The instron rheometer

It was shown some years ago by one of the authors (R. S. Higginbotham) that measurements of viscosity at a shearing stress of about 4500 dynes/cm² were especially useful for predicting the behaviour of colour pastes used for printing textile fabrics on engraved-roller machines. Such measurements could be made with various types of equipment, the most convenient to use being theFerranti-Shirley cone and plate viscometer, but it was felt that there was a need for a viscometer specifically designed for this purpose, and as cheap, simple, robust and easy to use as possible. A first attempt to produce such a viscometer (Higginbotham andBenbow, J. Sci. Instr.29, 221, 1952) was not entirely successful but a satisfactory, direct reading, cone and plate instrument has now been produced. It employs a permanentmagnet motor driven under conditions of constant torque to provide a constant shearing stress. The cone speed is then inversely proportional to the viscosity of the fluid under examination. A photoelectric tachometer with an associated electronic circuit generates a voltage proportional to the viscosity and the result is displayed on a linearly calibrated meter. The instrument has been tested in two printworks over a period of several months, and it has been shown to be suitable for the control of screen printing, as well as roller printing, pastes.     

The multipass rheometer a review

This review describes the development and application of the multipass rheometer; a servo hydraulically driven two piston device that enables rheology and precise processing measurements to be carried out within an enclosed volume. The apparatus development and then specific application areas are highlighted. In particular, application to rheology, polymer processing and foaming are considered.     

Transient filament stretching rheometer

The Lagrangian specification is used to simulate the transient filament stretching rheometer. Simulations are performed for a dilute PIB-solution modeled as a four mode Oldroyd-B fluid and a semidilute PIB-solution modeled as a non-linear single integral equation. The simulations are used to investigate a sequence of filament stretching rheometers. The questions of special and temporal homogeneity of the experiment are investigated. The simulations are compared with data from a specific rheometer by Tirtaadmadja and Sridhar.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Transient filament stretching rheometer

The filament stretching device which is used increasingly as an apparatus for measuring extensional properties of polymeric liquids is analysed. A force balance that includes the effects of inertia and surface tension is derived. The force balance may be used to correct for the effects of inertia and surface tension, provided online measurements of the filament surface shape are available. In addition, the question of initial asymmetry due to gravity is addressed.     

A versatile surface rheometer

Summary In the study of the physical properties of hydrocolloid films at the aqueous-air interface and aqueousoil interface it is necessary to be able to look at the whole range of rheological properties from low viscosity liquid to viscoelastic solid. It is desirable to follow all these stages, in succession, sometimes, with one piece of apparatus.The apparatus developed can be used in three basic modes without modification. Continuous shear (as a surface Couette viscometer). Free Oscillation, and Creep and Creep Recovery.In continuous shear, a cylindrical dish containing the aqueous solution of the hydrocolloid and the oil layer, is rotated about its vertical axis at a known constant velocity. The shear stress is determined from the angular deflection of a shallow angled biconical pendulum suspended in the oil-water interface by means of a long vertical wire. The shear rate is calculated from the speed of rotation of the dish.In free oscillation the amplitude and period of oscillation of the biconical pendulum, suspended on the wire are recorded using an optical lever, photo-cell, and pulse counting circuit. or observed directly from the movement of a spot of light projected onto a horizontal scale.In creep, constant surface shear stress is applied, by arranging that the twist in the vertical wire supporting the biconical. pendulum, remains constant during the experiment. A servomechanism, controlled by the optical lever and photo-cell, mentioned above, drives the cylindrical dish by an amount necessary to maintain the constant shear stress. The deformation of the interfacial film is recorded in digital form as the number of pulses fed to a stepping motor which, itself, is an integral part of the servomechanism.The smallest deformation of the interfacial film corresponds to an angular movement of the pendulum bob of about 3 × 10^–4 radian. The applied torque depends on the thickness of the suspension wire and the twist in it. The latter can be measured to 0.25°.

