Correlation between the crossover modulus and the molecular weight distribution using the Doi-Edwards theory of reptation and the Rouse theory

The crossover modulus in the dynamic mechanical spectrum was linked with the molecular weight distribution (MWD) over a wide range of polydispersity ( = 1 to 6). Reasonable agreement was obtained between theory and experiment for near monodisperse and narrow MWD polymers using the Doi-Edwards theory of reptation. For broad MWD polymers, the Doi-Edwards theory was found to be inapplicable. Using the Doi-Edwards theory for the shorter chains and a Rouse type mechanism for the longer chains, a good fit was obtained between the calculated and experimentally measured crossover modulus values.     

Shear flow properties of concentrated solutions of linear and star branched polystyrenes

Summary The linear viscoelastic and viscometric functions have been determined for solutions of wellcharacterized monodisperse linear and star-branched polystyrenes and for commercial, polydisperse polystyrene. The value of the product c for these solutions was large and was obtained by using both high and low The effect of structure on the rheological properties was determined by examining how parameters in a modified Carreau viscosity equation (used to fit the data) varied with c, , and branching. No enhancement effects on the rheological properties were observed because of branching.The Cox-Merz rule was observed to describe the similarities between the viscosity and complex viscosity for most of the monodisperse samples studied. The broad molecular weight distribution polystyrene solutions did not follow this empiricism.With 17 figures and 4 tables     

Molecular weight distribution from rheological measurements

Summary A simple and reliable relative method to derive the molecular weight distribution of linear polymers is proposed.It is shown that both the zero-shear viscosity, ₀, and the intrinsic viscosity, [], have a logarithmic dependence on the weight average molecular weight, , and the polydispersity, . The coefficients of these relationships can be determined by applying a multiple regression analysis to a series of samples for which andQ are known.By making use of the two established relationships, the determination of andQ for a given polymer sample reduces to the experimental measurement of its ₀ and [].An analysis has been performed to estimate to what extent experimental errors on ₀ and [] affect the calculated molecular weight distribution.It has been found that only the experimental error on [] contributes heavily to the final error on the polydispersity.

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Zusammenfassung Es wird eine einfache und zuverlässige Relativmethode vorgeschlagen, um die Uneinheitlichkeit linearer Polymere abzuleiten.Es wird gezeigt, daß alle beide, Nullschergradient-viskosität ₀, und Grenzviskositätszahl [], einfach logarithmisch vom Gewichtsmittel des Molekulargewichts , und vom Polymolekularitätsindex , abhängig sind.Die Koeffizienten dieser Beziehungen können mit statistischer Analyse festgesetzt werden, wenn undQ einer Probenreihe bekannt sind.Mit den zwei vorher festgesetzten Beziehungen besteht die Bestimmung von undQ einer gegebenen Polymersprobe nur aus den experimentellen Massen seiner ₀- und []-Werte.Eine Analyse wurde ausgeführt, um die Bedeutung des experimentellen Irrtums über die berechnete Uneinheitlichkeit zu wissen.Es wurde gefunden, daß ein experimenteller Irrtum betreffs [] schwer an endlichem Irrtum der Uneinheitlichkeit teilnimmt.

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With 2 figures and 2 tables     

Taylor-Couette stability analysis for a Doi-Edwards fluid

The stability of Taylor-Couette flow of entangled polymeric solutions to small axisymmetric stationary disturbances is analyzed using the Doi-Edwards constitutive equation in the small gap limit. A previous analysis of Karlsson, Sokolov, and Tanner for the general K-BKZ equation, of which the Doi-Edwards equation is a special case, reduces the problem to one of numerically evaluating seven viscoelastic functions of the shear rate in the gap. Of these seven, only three — two of which are related to the second normal stress difference, and one of them to shear thinning — significantly affect the flow stability. The negative second normal stress difference of the Doi-Edwards fluid stabilizes the flow at low values of the Weissenberg number ₁ , while shear thinning produces strong destabilization at moderate Weissenberg number. Here ₁ is the longest relaxation time. Non-monotonic effects of viscoelasticity on Taylor-Couette stability analogous to those predicted here have been observed in experiments of Giesekus. The extreme shear thinning of the Doi-Edwards fluid is also predicted to produce a large growth in the height of the Taylor cells, a phenomenon that has been seen experimentally by Beavers and Joseph.     

