiments in the region of moderate elastic strains using a polymer solution as an example. The 40% butyl rubber solution (M ≈ 3 ⋅ 104) in transformer oil has been employed as tested liquid. A major part of the experimental data has been obtained on the Weissenberg Rheogoniometer. The three and five constants rheologic models (the first and second approximations) have been discussed. Model constants have been defined in the linear region of the rheologic behaviour of the solution using dynamic characteristics.
107 citations
TL;DR: In this paper, a two-constants memory function is presented, which gives a qualitative description of the non-linear elongational behavior of a low-density polyethylene melt at constant elongation rate observed by Meissner.
Abstract: Based onLodge's theory of rubberlike liquids, a two-constants memory function is presented, which gives a qualitative description of the non-linear elongational behavior of a low-density polyethylene melt at constant elongation rate observed byMeissner. The two material constants necessary for the description are the steady-state zero-shear viscosity and a characteristic time constant, which can be determined from experiments in the linear viscoelastic region.
60 citations
TL;DR: The slow motion of a rigid sphere in a viscoelastic fluid is studied in this paper, where only rheologically slow flows are employed and the resulting hydrodynamic force and couple are calculated and shown to be fundamentally different from the corresponding results in a Newtonian fluid.
Abstract: The slow motion of a rigid sphere in a viscoelastic fluid is studied. Variations of the velocity gradient of the undisturbed fluid motion over the dimension of the sphere are neglected. Considering only rheologically slow flows the equations of a second-order fluid are employed. The resulting hydrodynamic force and couple are calculated and shown to be fundamentally different from the corresponding results in a Newtonian fluid: for the force a coupling is found not only for translation and rotation but also for translation and a pure straining motion. For the torque only a coupling between rotation and a pure straining motion exists. It is demonstrated that by means of this coupling the two material parameters can be obtained individually. Furthermore any lateral migration of a sphere in a vertical Poiseuille flow would immediately unmask the fluid as a non-Weissenberg fluid.
50 citations
TL;DR: In this paper, the so-called stress-optical law is checked with the aid of flow birefringence technique, which is used for the analysis of polymer melts.
Abstract: Transient stresses including normal stresses, which are developed in a polymer melt by a suddenly imposed constant rate of shear, are investigated by mechanical measurement and, indirectly, with the aid of the flow birefringence technique. For the latter purpose use is made of the so-called stress-optical law, which is carefully checked.
49 citations
TL;DR: In this article, a series of models for the prediction of the viscoelastic behavior of isotropic soft polymers was developed for the time dependent stress through the Boltzmann superposition integral incorporating into it an appropriately chosen nonlinear measure of strain.
Abstract: Restricting consideration to deformations in which time shift invariance is preserved, a series of models was developed for the prediction of the viscoelastic behavior of isotropic soft polymers. The models describe the time dependent stress through the Boltzmann superposition integral incorporating into it an appropriately chosen nonlinear measure of strain. The theory was developed in its most general threedimensional form. It requires a single time function, the relaxation modulus of linear viscoelastic theory. In its simplest form the strain measure contains a single material parameter.
40 citations
TL;DR: In this article, a kurzen Uberblick is described, in which Beziehungen zwischen Widerstandsverminderung (drag reduction) and Laminarisierung bei verdunnten Losungen sehr langkettiger Polymerer in einer Rohrstromung · wird auf die bisherigen Untersuchungen der Stabilitat solcher Losungens in der Couette-Stromung eingegangen, and es werden die noch best
Abstract: Nach einem kurzen Uberblick uber die Beziehungen zwischen Widerstandsverminderung (drag reduction) und Laminarisierung bei verdunnten Losungen sehr langkettiger Polymerer in einer Rohrstromung · wird auf die bisherigen Untersuchungen der Stabilitat solcher Losungen in der Couette-Stromung eingegangen, und es werden die noch bestehenden Unklarheiten und Widerspruche aufgezeigt. Anschliesend werden die zur Durchfuhrung der eigenen Untersuchungen konstruierte Couette-Apparatur sowie die Methoden der Temperierung und der Sichtbarmachung der Stromung beschrieben.
