Dynamic measurements on polymer solutions and melts

Summary An apparatus for the measurement of the dynamic viscosity is described. In a coaxial cylinder geometry forced vibrations are executed in the frequency region from 2·10^–4 to 50 cycles/sec. Fluids with a wide range of viscosities (10^–1 to 10⁷ poise) can be measured. A number of experimental results obtained on dilute solutions and melts of polymers are given and compared with results of the molecular theories.

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Zusammenfassung Es wird ein Gerät für die Messung der dynamischen Viskosität beschrieben. Innerhalb eines koaxialen Zylindersystems werden im Frequenzgebiet von 2 · 10^–4 bis 50 Hz erzwungene Schwingungen ausgeführt. Messungen an Flüssigkeiten sind in einem weiten Viskositätsbereich (10^–1 bis 10⁷ Poise) möglich. Einige Messungen an verdünnten Lösungen oder Schmelzen von Hochpolymeren werden mitgeteilt und mit Voraussagen molekularer Theorien verglichen.

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Paper read at the Annual Meeting of the German Rheologits, Berlin-Dahlem, May 20–21, 1968).     

Supersonic molecular beams production and temperature distribution in free expanding jets

Summary A supersonic molecular beam production system is described in which a continuous flux of Argon molecules can be produced as high as4 · 10 ¹⁸ molecules sterad^–1 sec^–1 in a vessel where the background pressure can be kept below10 ^–6 mmHg using relatively little cryo and diffusion pumping facilities. The beam intensity is measured at different stagnation pressures as a function of nozzle-skimmer separation and skimmer diameter. The results are compared with the existing theories, and information is obtained on the radial temperature distribution in the free expanding jet.

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Sommario Si descrive un apparecchio per la produzione di fasci molecolari supersonici nel quale, facendo uso di stazioni di pompaggio, a diffusione e criogenico, relativamente modeste, si può produrre un flusso continuo di molecole di Argon di4 · 10 ¹⁸ molecole sterad^–1 sec^–1 in un ambiente in cui la pressione di fondo è mantenuta inferiore a10 ^–6 mmHg. Vengono riportate misure di intensità del fascio, a diversi valori della pressione nell'ugello, in funzione della distanza ugello-primo collimatore e del diametro del primo collimatore. I risultati vengono confrontati con le teorie esistenti e dal confronto si ottiene informazioni sulla distribuzione della temperatura radiale nei getti in espansione libera.

     

Direct measurement of static yield properties of cohesive suspensions

A technique of yield stress investigation based upon the combined use of two devices (an applied stress rheometer and an instrument for measuring the propagation velocity of small amplitude, torsional shear waves) is described. Investigations into the low shear rate rheological properties of illitic suspensions are reported for shear rates, typically, in the range 10^–4— 10^–1 s^–1 under applied stresses in the range 0.01 — 10 Nm^–2 and involving shear strains between 10^–1 and 10^–4. Results are presented which demonstrate that the technique does not invoke the excessive structural disruption of material associated with applied shear rate based methods (direct and otherwise) and the widely encountered problem of wall slip at the surface of rotational measuring devices is avoided using miniature vane geometries. Results are compared with those obtained using smooth-walled cyclindrical measuring devices in both applied stress and applied shear rate instruments.Yield measurements are considered in relation to the structural properties of the undisturbed material state and shear moduli obtained by studying the propagation of small amplitude (10^–5 rad), high frequency (~ 300 Hz) torsional shear waves through the test materials are reported. Experimental techniques and instrument modifications to permit these measurements are described.     