Apparent thickening behavior of dilute polystyrene solutions in extensional flows

An experimental investigation was undertaken to study the apparent thickening behavior of dilute polystyrene solutions in extensional flow. Among the parameters investigated were molecular weight, molecular weight distribution, concentration, thermodynamic solvent quality, and solvent viscosity. Apparent relative viscosity was measured as a function of wall shear rate for solutions flowing from a reservoir through a 0.1 mm I.D. tube. As increased, slight shear thinning behavior was observed up until a critical wall shear rate was exceeded, whereupon either a large increase in or small-scale thickening was observed depending on the particular solution under study. As molecular weight or concentration increased, decreased and, the jump in above , increased. increased as thermodynamic solvent quality improved. These results have been interpreted in terms of the polymer chains undergoing a coil-stretch transition at . The observation of a drop-off in at high (above ) was shown to be associated with inertial effects and not with chain fracture due to high extensional rates.     

An approach to the estimation of polymer melt elasticity

An effective method has been proposed to estimate the primary normalstress difference versus shear rate curves at temperatures relevant to the processing conditions only from the knowledge of the melt flow index, the molecular-weight distribution and the glass transition temperature of the polymer. The method involves the use of a unified curve obtained by coalescing the elastic response curves of various grades in terms of the modified normal-stress coefficient ₁ (MFI)² and a modified shear rate . Unified curves have been reported for low density polyethylene, high density polyethylene, polypropylene and nylon.Nomenclature C ₁ constant in eq. (4) - J _e steady state compliance (cm²/dyne) - proportionality constant in eq. (6) - L load (kg) - L ₁ load (kg) at ASTM test conditions - L ₂ load (kg) at required conditions - MFI melt flow index (gm/10 min) - number average molecular weight - weight average molecular weight - z-average molecular weight - (z+1)-average molecular weight - n slope of the shear stress vs. shear curve on a log-log scale - N ₁ primary normal-stress difference (dynes/cm²) - Q molecular weight distribution expressed as - T ₁is> temperature (K) at condition 1 - T ₂is> temperature (K) at condition 2 - T _g glass transition temperature (K) - T _s standard reference temperature equal toT _g + 50 K - shear rate (s^–1) - ₀ zero-shear viscosity (poise) - apparent viscosity (poise) - density (g/cm³) - ₁₂ shear stress (dynes/cm²) - ₁₁– ₂₂ primary normal-stress difference (dynes/cm²) - _1,0 zero shear rate primary normal-stress coefficient (dynes/cm² · sec²) - ₁ primary normal-stress coefficient (dynes/cm² · sec²) - ₂ secondary normal-stress coefficient (dynes/cm² · sec²) NCL-Communication No. 3106     

Die swell and melt fracture: Effects of molecular weight distribution

Summary The equations for determining die swell of molten polymers are discussed. The critical conditions for melt fracture and die swell results are combined in order to explain the flow behavior at the onset of instability. It is shown that the factor is the most important parameter in die swell and melt fracture studies.

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Zusammenfassung Die Formeln für die Bestimmung der Schwellrate von Kunststoffschmelzen wurden behandelt. Die kritischen Bedingungen für die Ergebnisse von Schmelzbruch und Schwellrate sind kombiniert, um das Flußverhalten beim Einsetzen der Instabilität zu erklären. Es wurde dargestellt, daß der Faktor in der Schwellrate sowie im Schmelzbruch der wichtigste Parameter ist.

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With 3 figures     

Effects of couple-stresses on the dispersion of a soluble matter in a pipe flow of blood

Summary An analysis of the effects of couple-stresses on the effective Taylor diffusion coefficient has been carried out with the help of two non-dimensional parameters based on the concentration of suspensions and , a constant associated with the couple-stresses. It is observed that the concentration distribution increases with increasing or The effective Taylor diffusion coefficient falls rapidly with increasing when is negative.