38 citations
TL;DR: The motion of a sphere, freely suspended in a second-order fluid under the condition of a nonhomogeneous flow field is investigated in this article, neglecting fluid inertia and, to be consistent, also particle inertia.
Abstract: The motion of a sphere, freely suspended in a second-order fluid under the condition of a non-homogeneous flow field is investigated. Neglecting fluid inertia and, to be consistent, also particle inertia a general result is derived. For Couette flow between rotating cylinders as well as for two-dimensional and circular Poiseuille flow, respectively, excellent agreement with experimental observations results. While for the two-dimensional converging flow essentially no deviation from the corresponding results for a Newtonian fluid is found drastic differences show up for the converging flow in a conical duct. Preferably in the narrow cones rather large spheres come to a halt (Uebler-effect). For small spheres no such effect is predicted but a now phenomenon arises: For cones whose half angle lies close to 80° or exceeds that value some of the spheres end up in the region of secondary flow. The resulting separation effect could be diminished by decreasing the cone angle.
TL;DR: In this article, a modified cone-and-plate apparatus was designed for the measurement of the flow birefringence of polymer melts in a wide range of shear rates.
Abstract: A description is given of a modified cone-and-plate apparatus designed for the measurement of the flow birefringence of polymer melts in a wide range of shear rates. Results are given of measurements on samples of high and low density polyethylene and polystyrene. Anomalies, as found in the extinction angle curves near the fringes, where the phase differences become equal to multiples of 2π, point to pronounced edge effects which appear to depend on the type of polymer. The measurements on the high density polyethylene were used to check the validity of the stress-optical law. The measurements on the low density polyethylene sample show mechanical degradation of this polymer. Some typical transient measurements on the polystyrene sample are presented and successfully related to the corresponding mechanical measurements, as obtained with the aid of a cone-and-plate Weissenberg rheogoniometer.
TL;DR: In this paper, the slip velocity in the direction of the flow so that the apparent viscosity goes down by increasing the ratio of the length of the molecules to the distance between the plates.
Abstract: In the vicinity of a wall the behavior of the molecules of a fluid is not only influenced by neighboring molecules but also by the wall. For a macromolecular solution this implies that the constitutive equations cannot be employed in any finite system except for the calculation of average quantities if, in addition, one accounts for a velocity slip at the solid wall. For planeCouette flow of a dilute solution of flexible macromolecules idealized asHookean dumbbells the slip velocity,u s , is evaluated under the assumption that the interaction between the solute molecules and the wall is a hard core repulsion. This furnishes a slip velocity in the direction of the flow so that the apparent viscosity goes down by increasing the ratio of the length of the molecules to the distance between the plates. Increasing the intrinsic viscosity and/or the concentration will enhance that effect.
TL;DR: In this article, a coaxial cylinder was used for the measurement of flow birefringence of polymer melts at extremely low shear rates (10−3 s−1) under transient conditions.
Abstract: A description is given of a coaxial cylinder apparatus, suitable for the measurement of the flow birefringence of polymer melts at extremely low shear rates (~10−3 s−1) and, in particular, under transient conditions.
TL;DR: In this article, a gute Ubereinstimmigung zwischen dem errechneten and dem gemessenen Stutzluftdruck unter der Annahme einer mittlerennewtonschen Viskositat erhalt, die mit zunehmendem Abzugsverhaltnis stark abnimmt.
Abstract: Die bisherige Forschung hat gezeigt, das die getrennte Untersuchung der rheologischen und der thermischen Vorgange beim Folienblasprozes zu keiner vollstandigen Analyse des Verfahrens fuhrt. Nachdem durch intensive experimentelle Arbeiten in den letzten Jahren der Abkuhlvorgang und damit die thermischen Randbedingungen des Folienblasverfahrens geklart wurden, ist jetzt eine derartige Analyse moglich. Die auf Grund des aufgestellten Modells fur verschiedene Betriebspunkte berechneten Werte von Stutzluftdruck und Abzugskraft werden mit experimentellen Ergebnissen verglichen. Dabei zeigt es sich, das man eine gute Ubereinstimmung zwischen dem errechneten und dem gemessenen Stutzluftdruck unter der Annahme einer mittlerennewtonschen Viskositat erhalt, die mit zunehmendem Abzugsverhaltnis stark abnimmt. Die gemessene Abzugskraft last sich jedoch nicht ohne Berucksichtigung elastischer Effekte erklaren.