Rheologische Messungen an Polypropylenschmelzen

Zusammenfassung Es wurden Fließkurven von Polypropylenschmelzen bei 190 °C in einem Schergefällebereich von etwa 10^–1 bis 10² sec^–1 aufgenommen, wobei drei Serien von Polymerproben herangezogen wurden: eine Serie PP 1–7 von isotaktischen Propylenpolymerisaten mit einer Molekulargewichtsverteilung, die durch¯M _w /¯M _n 4–6 gekennzeichnet war; eine zweite Serie PP 1d–5d von abgebauten Polymerproben mit¯M _w /¯M _n 2–3; eine dritte Serie PP 1m–3m, die aus Mischungen von Polypropylenen bestand und die durch¯M _w /¯M _n >10 gekennzeichnet war. Es wurde der Einfluß des Molekulargewichts und der Molekulargewichtsverteilung auf die Fließkurven untersucht, insbesondere der Einfluß auf den Exponentenn in derOstwald-de Waele-Gleichung=KD ⁿ . Es wurde versucht, die Ergebnisse durch die universaleVinogradov-Viskositätsfunktion darzustellen, wobei sich aber sehr wesentliche Abweichungen infolge Variation des Molekulargewichts und der Molekulargewichtsverteilung ergaben.

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Summary Flow curves of molten polypropylene were determined at 190 °C over a shear gradient range of about l0^–1 to 10² sec^–1. Three series of polymer samples have been used: one series PP 1–7 of isotactic propylene polymerization products with a molecular weight distribution characterized by¯M _w /¯M _n 4–6, another series of degraded polymer samples PP 1d–5d with¯M _w /¯M _n 2–3, and still another series of polymer mixtures PP 1m–3m with¯M _w /¯M _n >10. The influence of molecular weight and molecular weight distribution on the flow curves was investigated, particularly on the exponentn in theOstwald-de Waele-power law=KD ⁿ . An attempt to plot the results by the universalVinogradov-viscosity function produced marked deviations due to variation of molecular weight and molecular weight distribution.

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Vorgetragen auf der Arbeitstagung der Sektion Rheologie des Vereins Österreichischer Chemiker am 17. November 1967 in Graz. Mitteilung I, II: Rheol. Acta5, 89 (1966); ibid. im Druck [Messung und Interpretation von Filmkurven].     

Density distribution in rarefied gas flow behind a perforated plate

The relative density distribution in the rarefied CO₂ flow field behind a perforated plate has been experimentally investigated on the range of Knudsen numbers 10^–3 Kn 10^–1. The results of these experiments serve to demonstrate the validity of using the molecular velocity distribution function for determining the relative density on the Knudsen number interval in question. This distribution function was previously employed for calculating the parameters in molecular beams formed by capillary sieves in the free-molecular flow regime [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 183–184, May–June, 1989.     

Electrical Conductivity of Rocks under Shock Compression

The electrical conductivity of silicate rocks (quartzite, granite, and dry and wet tuffs) under single shock–wave loading is measured. It is shown that even at a shock–wave pressure of 20 GPa, the conductivity of rocks changes by several orders of magnitude compared to the initial value (10^–9 — 10^{–12 –1} · m^–1 for dry rocks) and reaches 0.01 ^–1 · m^–1 for quartzite and granite and 0.1 — 1.0 ^–1 · m^–1 for tuff. As the shock–wave amplitude increases from 20 to 60 GPa, the electrical conductivity increases by further one or two orders of magnitude. The experiments with rocks did not reveal a drastic change in electrical conductivity similar to the that observed for silicon dioxide (fused quartz) at a pressure of about 40 GPa.     

Dynamic viscoelastic properties of polymer melts

Summary An apparatus has been designed and constructed to measure the dynamic viscoelastic properties of polymer melts over the frequency range 10^–2–10³ Hz. The measurements made on two samples of polythene are discussed, the samples differing in their molecular weight distributions. Some fractions from these two parent polymers have also been studied. The results are compared with the modifiedRouse (3) theory for polymer melts, and with the liquid model proposed byBarlow,Erginsav andLamb (4).