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Zusammenfassung Der Einfluß der Momentenspannungen auf den effektiven Taylorschen Diffusionskoeffizienten wird untersucht. Dabei treten zwei dimensionslose Parameter and auf: Der erste bezieht sich auf die Suspensionskonzentration, der zweite kennzeichnet die Momentenspannungen. Man findet, daß die Verteilungsgeschwindigkeit mit wachsendem oder zunimmt. Dagegen fällt der Taylorsche Diffusionskoeffizient bei wachsendem stark ab, wenn negativ ist.

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a Tube radius - C Concentration - C _i Body moment vector - C ₀ Concentration at the axis of the tube - C _m Mean concentration - D Molecular diffusion coefficient - d _ij Symmetric part of velocity gradient - F Function of and characterising effective Taylor diffusion coefficient - f _i Body force vector - H A function of and - K ₂ Integration constant - K ^* Effective Taylor diffusion coefficient - k Radius of gyration of a unit cuboid with its sides normal to the spatial axes - I _n Modified Bessel's function ofnth order - L Length of the tube over which the concentration is spread - M Function ofH and - M _ij Couple stress tensor - P Function of - p Fluid pressure - Q Volume rate of the transport of the solute across a section of the tube - r Radial distance from the axis of the tube - T _ij Stress tensor - t Time coordinate - T _ij ^A Antisymmetric part of the stress tensor - u Relative fluid velocity - Average velocity - v _i Velocity vector - Fluid velocity at any point of the tube - v ₀ ⁿ Velocity of Newtonian fluid at the axis of the tube - _i Vorticity vector - x Axial coordinate - x ₁ Relative axial coordinate - z Non-Dimensional radial coordinate - Density - _ij Symmetric part of the stress tensor - µ Viscosity of the fluid - µ _ij Deviatoric part ofM _ij - , Constants associated with couple-stress With 3 figures     

Single droplet combustion in a gravitational environment

A theoretical analysis is developed to study the combustion characteristics of a fuel droplet in a gravitational field. The normalized governing system consists of the complete conservation equations inr-z coordinates and includes finite-rate global kinetics. The Clausius-Clapeyron law is applied at the liquid-vapor interface to describe the evaporation process. A modified body-fitted grid generation technique is used to handle irregular boundaries. The effects of changing the droplet diameter and the gravity level are investigated. Under the variation of droplet diameter, flame structures, including isotherms, flame shape, velocity vector field, and mass burning rate are studied in detail. The predicted results exhibit good agreement with experimental data. When the gravity level increases, the computed results show that the flame shape is sensitive to variation in gravity. A simple correlation, , is found. Within the elevated gravity domain of experiment, the computed data agree well with measurements obtained by Okajima and Kumagai [10].In einer theoretischen Studie wird die Verbrennungscharakteristik eines Ethanoltröpfchens in einem Gravitationsfeld untersucht. Die normierten Grundbeziehungen umfassen die vollständigen Erhaltungsgleichungen inr-z-Koordinaten unter Einschluß einer Globalkinetik endlicher Umsatzrate. Das Clausius-Clapeyronsche Gesetz wird an der Flüssigkeits-Dampf-Phasengrenze angesetzt, um den Verdampfungsprozeß zu beschreiben. Eine spezielle Gittergenerierungstechnik ermöglicht die Behandlung irregulärer Berandungen. Die Einflüsse veränderlichen Tropfendurchmessers bzw. variablen Gravitationsniveaus werden untersucht. Bei variablem Tröpfchendurchmesser erfolgt eine Detailuntersuchung der Flammenstrukturen nach Isothermenfeld, Flammenform, Feld der Geschwindigkeitsvektoren und Verbrennungsrate. Die vorausberechneten Ergebnisse stimmen gut mit experimentellen Daten überein. Bei Anstieg des Gravitationsniveaus zeigen die Rechnungen eine empfindliche Veränderlichkeit der Flammenform. Es läßt sich eine einfache Beziehung aufstellen. Im Bereich höheren Gravitationspegels stimmen die berechneten Werte gut mit den Messungen von Okajima und Kumagai [10] überein.Financial support of this research by the National Science Council of the R.O.C., under project NSC 81-0401-E-009-531 is greatly appreciated. The authors also wish to express their gratitude to National Chiao Tung University for providing computer facility.     