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Zusammenfassung Bei Untersuchungen der physikalischen Eigenschaften hydrokolloidaler Filme an den Grenzflächen von einem wäßrigen Medium und Luft sowie wäßrigem Medium und Öl sollte man unbedingt den gesamten Bereich der Theologischen Eigenschaften in Betracht ziehen, d. h. von Flüssigkeiten mit geringer Viskosität bis zu viskoelastischen Feststoffen. Es ist wünschenswert, alle diese aufeinanderfolgenden Stufen mit einem Gerät zu untersuchen.Das Gerät, das entwickelt wurde, kann ohne Modifikation auf drei verschiedene Arten gebraucht werden: Kontinuierliche Scherversuche (als Oberflächen-Couette-Viskosimeter), freie Schwingungen und Kriech- sowie Kriecherholungsversuche.Bei kontinuierlich-veränderlicher Schubspannung wird eine zylinderförmige Schale mit der wäßrigen Lösung des Hydrokolloids und der Ölschicht mit einer bekannten konstanten Geschwindigkeit um die senkrechte Achse gedreht. Vom Ausschlagwinkel eines zweiseitig konisch zulaufenden Pendels, das mit einem langen Draht in der Öl-Wassergrenzschicht hängt, wird die Schubspannung bestimmt. Die Schergeschwindigkeit folgt aus der Umlaufgeschwindigkeit der Schale.Bei der freien Schwingung werden die Amplitude und die Periode des bikonischen Pendels durch ein optisches System mit Photozelle und Impulszähleinheit oder direkt durch die Bewegung eines Lichtstrahles, der auf eine horizontale Skala projiziert wird, bestimmt.Beim Kriech-Versuch wird eine konstante Oberflächen-Schubspannung erzeugt, indem die Verdrehung des vertikalen Drahtes, an dem das bikonische Pendel aufgehängt ist, während des Experimentes konstant gehalten wird. Ein mit Lichtstrahl und Photozelle kontrollierter Servomechanismus dreht die zylinderförmige Schale immer so, daß die Schubspannung gleichbleibt. Die Deformation des Grenzflächenfilmes wird als Anzahl von Impulsen numerisch gespeichert, die dem Schrittmotor des Servomechanismus zugegangen sind.Die geringste Deformation des Grenzflächenfilmes entspricht einer Winkelbewegung des Pendelkörpers von etwa 3·10^–4 im Bogenmaß. Das übertragene Moment ist unabhängig von der Stärke und der Verdrehung des Aufhängedrahtes. Die geringste Verdrehung, die gemessen werden kann, beträgt 0.25°.

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Paper presented to the British Society of Rheology Conference on Rheology in Medicine and Pharmacy, London, April 14–15, 1970.     

A new eccentric-cylinder rheometer

A new eccentric-cylinder rheometer with guard-ring equipment was constructed as an auxiliary set-up to a Rheometrics Mechanical Spectrometer, type 7200, which enables measurements with the eccentric disk technique. Experimental tests with Newtonian fluids and polymer solutions of relatively low viscosity show that this instrument yields reliable plots of shear viscosity and first normal-stress coefficient over several decades of the effective average shear rate. These coincide very well with plots from a commercial cone-and-plate rheometer even for higher relative eccentricities (up to 0.75). However, no systematic effects of eccentricity, to be expected for higher shear rates, could be observed with these fluids, so that supplementary tests applying fluids with more pronounced viscoelastic properties are to be carried out.     

The end correction for power-law fluids in the capillary rheometer

The finite element scheme developed by Nickell, Tanner and Caswell is used to compute the entry and exit losses for creeping flow of power-law fluids in a capillary rheometer. The predicted entry losses for a Newtonian fluid agree well with available experimental and theoretical results. The entry losses for inelastic power-law fluids increased with decreasing flow behaviour index and show an increasing deviation from available upper bound results as the flow behaviour index in the power-law decreases.The exit losses are found to be finite for inelastic power-law fluids and increase as the flow behaviour index decreases. The predicted die swell for Newtonian fluids agrees well with the available experimental data while the influence of shear thinning is to reduce the die swell.The end correction which is the sum of the entry and exit losses relative to twice the viscometric wall shear stress varies from 0.834 for n = 1 to 2.917 for n = 1/6. This figure reaches a very high value as n tends to zero. The experimental variation in the Couette correction factor in capillary rheometry is explained in terms of the shear thinning characteristics of the fluid. It is concluded that the exit flow is not viscometric, contrary to a common assumption.     