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Zusammenfassung Mit Hilfe einer neuentwickelten Apparatur wurden Messungen der dynamischen viskoelastischen Eigenschaften von polymeren Schmelzen im Frequenzbereich 10^–2 bis 10^–3 Hz durchgeführt. Die Meßergebnisse, die an zwei Polyäthylenproben unterschiedlicher Molekulargewichtsverteilung erhalten wurden, werden diskutiert. Einige Fraktionen dieser beiden Polymeren wurden auch untersucht. Es wurden schließlich die Ergebnisse mit derRouseschen Theorie über polymere Schmelzen (3) und mit dem vonBarlow, Erginsav undLamb (4) vorgeschlagenen Flüssigkeitsmodell verglichen.

     

Viskositätsmessungen bei kleinen Schergefällen

Zusammenfassung Große, stark strukturierte Moleküle können Konformationswechselzeiten haben, die in der Größenordnung der Deformationsperiode bei der Scherung der Moleküle in Lösung liegen, wenn das Geschwindigkeitsgefälle kleine Werte annimmt. Es werden einige Viskosimeter beschrieben, die zur Untersuchung verdünnter Lösungen in einem Geschwindigkeitsgefälle-Intervall von 10^–2–10⁴ sec^–1 geeignet sind. Anhand von Messungen an DNA wird gezeigt, daß bei Geschwindigkeitsgefällen von 10 sec^–1 noch starke Strukturviskosität auftreten kann.

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Summary Large strongly structured molecules may have change of constellation times comparable to the deformation period in shearing the molecules in solution, if the shear rate assumes low values. Several viscometers are described, which are suitable for the investigation of diluted solutions in a shear rates range of 10^–2–10⁴ sec^–1. With the help of measurements with DNA, it is shown that strong shear dependence is observed for shear rates of 10 sec^–1.

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Vorgetragen auf der Rheologen-Tagung in Darmstadt am 7. und 8. Juni 1971

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Diese Arbeiten wurden von der DFG im Rahmen des SFB 41 Mainz-Darmstadt unterstützt, wofür wir herzlich danken.     

Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

Peculiarities of rheological behavior of filled polymer melts in uniaxial stretching

The peculiarities of theological behavior of filled polymer melts in uniaxial extension in a wide range of strain rates (from 2× 10^–5 to 1 × 10^–1 s^–1) have been studied. Linear polyethylene and 1,4-polybutadiene containing up to 21.5 vol.% of carbon black, silica, calcium carbonate or glass fibers were used. It has been found that the transition from uniform to nonunion stretching due to the neck formation is typical of all specimen compositions, when they approach steady-state straining. Depending on the structure and rheological characteristics of the compositions general conditions for this transition have been established. The general regularities for varying the rheological characteristics of filled polymers in the course of their uniform stretching have been recognized. These regularities depend on the molecular characteristics of the polymer matrix and the presence in the compositions of the structural framework of high disperse filler or the network formed by the entangled fibers. Using polyethylene compositions it has been shown that the introduction of small amounts of disperse or fibrous fillers can give rise to acceleration of the relaxation process in filled polymers.     

Nonequilibrium ionization accompanying hypersonic flow of carbon dioxide gas over blunt bodies

A study is made of the nonequilibrium ionization in the shock layer when carbon dioxide gas flows over cones with spherical noses at velocity 4–7 km/sec, the density of the oncoming flow being 10^–8-10^–5 g/cm³. The influence of admixtures of nitrogen and sodium on the electron concentration is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1981.     

An appraisal of rheological models as applied to polymer melt flow

Summary An attempt is made at giving an appraisal of some representative rheological models of both differential and integral type, using the standard rheological measurements of six polymer melts. Experimental data obtained were the steady shear viscosity and the first normal stress difference by means of aWeissenberg rheogoniometer over the range of shear rates: 10^–2 ~ 10 sec^–1, and by means of aHan slit/capillary rheometer over the range of shear rates: 10 ~ 10³ sec^–1. Also measured by means of theWeissenberg rheogoniometer were the dynamic viscosity and dynamic elastic modulus over the range of frequencies: 0.3 × 10^–2 ~ 3 × 10² sec^–1. Rheological models chosen for an appraisal are theSpriggs 4-constant model, theMeister model, and theBogue model.It is found that the capability of the three models considered is about the same in their prediction of the rheological behavior of polymer melts in simple shearing flow. It is pointed out however that, due to the ensuing mathematical complexities, the usefulness of these models is limited to the study of flow problems associated with simple flow situations. Therefore, in analysing the complex flow situations often encountered with various polymer processings, the authors suggest use of the empirical models of the power-law type for both the viscosity and normal stress functions.With 11 figures, 4 schemas and 1 table     