On the dynamic behaviour of an elastically supported beam of infinite length, loaded by a concentrated force

Summary An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by =0 for and =K=const. for ; the second one by =0 for 0 > > , given function of for 0 ; the third one applies to problems in which, during the period of impact, itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties.     

Transient stress responses predicted by the internal viscosity model in elongational flow

Predictions are made for the elongational-flow transient rheological properties of the dilute-solution internal viscosity (IV) model developed earlier by Bazua and Williams. Specifically, the elongational viscosity growth function _e ⁺ (t) is presented for abrupt changes in the elongational strain rate . For calculating _e ⁺, a novel treatment of the initial rotation of chain submolecules is required; such rotation occurs in response to the macroscopic step change of at t = 0. Representative are results presented for N = 100 (N = number of submolecules) and = 1000 f and 10000 f (where is the IV coefficient and f is the bead friction coefficient), using h ^* = 0 (as in the original Rouse model) for the hydrodynamic interaction. The major role of IV is to cause the following changes relative to the Rouse model: 1) abrupt stress jump at t = 0 for _e ⁺; 2) general time-retardance of response. There is no qualitative change from the Rouse-model prediction of unbounded il growth when exceeds a critical value ( ), and calculations of submolecule strains at various show that the unbounded- _e ^– behavior arises from unlimited submolecule strains when . However, the time-retardance could delay such growth beyond the timescale of most experiments and spinning processes, so that the instability might not be detected. Finally, _e ⁺ (t) and _e ( ) in the limit are presented for N = 1 and compared with exact predictions for the analogous rigid-rod molecule; close agreement lends support for the new physical approximation introduced for solving the transient dynamics for any N.     

Temperature and concentration dependent viscosity and gelation temperature of ABA triblock copolymer solutions

In solutions of ABA-triblock copolymers in a poor solvent for A thermoreversible gelation can occur. A three-dimensional dynamic network may form and, given the polymer and the solvent, its structure will depend on temperature and polymer mass fraction. The zero-shear rate viscosity of solutions of the triblock-copolymer polystyrene-polyisoprene-polystyrene in n-tetradecane was measured as a function of temperature and polymer mass fraction, and analyzed; the polystyrene blocks contained about 100 monomers, the polyisoprene blocks about 2000 monomers. Empirically, in the viscosity at constant mass fraction plotted versus inverse temperature, two contributions could be discerned; one contribution dominating at high and the other one dominating at low temperatures. In a comparison with theory, the contribution dominating at low temperatures was identified with the Lodge transient network viscosity; some questions remain to be answered, however. An earlier proposal for defining the gelation temperature T _gel is specified for the systems considered, and leads to a gelation curve; T _gel as a function of polymer mass fraction.Mathematical symbols {} functional dependence; e.g., f{x} means f is a function of x - p _log logarithm to the base number p; e.g., ¹⁰log is the common logarithm - exp exponential function with base number e - sin trigonometric sine function - lim limit operation - – in integral sign: Cauchy Principal Value of integral, e.g., - derivative to x - partial derivative to x Latin symbols dimensionless constant - b constant with dimension of absolute temperature - constant with dimension of absolute temperature - B dimensionless constant - c mass fraction - dimensionless constant - constant with dimension of absolute temperature - d ^* dimensionless constant - D{0} constant with dimension of absolute temperature - e base number of natural (or Naperian) logarithm - g distribution function of inverse relaxation times - G relaxation strength relaxation function - h distribution function of relaxation times reaction constant enthalpy of a molecule - H Heaviside unit step function - i complex number defined by i ² = –1 - j{0} constant with dimension of viscosity - j index number - k Boltzmann's constant - k _H Huggins' coefficient - m mass of a molecule - n number - N number - p index number - s entropy of a molecule - t time - T absolute temperature Greek symbols as index: type of polymer molecule - as index: type of polymer molecule - shear as index: type of polymer molecule - shear rate - small variation; e.g. T is a small variation in T relative deviation Dirac delta distribution as index: type of polymer molecule - difference; e.g. is a difference in chemical potential - constant with dimension of absolute temperature - (complex) viscosity - constant with dimension of viscosity - [] intrinsic viscosity number - inverse of relaxation time - chemical potential - number pi; circle circumference divided by its diameter - mass per unit volume - relaxation time shear stress - angular frequency     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. I. Theory