A low frequency torsional rheometer

Summary An instrument has been developed for measuring the viscoelastic behaviour of polymer melts at low frequencies, in the range 10^–3 to 50 Hz. The sample is contained between a cone and a fixed plate, or between parallel plates. The moving member is driven in torsional oscillation through a torsion wire. The amplitude of the resulting oscillation is compared in amplitude and phase with the driven end of the torsion wire. The amplitudes are measured digitally using optical diffraction gratings, and either an oscilloscope or a high-speed ultra-violet recorder is used to determine the phase angle between the two signals. The moving member is supported on an air bearing, which provides a very low friction support with a high degree of positional control thus giving a well defined sample geometry. The torsion wire is driven using a vibrator with a d.c. drive amplifier fed from a very low frequency oscillator. The sample temperature is controlled to better than 0.01 °C, with temperature gradients across the sample of a similar order of magnitude. The temperature range of the instrument is from –50 °C to +200 °C.The angular resolution of the measuring system is 3 × 10^–5 radius, so that an accuracy of better than ±1% in the amplitude measurements can be obtained with the amplitude of shear in the sample kept sufficiently low that a linear stress-strain relation is maintained.With 3 figures     

Micro-Fourier rheometer: Inertial effects

The inertial effects in a random squeezing rheometer are examined, both theoretically and experimentally. The rheometer is based on small amplitude random squeezing between two parallel plates, where the upper plate is driven by a random displacement with a broad band spectrum. A fast Fourier transform is used to deliver the complex modulus (or viscosity) of the fluid in a single brief test, over more than two decades of frequency. The inertia of the fluid is shown to produce an error factor, which is also a function of the frequency. The correction factor can be well approximated by a first-order correction in the Reynolds number, for a very large range of Reynolds number, making the inertial correction a very simple procedure for light fluids.     

The concept of a rotational rheometer with helical screw impeller

The paper is concerned with the development of an on-line rheometer for suspensions with settling particles. A new concept of a rotational rheometer with helical screw impeller is discussed. On the basis of model considerations a procedure for the flow curve determination of the investigated fluid has been proposed. Contrary to previous attempts, in the developed procedure no calibration of the instrument is necessary. The preliminary experimental verification of the developed approach proved its applicability.     

A concentric-cylinder rheometer for polymer melts

Summary If one wishes to measure the viscosity of a polymer melt at high shear rates there are substantial fluid dynamical and heat transfer difficulties. Cone-plate instruments are limited because of secondary flows and because the fluid tends to leave the gap. In capillary-flow instruments, there are substantial radial temperature gradients and the possibility of flow irregularities.Similar difficulties are met in trying to study the response of melts to large-amplitude oscillatory shear, and fluid inertia must be added to the list. However, large-amplitude oscillatory shear is a test which is useful for studying non-linear viscoelasticity, and many flows of practical importance involve deformations outside the range of validity of the assumptions of linear viscoelasticity theory.A heavy duty rheometer has been designed in which shear viscosity can be measured at high shear rates, and which can also be used for large-amplitude oscillatory shear tests. The melt is sheared between concentric cylinders; the torque on the inner, stationary cylinder is monitored while the outer cylinder either rotates at steady speed or oscillates. The shear rate of frequency and amplitude are continuously variable over wide ranges.Careful consideration was given to the problems posed by hydrodynamic stability, fluid acceleration, heat generation and end effects, and the final design represents what the authors feel is a reasonable compromise between minimizing the influence of these factors and the basic practical requirement that the instrument have a reasonable cost and uncomplicated operating procedure.In large-amplitude oscillatory shear, the interpretation of the experimental results poses special problems. The stress response is periodic, but not sinusoidal so that it is not possible to apply the methods of linear viscoelasticity. A number of possibilities suggest themselves, but it has been concluded that the best method of representation involves the plotting of stress versus strain or rate-of-strain. This results in closed curves which have distinctive shapes depending on the basic nature of the fluid response.

