Showing papers in "Rheologica Acta in 1983"
TL;DR: In this paper, a piston driven high pressure slit die rheometer with three pressure holes along the die and one in the barrel was used to investigate viscosity, entrance and exit pressure losses.
Abstract: A piston driven high pressure slit die rheometer with three pressure holes along the die and one in the barrel was used to investigate viscosity, entrance and exit pressure losses, and pressure coefficient of viscosity of a LDPE melt. Hydrostatic calibration of melt pressure transducers can be performed in the rheometer. The slit die results are compared with measurements on circular dies assuming linear and parabolic pressure profiles in both cases. A simplified conversion from apparent to true viscosity, applicable for single point measurements, has been used. In spite of the different symmetries the Bagley correction from the linear pressure profile of circular dies was found to be equal to the sum of exit and entrance pressure losses in the slit. The magnitude and sign of the exit pressure loss depend on the type of pressure profile used. The influence of a pressure dependent viscosity and a temperature gradient along the die on the curvature of the pressure profile is discussed. To directly investigate the effect of pressure the pressure level at constant flow rate was increased stepwise by means of a valve attached to the exit of the slit die.
146 citations
TL;DR: In this paper, published exponential relaxation equations, derived from Maxwellian models, were used to generate data for linear representation in the form ofP(0) ·t/(P( 0) ) =k 1 +k 2t whereP(t) is the decaying parameter (force, stress or modulus), P(0), its initial value (att = 0) andk 1 andk 2 constants.
Abstract: Published exponential relaxation equations, derived from Maxwellian models, were used to generate data for linear representation in the form ofP(0) ·t/(P(0) —P(t)) =k 1 +k 2t whereP(t) is the decaying parameter (force, stress or modulus),P(0) its initial value (att = 0) andk 1 andk 2 constants. The computer plots indicated that the fit of this normalized and linearized form was excellent for equations containing at least three exponential decay terms. The fit was not as good for some of the two-term exponential equations mainly due to the lack of accurate account for the initial stage of the relaxation process. In all the cases, however, the linear representation could clearly reveal the general rheological character of the analysed materials in terms of the relative degree of solidity.
134 citations
TL;DR: In this paper, a method has been proposed to estimate the rheograms of a polymeric melt at temperatures relevant to its processing conditions with the use of a master curve, knowing the melt flow index and glass transition temperature of the material.
Abstract: A knowledge of the complete flow curve or rheogram of a polymeric melt depicting the variation of the melt viscosity over industrially relevant range of shear rate and temperature is essential in the design of polymer processing equipment, process optimization and trouble-shooting. These data are generated on sophisticated rheometers that are beyond the financial and technical means of most plastics processors. The only flow parameter available to the processor is the melt flow index of the material. In the present work, a method has been proposed to estimate the rheograms of a melt at temperatures relevant to its processing conditions with the use of a master curve, knowing the melt flow index and glass transition temperature of the material. Master curves that coalesce rheograms of different grades at various temperatures have been generated and presented for low density polyethylene, high density polyethylene, polypropylene, polystyrene and styrene-acrylonitrile copolymer.
65 citations
TL;DR: In this paper, the relationship between molecular weight and rheological properties of agarose gels was examined and the results were compared with those reported in the literature for gelatin gels.
Abstract: Four samples of agarose whose sulfate residue content was virtually the same and for which the degrees of regularity of alternation of D-galactose and 3,6-anhydro-L-galactose were almost equal, were prepared with differing values of the intrinsic viscosity of dilute aqueous solutions. They were used to examine the relationship between molecular weight and the rheological properties of agarose gels. The stress relaxation, dynamic Young's modulus, stress-strain relation and absorbance of light were observed at several temperatures for agarose gels prepared from these fractions at various concentrations. The results are compared with those reported in the literature for gelatin gels.
58 citations
TL;DR: In this article, a slit die rheometer was constructed to measure elastic and viscous properties of molten polymers at low shear rates, and the wall shear stress σ and the extrapolated exit pressurePx were determined by means of two pressure transducers mounted flush with a die wall.