Assuming the formation of doublets in the flow according to a mass action law, the shear rate and the concentration dependence of the extinction angle, of the birefringence, and of the average coil expansion are calculated for dilute solutions of flexible macromolecules. It is shown that this reversible association process has a strong influence on the measurable parameters in a flow birefringence experiment. c concentration (g/cm³) - h ² mean square end-to-end distance at shear rate - h ₀ ² mean-square end-to-end distance at zero-shear rate - n refractive index of the solution (not very different from the solvent for a very dilute solution) - E mean coil expansion - K ₀,K constant of the mass action law - M molecular weight - R _G gas constant - T absolute temperature - ₁ – ₂ optical anisotropy of the segment - ₀ Deborah number: - Deborah number: - shear rate - ₀, reduced concentration - _s viscosity of the solvent - [] ₀ intrinsic viscosity at zero-shear rate - [] intrinsic viscosity at shear rate - extinction angle - N _a Avodagro's number - _n magnitude of the birefringence     

Multiaxial elongation of polyisobutylene with various and changing strain rate ratios

The multiaxial elongational rheometer equipped with rotary clamps is modified such that in addition to simple, equibiaxial and multiaxial elongations also tests with new modes of elongation can be performed. As an example, polyisobutylene is elongated with a ratio of the principal strain rates of and magnitudes of the maximum strain rate , 0.04 and 0.08 s^–1. As a test result, the first elongational viscosityµ ₁ (t) is obtained which follows closely the linear viscoelastic shear viscosity . In contrast, the second elongational viscosityµ ₂ (t) remains below . By means of a further modification of the rheometer, the test modes can be varied during the deformation period. This allows one to investigate the influence of a well-defined rheological pre-history on the following rheological behaviour. As an example a variation ofm = 0.5 2 was performed. The measured normal-stress differences superpose from the single steps of deformation similar to the linear viscoelastic prediction.Dedicated to Prof. F. R. Schwarzl on the occasion of his 60th birthday     

Experimentelle Bestimmung Binghamscher Stoffparameter

An experiment is described to determine the two Bingham material constants (yield stress _f and differential viscosity ) of viscoplastic fluids. The principle of the experiment is based on the falling-ball technique, where the stationary velocities of balls with different diameters and densities are measured. The required theory to calculate the Bingham material constants is illustrated. Experimental results of aqueous Carbopol 941-solutions are reported. These are listed in dependence of concentration in tables and diagrams.

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Zusammenfassung Es wird ein Versuchsaufbau beschrieben, der es ermöglicht, die beiden Binghamschen Stoffparameter (Fließspannung _f und differentielle Viskosität ) einer viskoplastischen Flüssigkeit zu bestimmen. Der Versuch basiert auf dem Kugelfallprinzip, bei dem in einem Zylinder die stationäre Sinkgeschwindigkeit von Kugeln im Schwerefeld gemessen werden. Neben der Geschwindigkeit gehen das spezifische Gewicht der Flüssigkeit sowie die Geometrie und das spezifische Gewicht verschieden großer Kugeln in die Berechnung der Stoffparameter ein. Die zugehörige Theorie wird kurz erläutert. Im experimentellen Teil werden wäßrige Carbopol 941-Lösungen untersucht. Die Ergebnisse sind in Abhängigkeit der Konzentration tabellarisch angegeben und graphisch dargestellt.