TL;DR: In this article, a model for analysing the Fliesens einer direkt an der Dusenwand gleitendenOstwald-deWaele-Flussigkeit (Potenzgesetz) wird ein Modell entwickelt, das die rheologischen Vorgange „tribologisch“, d. h. analog derCoulombschen Reibung fester Korper beschreibt.
Abstract: Zur Analyse des Fliesens einer direkt an der Dusenwand gleitendenOstwald-deWaele-Flussigkeit (Potenzgesetz) wird ein Modell entwickelt, das die rheologischen Vorgange „tribologisch“, d. h. analog derCoulombschen Reibung fester Korper beschreibt. Es zeigt sich, das in der Duse zwei Bereiche zu unterscheiden sind: ein Haftbereich in der Nahe des Duseneinlaufs und ein am Dusenaustritt liegender Gleitbereich. Die Lange des Gleitbereichs, der Verlauf des Drucks und der Schubspannung langs der Duse sowie die Anderung des Geschwindigkeitsprofils im Gleitbereich werden ermittelt. Uberschreitet die Wandschubspannung einen kritischen Betrag, so entsteht am Dusenende ein labiler Bereich, in dem der Betrag der Wandschubspannung sprunghaft auf einen kleineren Wert sinken kann. Der von verschiedenen Autoren gefundene Sprung in der Flieskurve bestimmter Polymerschmelzen kann damit grundsatzlich erklart werden.
TL;DR: In this paper, the rheology of lecithin was studied as a function of concentration in both water and hydrocarbon solvent, and the results were described by a modified Einstein equation.
Abstract: The rheology of lecithin was studied as a function of concentration in both water and hydrocarbon solvent. The results in hydrocarbon solvent were very Newtonian and could be described by a modified Einstein equation. The aqueous solutions were studied in dilute solution where micelles are formed and in more concentrated solution where the lyotropic smectic liquid crystal is the predominating structure. The viscosity of the aqueous solutions was very non-Newtonian and a concentration-shear rate superposition curve could be constructed in spite of the occurrence of a phase transition. The results could be described in terms of a yield stress or a Bingham body. Unexpected non-linearities in the viscoelastic behavior were observed.
TL;DR: In this paper, an explicit solution to the Stokes problem for a sphere in an arbitrary flow field is obtained, valid even under conditions that the sphere is so small that the customary no-slip assumption need no longer be valid (Richardson).
Abstract: A system consisting of an incompressible Newtonian fluid in which solid particles of spherical shape are suspended is investiged. Employing irreducibleCartesian tensors an explicit solution to the Stokes problem for a sphere in an arbitrary flow field is obtained, valid even under conditions that the sphere is so small that the customary no-slip assumption need no longer be valid (Richardson). Since in that case Brownian motion cannot be neglected the effect of thermal agitation is studied. While no influence is found for a Couette flow the results for Poiseuille flow are markedly effected: In a vertical tube flow a nonuniform radial distribution of spheres results while for horizontal Poiseuille flow the effective viscosity becomes dependent upon the sphere radius. It increases with increasing sphere radius and is always larger than the corresponding result for truly neutrally buoyant spheres. These results are obtained from the equations governing the mechanical behavior of such a suspension, equations which are derived by means of ensemble averages. The advantage of these averages over the volume averages is demonstrated.
TL;DR: In this article, the authors give theoretical and experimental consideration to the stress overshoot phenomenon and attempt to distinguish between apparent overshoot arising from instrument effects and real overshoot which can be regarded as a property of the material.