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Zusammenfassung Bei der Viskositätsmessung an Polymerschmelzen unter hohen Schergeschwindigkeiten treten strömungsdynamische und Wärmeübergangsprobleme in Erscheinung. Kegel-Platte-Rheometer sind nur bei relativ geringen Deformationen brauchbar, weil bei höherer Scherbeanspruchung die Meßsubstanz infolge Sekundärströmungserscheinungen bzw. Trägheitskräften aus dem Meßspalt austritt. Bei Kapillarrheometern ergeben sich unter hohen Scherbedingungen gravierende radiale Temperaturgradienten und Fließinstabilitäten.Die gleichen Probleme finden sich, wenn das Verhalten von Schmelzen bei oszillatorischer Beanspruchung mit großer Scheramplitude untersucht werden soll. Allerdings ist diese Beanspruchungsart besonders geeignet, wenn die nicht-lineare Viskoelastizität studiert werden soll — und viele praktische Strömungsverhältnisse lassen sich durchaus nicht im Rahmen der linearen Viskoelastizitätstheorie behandeln.Es wurde ein robustes Rheometer vom Couettetyp entworfen, mit dem die Scherviskosität bei hohen Schergeschwindigkeiten gemessen werden kann und das ebenso für Oszillationsversuche mit großer Scheramplitude geeignet ist. Der stetige oder oszillatorische Antrieb erfolgt auf den äußeren Zylinder, während am inneren, ruhenden Zylinder das übertragene Drehmoment gemessen wird.Besonderer Wert wurde bei dem Entwurf des Rheometers den Problemen beigemessen, die sich durch hydrodynamische Stabilität, Beschleunigungsvorgänge, Wärmeentwicklung sowie Endeffekte ergeben. Die endgültige Form des Rheometers ist in den Augen der Autoren ein vernünftiger Kompromiß zwischen der Minimierung der genannten Einflüsse und den praktischen Voraussetzungen, daß ein Rheometer nicht zu teuer ist, aber einfach zu bedienen sein muß.Die Interpretation der experimentellen Ergebnisse solcher Oszillationsversuche ist einigermaßen problematisch. Der resultierende Spannungsverlauf ist zwar periodisch, aber nicht sinusförmig, so daß die Methoden der linearen Viskoelastizität nicht anwendbar sind. Obwohl sich mehrere Möglichkeiten anbieten, dürfte die beste Darstellungsmethode der Ergebnisse durch die Auftragung der Spannung in Abhängigkeit von der Scherung bzw. der Schergeschwindigkeit gegeben sein. Dieses ergibt geschlossene Kurven, deren besonderes Aussehen durch die Eigenschaften des Testmaterials gekennzeichnet ist.

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C Cauchy-Green strain tensor - C ^–1 Finger strain tensor - h gap spacing - k thermal conductivity - T difference between maximum and minimum temperatures in sheared fluid - II second invariant of rate-of-strain tensor;: - material constant of second-order fluid - material constant of second-order fluid - ₀ shear strain amplitude - shear rate in simple shear - ₀ maximum shear rate; equal to ₀ - rate-of-deformation tensor; grad velocity plus its transpose - material constant in eq. [8] - viscosity - ^* complex viscosity - dynamic viscosity - characteristic time of fluid - µ material constant with units of viscosity - fluid density - viscous or extra stress tensor - frequency (radians/sec.) With 3 figures     

Model-free inversion of squeeze-flow rheometer data

A method for extracting rheological data from squeeze-flow tests is proposed. The analysis, based upon the lubrication approximation for a generalized Newtonian fluid, differentiates experimental data in order to obtain an estimate of the wall shear rate (as in the Weissenberg–Rabinowitsch correction for the capillary rheometer) and of the wall shear stress. Two examples are discussed. The first is based on an approximate expression for the force required to squeeze a Herschel–Bulkley fluid. The second example concerns a power-law fluid with partial slip at the plates (but non-zero wall shear stress). Second derivatives of the experimental data are required: the interpretation of noisy results is therefore likely to be difficult.     

Thermal effects in the capillary rheometer

Summary The effect of viscous heating in a capillary rheometer is analysed for a power-law fluid by means of a perturbation expansion based upon a boundary-layer-core structure. This expansion is found to complement the eigenfunction series solution obtained by earlier investigators. A similar analysis is presented for the work-of-expansion effect. These two thermal effects are superimposed together with a third perturbation effect due to the pressure dependence of viscosity.On the basis of the present theory, earlier work in this area is discussed and, in some cases, apparent inaccuracies or inconsistencies are pointed out. A means is indicated for correcting data on the basis of the present theory.