     

Druckabhängigkeit der Viskosität einiger Polyolefinschmelzen

Zusammenfassung Es wird die Druckabhängigkeit des nicht -Newtonschen Fließverhältens von Polyolefinschmelzen (Hochdruck-, Niederdruck-,Phillips-Polyäthylen und Polypropylen) experimentell untersucht und gefunden, daß der durch Gl. [1] definierte Druckkoeffizient mit zunehmender Deformationsgeschwindigkeit kleiner wird und dabei die (im einzelnen in der Tabelle 1 angeführten) Werte annimmt. Der Druckkoeffizient der Polyolefinschmelzen ist ebenso wie für vieleNewtonsche Flüssigkeiten bis 2000 kp cm^–2 unabhängig vom Druck, er wird mit zunehmender Temperatur kleiner und nimmt mit zunehmender Verzweigung zu. Die Meßergebnisse werden mit Hilfe eines Aufweitungsvolumens interpretiert. Es wird gezeigt, daß eine Deutung des Fließverhaltens von Polyäthylen durch das freie Volumen allein nicht möglich ist.

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Summary The influence of pressure of the non-Newtonian flow behaviour of polyolefin melts (Low- and High density Polyethylene,Phillips-Polyethylene and Polypropylene) was investigated. The results are: the coefficient of pressure as defined by eq. [1], decreases with increasing shear rate and reaches the values given in table 1 . The pressure coefficient of polyolefin melts does not depend on pressure up to 2000 kp cm^–2. As observed with manyNewtonian fluids, decreases with increasing temperature and increases with the degree of branching. The experimental results are explained by means of a so called volume of expansion. It has been shown that it is impossible to explain the flow behaviour of polyethylene exclusively with the free volume.

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Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe.     

Optimal cupolas of uniform strength: Spherical M-shells and axisymmetric T-shells

Summary The first part of this paper is concerned with the optimal design of spherical cupolas obeying the von Mises yield condition. Five different load combinations, which all include selfweight, are investigated. The second part of the paper deals with the optimal quadratic meridional shape of cupolas obeying the Tresca yield condition, considering selfweight plus the weight of a non-carrying uniform cover. It is established that at long spans some non-spherical Tresca cupolas are much more economical than spherical ones.

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Optimale Kuppeln gleicher Festigkeit: Kugelschalen und axialsymmetrische Schalen

Übersicht Im ersten Teil dieser Arbeit wird der optimale Entwurf sphärischer Kuppeln behandelt, wobei die von Misessche Fließbewegung zugrunde gelegt wird. Fünf verschiedene Lastkombinationen werden untersucht. Der zweite Teil befaßt sich mit der optimalen quadratischen Form des Meridians von Kuppeln, die der Fließbedingung von Tresca folgen.

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List of Symbols a_k, b_k, c_k, A_k, B_k, C_k coefficients used in series solutions - A, B constants in the nondimensional equation of the meridional curve - normal component of the load per unit area of the middle surface - meridional and circumferential forces per unit width - radial pressure per unit area of the middle surface, - skin weight per unit area of the middle surface, - vertical external load per unit horizontal area, - base radius, - R radius of convergence - s - cupola thickness, - u, w subsidiary functions for quadratic cupolas - vertical component of the load per unit area of middle surface - resultant vertical force on a cupola segment - structural weight of cupola, - combined weight of cupola and skin, - distance from the axis of rotation, - vertical distance from the shell apex, - z auxiliary variable in series solutions - specific weight of structural material of cupola - radius of the middle surface, - uniaxial yield stress - meridional stress, - circumferential stress, - _a, _b, _c, _d, _e subsidiary variables used in evaluating the meridional stress - auxiliary function used in series solutions This paper constitutes the third part of a study of shell optimization which was initiated and planned by the late Prof. W. Prager     

Mathematical model of the entry length in the flow of suspensions of solid particles in a gas