Abstract: We give theoretical and experimental consideration to the stress overshoot phenomenon and attempt to distinguish between (apparent) overshoot arising frominstrument effects and (real) overshoot which can be regarded as a property of the material. The experiments are performed on a Weissenberg Rheogoniometer and particular attention is paid to the effect of the natural frequency of the torquemeasuring system and also to edge effects. The experimental results for Newtonian liquids are found to be in excellent quantitative agreement with the theoretical predictions. In the case of elastic liquids, the experimental results are in qualitative agreement with the predictions for a simple elastico-viscous model. We do not find any significant evidence of aberrations due to edge effects. It is concluded that although stress overshoot can be significantly affected by instrument factors, it is nevertheless a true material property.
TL;DR: In this paper, the erste Normalspannungsdifferenz von viskoelastischen Flussigkeiten bestimmen kann be found.
Abstract: Es wird beschrieben, wie man mit Hilfe des „Mechanischen Spektrometers“ der Firma Rheometrics Inc. die erste Normalspannungsdifferenz von viskoelastischen Flussigkeiten bestimmen kann. Bei der Durchfuhrung dieser Messungen in einer Kegel-Platte-Anordnung traten Normalkraftschwankungen auf, die sich als von einer sehr geringen Axialbewegung der Antriebswelle herruhrend nachweisen liesen. Die an linearen Polysiloxanen durchgefuhrten Messungen zeigten in einem weiten Bereich ein Fliesverhalten entsprechend einer Theorie zweiter Ordnung. Bei Stoffen mit hinreichend enger Molmassenverteilung hangt der mittlere Elastizitatsmodul weder von der mittleren Molmasse noch von der Temperatur merklich ab. Bei orientierenden Messungen an wasrigen Losungen von relativ niedermolekularem Polyacrylamid last sich ein unterer Bereich nachweisen, in dem die Losung ebenfalls das Verhalten einer Flussigkeit zweiter Ordnung zeigt, sowie ein oberer Bereich, in dem Schubspannung und erste Normalspannungsdifferenz entsprechend einem Potenzgesetz anwachsen.
TL;DR: In this paper, it is shown how the interpretation of dynamic experiments on fluids in terms of apparent Maxwell parameters is more simple, more sensitive, more consistent with steady flow behaviour, and physically more realistic.
Abstract: To define the dynamic shear behaviour of a viscoelastic fluid we require two functions — one elastic and one viscous There are two simple alternatives based on the Voigt and Maxwell concepts which are mathematically interrelated Current practice interprets the dynamic response of fluids as a function of angular frequency (ω) in terms of the storage (G′) and loss (G″) moduli: the loss function is commonly converted to a viscosityη′ = G″/ω As is well known the parametersη′ andG′ are the elements of a Voigt model whereas it is near universal practice to interpret steady flow in terms of the Maxwell model This paper shows how the interpretation of dynamic experiments on fluids in terms of the apparent Maxwell parameters is more simple, more sensitive, more consistent with steady flow behaviour, and physically more realistic
TL;DR: In this paper, the authors used continuous shear viscometry and creep testing on two major mesophases previously found in systems containing phosphated nonyphenol ethoxylate (PNE), phosphated fatty alcohol (PFE), water and n-hexane.
Abstract: Rheological measurements have been carried out using continuous shear viscometry and creep testing on two major mesophases previously found in systems containing phosphated nonyphenol ethoxylate (PNE), phosphated fatty alcohol ethoxylate (PFE), water andn-hexane. Systems containing lamellar liquid crystals exhibited a clockwise (rheopectic) hysteresis loop on the Ferranti-Shirley cone-and-plate viscometer which increased in area with increasing water content. On the other hand, both the hexagonal liquid crystalline phase and an intermediate amorphous gel phase showed an anti-clockwise (thixotropic) hysteresis.