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Zusammenfassung Es wird der Effekt der Erwärmung einer Potenzflüssigkeit infolge viskoser Reibung in einem Kapillar-Rheometer mittels einer Störungsrechnung untersucht, die auf der Unterteilung der Strömung in eine Grenzschicht und einen Kern basiert. Diese Störungsentwicklung ergänzt eine früher von anderen Autoren gefundene Reihenentwicklung mit Hilfe von Eigenfunktionen. Eine ähnliche Untersuchung wird für die thermische Ausdehnungsarbeit durchgeführt. Diese beiden thermischen Effekte sind zusammen einem dritten Störeffekt superponiert, der von der Druckabhängigkeit der Viskosität herrührt.Aufgrund der vorgelegten Theorie werden verschiedene auf diesem Gebiet früher durchgeführte Arbeiten diskutiert, und es werden in einigen Fällen offensichtliche Ungenauigkeiten und Folgewidrigkeiten aufgedeckt. Schließlich wird eine Methode zur Korrektur von Meßdaten mit Hilfe der vorliegenden Theorie angegeben.

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Nomenclature a tube radius - b ; evaluated atT ₀ andp = 0 when used in perturbation expansion - C _p specific heat - f - f ^* - h defined by eq. [15] - k thermal conductivity - L tube length - m defined by eq. [8] - m ₀ m(T₀, 0) - n power-law index - p pressure - Pe C _p W a/k Peclet number - Pr C _pa/k Prandtl number - Q volumetric flow rate - Q ₀ unperturbed value ofQ in specified-p formulation - r radial coordinate - Re W a/ _a Reynolds number - T temperature - T ₀ inlet temperature - u radial velocity component - u ₀ 0 unperturbed radial velocity - w axial velocity component - w ₀ /W(1 – ) unperturbed axial velocity - W Q/(a ²) average axial velocity - W ₀ Q ₀/(a ²) - z axial coordinate - (3n + 1)/n - ^* ; evaluated atT ₀ andp = 0 when used in perturbation expansion - 4^1-n - ^* - (n + 1)/n - ... shear rate - 4W/a apparent shear rate - p total pressure drop - T _a W ²/k characteristic temperature difference - T _b total bulk-temperature rise - ^* T - r/a - shear viscosity - _a m₀ - (1 –)/ ^1/3 - —p/z - ₀ ... unperturbed value of - z-averaged value of - µ ^{n + 1}/n - z/(a Pe) - _L L/(a Pe) - mass density - _w shear stress at wall - streamfunction - ^*T₀ (absolute temperature scale) - ( )₁ leading-order effect due to viscous heating - ( ) ₁ ^* leading-order effect due to work-of-expansion Note: in specified-p formulation,W gets replaced byW ₀ in definition of Pe, Re, and. With 7 figures and 7 tables     

A multidirectional shear rheometer for polymer melts

A parallel plate shear rheometer for polymer melts was built for superposed shear tests in two orthogonal directions. To examine its performance, a standard test was developed, including a change of the shear direction by angles between 0° and 180°. The results were analyzed to obtain preliminary information on the multidirectional shear behavior of a low-density polyethylene melt. The measured orthogonal components of the shear force were added and then split again into components of the original and of the changed shear direction. It was found, within the range of error, that these components depend only on time and on the shear rate, but not on the angle by which the shear direction is changed. The total shear rate was 0.56 s^–1.Dedicated to Prof. Dr. Joachim Meissner on the occasion of his 60th birthday.     

A new elongational rheometer for polymer solutions

Design and operation of a new elongational rheometer for low elastic polymer solutions are described. The free jet elongational rheometer is easy to operate and for suitable operating conditions a transient elongational flow with an approximately constant rate of strain can be realized. In any case, convenient comparative parameters can be obtained. The method of rheological curve fitting leads to a deformation dependent ralaxation time parameter of a modified upper convected Jeffreys-law.     

A newly designed coaxial cylinder-type dynamic rheometer

A newly designed dynamic rheometer is described. This apparatus is designed for the purpose of the investigation of the physical ageing process of gels and for the determination of the viscoelastic properties of polymer melts. With this instrument the dynamic moduli can be determined very accurately in a range of about 8 decades (– 2 < logG < 5.3 and – 3 < logG < 5.4;G andG in N/m²) and in a frequency range of more than 6 decades (5 10^–5 – 100 Hz) with an accuracy and stability of 0.025%. Results are shown of measurements on a silicon oil (with loss angles deviating only little from 90°), on a gel of polyvinyl chloride in Reomol (with loss angles deviating only little from 0°) and on a polystyrene melt for which, at low frequencies, the dependencies of the storage and loss moduli on the frequency are quadratic and linear, respectively.Dedicated to the Sixtieth birthday of Prof. Dr. H. R. K. N. Janeschitz-Kriegl, Johannes Kepler University, Linz, Austria.