Extensional flow of polystyrene melt

Summary The extensional flow of molten polystyrene was studied in the strain rate range of 7.8×10^–4 sec^–1 to 2.2×10^–2 sec^–1 at a test temperature of 300F (149 C) Extensional viscosity was compared to shear viscosity measured at the same degree of stress and temperature and found to be from 3 to 350 times greater in magnitude but much less stress dependent.     

Rheologische Eigenschaften gesunder Synovialflüssigkeiten

Zusammenfassung Die rheologischen Eigenschaften gesunder menschlicher Gelenksflüssigkeiten im Geschwindigkeitsgefällebereich vonD = 10^–3-10³ s^–1 wurden untersucht. Es wurden die Scherviskosität und die erste Normalspannungsdifferenz gemessen. Gesunde Synovialflüssigkeiten besitzen hohe Anfangsviskosität (~40 Pa · s) und zeigen eine starke Abhängigkeit vom Geschwindigkeitsgefälle. Der SchermodulG ist im Gegensatz zu pathologischen Proben niedrig und über weite Bereiche konstant. Die längsten Relaxationszeiten betragen 5–10 s. Die kritische Konzentration, bei der Netzwerkbildung einsetzt, beträgt 0,75 10^–3 g/ml. Die Proben lassen sich zu einer Masterkurve vereinigen, die als verallgemeinertes Fließgesetz für gesunde Synovia aufgefaßt werden kann. Eine Untersuchung über die zeitliche Abhängigkeit der post-mortem-Synovia zeigt, daß innerhalb von 12 Stunden keine nennenswerten Veränderungen eintreten.

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The rheology of healthy human synovial fluids has been investigated at a shear-rate between 10^–3-10³ s^–1. Shear viscosity and first normal-stress difference were measured. Healthy synovial fluids show high zero-shear viscosity (about 40 Pa · s) and a strong shear rate dependence. The modulusG is constant over a large range, in contrast to pathological samples. The longest relaxation times are 5–10 s. The critical concentrationc _cr , at which entanglement occurs is about 0.75 10^–3 g/ml. The samples can be represented by a master-curve, which may be regarded as the constitutive equation of healthy synovial fluids. An investigation of the time dependency of synovial fluids indicated no changes within 12 hours post mortem.

Herrn Prof. Dr. DDr. h. c. O. Kratky zum 80. Geburtstag mit den besten Wünschen gewidmet.     

Mixing of Stably Stratified Gases in Subsurface Reservoirs: A Comparison of Diffusion Models

Numerical simulations of the mixing of carbon dioxide (CO₂) and methane (CH₄) in a gravitationally stable configuration have been carried out using the multicomponent flow and transport simulator TOUGH2/EOS7C. The purpose of the simulations is to compare and test the appropriateness of the advective–diffusive model (ADM) relative to the more accurate dusty-gas model (DGM). The configuration is relevant to carbon sequestration in depleted natural gas reservoirs, where injected CO₂ will migrate to low levels of the reservoir by buoyancy flow. Once a gravitationally stable configuration is attained, mixing will continue on a longer time scale by molecular diffusion. However, diffusive mixing of real gas components CO₂ and CH₄ can give rise to pressure gradients that can induce pressurization and flow that may affect the mixing process. Understanding this coupled response of diffusion and flow to concentration gradients is important for predicting mixing times in stratified gas reservoirs used for carbon sequestration. Motivated by prior studies that have shown that the ADM and DGM deviate from one another in low permeability systems, we have compared the ADM and DGM for the case of permeability equal to 10^–15 m² and 10^–18 m². At representative reservoir conditions of 40 bar and 40°C, gas transport by advection and diffusion using the ADM is slightly overpredicted for permeability equal to 10^–15 m², and substantially overpredicted for permeability equal to 10^–18 m² compared to DGM predictions. This result suggests that gas reservoirs with permeabilities larger than approximately 10^–15 m² can be adequately simulated using the ADM. For simulations of gas transport in the cap rock, or other very low permeability layers, the DGM is recommended.     