TL;DR: In this article, an eigens fur hohe Schergeschwindigkeiten entwickelten Kegel-Platte-Rheometer wird wahrend des Schervorganges das Drehmoment, die Axialkraft and die Druckverteilung in Abhangigkeits vom Radius im Scherspalt gemessen Scherexperimente an Silikonol with konstanter Schergeshwindig keiten ergeben, das sowohl die Grose als
Abstract: Mit einem eigens fur hohe Schergeschwindigkeiten entwickelten Kegel-Platte-Rheometer wird wahrend des Schervorganges das Drehmoment, die Axialkraft und die Druckverteilung in Abhangigkeit vom Radius im Scherspalt gemessen Scherexperimente an Silikonol mit konstanter Schergeschwindigkeit ergeben, das sowohl die Grose als auch der zeitliche Verlauf der gemessenen Axialkraft stark vom Offnungswinkel des Scherspaltes beeinflust wird Die normierte Darstellung der bei einem Experiment gemessenen Drucke zeigt eine sehr starke Abhangigkeit der zeitlichen Druckverlaufe vom Radius Die erwartete logarithmische Abhangigkeit der Drucke stellt sich nach dem Scherbeginn erst dann ein, wenn die Axialkraft ihr Maximum erreicht hat und sich nur noch langsam andert Die wahrend des Axialkraftanstieges aus der Axialkraft berechneten Normalspannungen sind somit nicht die erwarteten Materialfunktionen Vergleichbare Einflusse zeigen sich auch beim Abfall der Axialkraft nach dem Abbremsen eines Scherexperimentes
TL;DR: In this paper, Kriechverhalten von Plastomeren mit Hilfe von kriechfunktionen in Form of Prony-Dirichlet-Reihen sehr gut beschreiben.
Abstract: Unterhalb der Glastemperatur kann man das Kriechverhalten von Plastomeren mit Hilfe von Kriechfunktionen in Form von Prony-Dirichlet-Reihen sehr gut beschreiben. Zahlreiche einachsige Kriechversuche zeigen, das zusammen mit dem erwarteten Temperatureinflus auch ein Einflus der anliegenden Spannung auftritt, welcher nicht vernachlassigt werden kann.
TL;DR: In this article, an unusual drag reducing behaviour of the nonionic surfactant Lubrol 17 A 10 in the presence of the electrolyte K2SO4 has been observed, showing normal turbulent flow behaviour at room temperature, but depicts an ability to reduce friction when flowing at a temperature at and around its cloud point.
Abstract: An unusual drag reducing behaviour of the nonionic surfactant Lubrol 17 A 10 in the presence of the electrolyte K2SO4 has been observed. The system shows normal turbulent flow behaviour at room temperature, but depicts an ability to reduce friction when flowing at a temperature at and around its cloud point. The consequences of this elevated temperature drag reduction have been discussed from the viewpoint of using drag reducers in central heating systems.
TL;DR: In this paper, a Torsional Balance rheometer is used to measure shear and normal stress functions of greases. But the torsional flow between parallel plates is not held constant and the plate separation is allowed to adjust until the normal force is balanced by the axial load.
Abstract: A new instrument, a Torsional Balance rheometer, has been used to measure shear and normal stress functions of lubricating greases. The new rheometer is based on torsional flow between parallel plates, but differs from conventional torsional flow instruments in that the plate separation is not held constant but allowed to adjust until the normal force is balanced by the axial load. In dealing with materials that have a yield stress, such as greases, the Torsional Balance rheometer is superior to fixed-plate rheometers since the zero of the normal force measurement is not dependent on the yield stress. Results have been compared with those obtained on a capillary viscometer and a Weissenberg rheometer.
TL;DR: In this article, flow activation energy was deduced by a classical shear rate-temperature superposition method, and the obtained value suggests an aggregates flow mechanism for the star-shaped product.
Abstract: Flow curves and viscosity functions at 160, 180, 200 and 220 °C have been determined for a star-shaped butadiene-styrene block copolymer, by means of a slit die rheometer. At a critical shear stress, a transition occurs in flow curves, which suggests a modification in the melt structure. The flow activation energy is deduced by a classical shear rate—temperature superposition method, and the obtained value suggests an aggregates flow mechanism for the star-shaped product. Exit pressure and entrance pressure drop are obtained and show a dependence on the slit depth.
TL;DR: In this article, necessary and sufficient conditions to establish that a velocity field gives rise to a motion with constant stretch history are developed and illustrated with a number of examples, and extensions to determine whether a given strain history is of the above type are also made.
Abstract: Necessary and sufficient conditions to establish that a velocity field gives rise to a motion with constant stretch history are developed and illustrated with a number of examples. Extensions to determine whether a given strain history is of the above type is also made.