A mathematical model consisting of equations of mass and momentum and for the velocity field has been used for computing the entry length of the flow of non-Newtonian fluids in laminar, transition and turbulent regions. Experimental data measured in a vertical flow of a suspension of solid particles in air have been used for verifying the predictions. n flow index for laminar flow - Re Reynolds number defined for the flow of the carrier medium - q exponent for turbulent flow - ratio of core radius with a flat velocity profile to pipe radius - _c ratio of the axial component of local velocity in the core to mean velocity - w mean flow velocity - ratio of axial distance from the pipe entrance to the pipe radius - ratio of the entrance length to the pipe radius - relative mass fraction of particles - ratio of the distance from the pipe wall to the pipe radius - coefficient of pressure loss due to friction     

Rheology of concentrated disperse systems III. General features of the proposed non-newtonian model. Comparison with experimental data

Summary A non-newtonian viscosity equation where is the volume concentration and is an intrinsic viscosity, function of a relative shear rate and being structural parameters, has been proposed in a previous paper (1). From empirical grounds, the valuep = 1/2 holds for a large class of systems, like suspensions of rodand disc-shaped particles. In the high shear rate limit, aCasson law-type is recovered and discussed, especially the concentration dependence of the yield stress. However, the latter disappears in the low shear limit, and must be considered as a pseudo-yield stress. Good agreement is found in this low shear limit with some theoretical results ofBueche for polymers. More generally, the viscosity equation displays pseudo-plastic behaviour and fitting it on experimental data allows the determination of the structural parameters. Some examples (especially Red Blood Cell suspensions and Blood) are studied and support the model. Nevertheless, for spherical particle suspensions, the best fitting is reached forp = 1. Accurate values of particle diameters can be deduced from the structural parameter , in this case.

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Zusammenfassung In einer vorangegangenen Arbeit (1) wurde eine Viskositätsgleichung für eine nicht-newtonsche Flüssigkeit von der Form vorgeschlagen, worin die Volumenkonzentration und eine Grenzviskosität bedeutet; die letztere stellt eine Funktion der relativen Schergeschwindigkeit dar, die Konstantenk ₀,k und bezeichnen Strukturparameter. Empirisch wird gefunden, daß für eine große Klasse von Systemen, wie z. B. stäbchen- und scheibchenförmigen Teilchen,p = 1/2 gilt. In der Grenze hoher Schergeschwindigkeiten wird ein Verlauf gemäß einer Casson-Gleichung gefunden und diskutiert, insbesondere bezüglich der Konzentrationsabhängigkeit der Fließspannung. Allerdings verschwindet diese in der Grenze niedriger Schergeschwindigkeiten und muß daher als Pseudo-Fließspannung betrachtet werden. In diesem Grenzfall wird eine gute Übereinstimmung mit theoretischen Voraussagen vonBueche an Polymeren gefunden. Ganz allgemein beschreibt die obige Viskositätsgleichung ein pseudoplastisches Verhalten, und ihre Anpassung an experimentelle Werte erlaubt die Bestimmung der Strukturparameter. Einige Beispiele, insbesondere Suspensionen von roten Blutkörperchen und Blut, werden untersucht und bestätigen das Modell. Allerdings erhält man bei Suspensionen kugelförmiger Teilchen die beste Anpassung fürp = 1. In diesem Fall kann man mit Hilfe des Strukturparameters genaue Werte der Teilchendurchmesser bestimmen.

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With 5 figures and 3 tables     

A method for correction of the wall-slip effect in a Couette rheometer

A simple method for correction of the wall-slip effect in a Couette rheometer was derived. The method requires only two series of measurements (two flow curves) performed in two measuring sets of any dimensions, and therefore it may be applied for the results obtained in each rheometer with a standard cup and bob set. The method was checked for experimental data and also verified theoretically for a hypothetical liquid. H height of cylinder - M torque - r distance from axis - R _i ,R ₀ radius of inner and outer cylinder - R _m average radius defined by Eq. (7) - u slip velocity - shear rate - shear rate for no-slip conditions - Newtonian viscosity - angular speed - angular speed of the rotating cylinder