Numerical investigation and self-similar solutions of the glacier-ocean interaction problem

The mathematical modeling of the heat and mass transfer processes in glaciers is an effective means of investigating and predicting their development. A full explanation of the problem of constructing appropriate mathematical models is given in [1–5]. By analyzing the equations involved [3, 6] it is possible to establish the principal factors and dimensionless numbers determining glacier dynamics and provide justification for neglecting the secondary terms. In particular, a simplified closed system of differential equations for the detailed calculation of all the hydrodynamic characteristics of the glacier can be obtained for K_hj « 1 up to O(K _h ² ), where K_h is the ratio of the vertical and horizontal scales of the ice mass investigated (K_h 10^–4–10^–6). In this case many of the qualitative characteristics of glacier dynamics are preserved even in one-dimensional models within the subisothermal approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1986.     

Fluctuations of the flow parameters of an incompressible viscous fluid in a collar-type flow throttling device

The flow in channels of the labyrinth seal type with one or two throttling stages is calculated on the interval of Reynolds numbers Re from 1.9·10⁴ to 4.5·10⁵. The nonsteady flow structure and the distribution and fluctuations of the pressure on the body of the labyrinth are investigated. The results are compared with the data of a physical experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–8, January–February, 1990.     

Experimental investigation of the separation of flow around a sphere

The results of an experimental investigation of the flow around a sphere over a broad range of Mach numbers M=0.3–3 and Reynolds numbers Re=3·10⁴–3·10⁷ are presented. The experiments were carried out on a ballistic test stand and in a wind tunnel. Flow patterns and pressure distributions were obtained. In particular, the effect of the Mach and Reynolds numbers on the position of the separation point and the edge shock was studied; the pressure distribution on the sphere was measured; and a nonmonotonic displacement of the flow separation point upon passage through the speed of sound was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–156, January–February, 1991.     

A torsional creep apparatus

Summary 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.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

A rheological investigation of solid soap

Summary The rheological behaviour of solid soaps has been investigated over several orders in time and shear by means of creep experiments, measurement of stressstrain curves at constant shear rate and dynamic experiments. The modulus at small deformations is almost constant over a frequency range of 10^–3–10³ Hz; a transition from linear to non-linear behaviour has been observed at a strain of about 10^–3. The results suggest that some kind of network structure is responsible for the rheological behaviour of soap.

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Zusammenfassung Das Theologische Verhalten von Hartseifen wurde für mehrere Größenordnungen von Zeit und Schubgeschwindigkeit untersucht mittels Kriechversuche, Messung der Spannungs-Deformationskurven bei konstanter Schubgeschwindigkeit und dynamischer Experimente. Der Modul bei geringen Deformationen ist fast konstant im Frequenzbereich von 10^–3–10³ Hz; ein Übergang von linear zu nicht-linear wurde bei einer Deformation von etwa 10^–3 beobachtet. Die Ergebnisse lassen auf eine netzartige Struktur schließen, die für das Theologische Verhalten der Seife verantwortlich ist.

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The authors are indebted to Mr.C. J. Nederveen of the Central Laboratory T. N. O., Delft for the dynamic measurements, and thank Mr.D. W. Brinkman of the Unilever Research Laboratory, Vlaardingen for experimental assistance.