Abstract: A new slit die rheometer has been constructed to measure elastic and viscous properties of molten polymers at low shear rates. The wall shear stress σ and the extrapolated exit pressurePx are determined by means of two pressure transducers mounted flush with a die wall. The hole pressureP* is obtained from one of the flush-mounted transducers and a third transducer mounted in a transverse slot opposite the flush-mounted transducer. The wall shear rate\(\dot s\) is obtained from a metering pump. Electrical heaters give melt temperatures that are uniform to within ±0.1 °C at 150°C. For two low-density polyethylene samples of Melt Index 2 and 50, at shear rates in the range 0.1 to 8 s−1, it is found that (a) viscosity values agree with those obtained using two Weissenberg Rheogoniometers (WRGs); (b) hole pressure data agree with the predictions of the “HPB” transverse-slot equationN1 = 2σdP*/dσ when WRG data are used for the first normal stress differenceN1; and (c) exit pressures are large and negative, in marked disagreement with certain published equations relatingPx,N1 andσ. An error analysis shows thatPx values can contain significant negative contributions arising from the pressure dependence of viscosity, even at low shear rates. As a means for in-line measurement of melt elasticity at low shear rates, the results favor the use of the hole pressure, but raise serious questions about the use of the exit pressure.
52 citations
TL;DR: In this article, a rheological model consisting of a sole constitutive equation was defined according to the Cheng and Evans approach, which was correlated with the cement specific surface and the water/cement ratio.
Abstract: The present work reports an investigation on the rheological behaviour of fresh cement pastes. Three types of Portland cement were used. The water/cement ratio was varied in the range 0.35 ÷ 0.40. The rheological tests were performed using the coaxial-cylinder viscometer Rotovisko-Haake RV 11. The material to be tested was subjected immediately after mixing to a constant shear rate until a steady value of shear stress (equilibrium value) was attained. All the pastes tested exhibited a flow behaviour of the partially thixotropic type. A rheological model consisting of a sole constitutive equation\(\tau = \tau (\dot \gamma ,t)\) was defined according to the Cheng and Evans approach. The parameters of the constitutive equation were correlated with the cement specific surface and the water/cement ratio.
40 citations
TL;DR: In this paper, integral equations for the relative deformation gradient tensors were solved to give analytical expressions which involve velocities and velocity gradients along streamlines, and the expressions were used to obtain the analytical expressions for the deformation tensors.
Abstract: Integral equations for the relative deformation gradient tensors are solved to give analytical expressions which involve velocities and velocity gradients along streamlines.
34 citations
TL;DR: In this paper, the effects of chain branching and chain rigidity on the master curve of a resin type have been elucidated with reference to polyacetal and polysulfone, respectively.
Abstract: A method proposed earlier has been extended to estimate complete flow curves or rheograms of engineering plastics. Master curves that are independent of the grade and temperature have been generated and presented for acrylics, polyacetal, nylons, polyethylene terephthalate, polycarbonate and polysulfone. The influence of the various molecular parameters on the viscosity behaviour of polymer melts have been explained rationally. More specifically, the effects of chain branching and of chain rigidity on the master curve of a resin type have been elucidated with reference to polyacetal and polysulfone, respectively. The method presented here can be used effectively by processors of engineering plastics.
34 citations
TL;DR: In this article, exact solutions to the plane and axi-symmetric stagnation flows of a Maxwellian fluid including inertia are reported. And it is found that the fluid elasticity decreases the boundary layer thickness.
Abstract: Exact solutions to the plane and axi-symmetric stagnation flows of a Maxwellian fluid including inertia are reported It is found that the fluid elasticity decreases the boundary layer thickness
32 citations
TL;DR: Fibril formation in mixtures of incompatible polymers, in this case polyethylene and polystyrene, has been studied with their melt being deformed in a uniform shear field as discussed by the authors.
Abstract: Fibril formation in mixtures of incompatible polymers, in this case polyethylene and polystyrene, has been studied with their melt being deformed in a uniform shear field It has been found that when polyethylene is present in a smaller amount, it may form very long fibrils 5 to 8 µm in diameter in the deformed mixture The formation of such fibrils is determined by the relationship between the viscosity ratio of the mixture components and shear stress Also, just as in the case of a nonuniform shear field in a flow through a duct, fibril formation in melts of mixtures of incompatible polymers in a uniform shear field takes place upon reaching a certain shear stress The lower the ratio between the viscosities of the fibril-forming polymer and the other component, the lower this shear stress
31 citations
TL;DR: In this paper, the problems of uniform extension of liquids under constant strain rate and constant stretching force have been studied using a nonlinear rheological theory that describes the effects of finite elastic strains in viscoelastic liquids.
Abstract: The problems of uniform extension of liquids under constant strain rate and constant stretching force have been studied using a nonlinear rheological theory that describes the effects of finite elastic strains in viscoelastic liquids, with provision for the influence of deformative orientation on a scalar relaxation time. It has been shown that the predictions of the theory are in rather good agreement with numerous data for the extensional flow of polyisobutylene, even without taking the deformative orientation into account, (however, in cases where the latter was important it was considered in detail). Some new results for the extensional properties of polyethylene melts, as well as those from the literature, show that its behaviour is qualitatively different from that of polyisobutylene. The mathematical description of the extensional flow of polyethylene has to take into consideration the mechanism of flow thermoactivation and, apparently, an accumulation of ruptures of macromolecules in addition to the deformative orientation phenomenon.
TL;DR: In this article, a theoretische Begrundung fur die schlechte Berechenbarkeit von Funktionen gegeben, die aus mesfehlerbehafteten dataen uber die Losung der inversen Aufgabe berechnet werden.
Abstract: Unter Verwendung des Begriffs der „nichtkorrekt gestellten Aufgabe“ wird eine theoretische Begrundung fur die schlechte Berechenbarkeit von Funktionen gegeben, die aus mesfehlerbehafteten Daten uber die Losung der inversen Aufgabe berechnet werden. Die wichtigsten nichtkorrekten Aufgaben der Rheometrie werden angegeben sowie die Variante eines Regularisierungsverfahrens (Tichonovsche Regularisierung) vorgestellt, die numerisch stabile Losungen nichtkorrekter Aufgaben zulast. Dabei wird festgestellt, das die Gute der Losung u.a. von der Form des stabilisierenden Funktionals und der Anzahl sowie der Art der Nebenbedingungen beeinflust wird, es aber keine allgemeinen Regeln zur Formulierung der Restriktionen oder der Auswahl des Gutekriteriums gibt.
TL;DR: In this paper, the basic thermodynamic ideas from rubber-elasticity theory which Leonov employed to derive his constitutive model are summarized and compared to the experimental results for Melt I and to the Wagner model.
Abstract: The basic thermodynamic ideas from rubber-elasticity theory which Leonov employed to derive his constitutive model are herein summarized. Predictions of the single-mode version are presented for homogeneous elongational flows including stress growth following start-up of steady flow, stress decay following sudden stretching and following cessation of steady flow, elastic recovery following cessation of steady flow, energy storage in steady-state flow, and the velocity profile in constantforce spinning. Using parameters of the multiple-mode version which fit the linearviscoelastic data, the Leonov-model predictions of elongational stress growth during, and elastic recovery following, steady elongation are calculated numerically and compared to the experimental results for Melt I and to the Wagner model. It is found that the Leonov model, as originally formulated, agrees qualitatively with the data, but not quantitatively; the Wagner model gives quantitative agreement, but requires much nonlinear data with which to fit model parameters. Quantitative agreement can be obtained with the Leonov model, if the nonequilibrium potential which relates recoverable strain to strain rate is adjusted empirically. This can most simply be done by making each relaxation time dependent upon the recoverable strain. The Leonov model, unlike the Wagner model, is derived from an entropic constitutive equation, which is advantageous for calculating stored elastic energy or viscous dissipation. The Leonov model also has an appealingly simple differential form, similar to the upper-convected Maxwell model, which, in numerical calculations, may be an important advantage over the integral Wagner model.
TL;DR: Theoretical analyses of such flows are presented in this article, where the authors show that during injection molding of thermoplastic polymers, during mold filling, flows of hot melts into mould networks, the walls of which are so cold that frozen layers form on them.
Abstract: The injection moulding of thermoplastic polymers involves, during mould filling, flows of hot melts into mould networks, the walls of which are so cold that frozen layers form on them. Theoretical analyses of such flows are presented here.
TL;DR: In this article, a finite element method was used to simulate the drawing process of the glass fiber drawing process and the two-dimensional energy and momentum equations were solved in their fully non-linear forms.
Abstract: The glass fibre drawing process is simulated using a finite-element method. The two-dimensional energy and momentum equations are solved in their fully non-linear forms. These are coupled via the temperature-sensitive viscosity function. Both convective and radiative cooling mechanisms are taken into account on the filament surface. An effective emissivity of about 0.2 is found to be applicable to the drawing conditions in this paper. Even at this fairly low effective emissivity, radiation is found to be the dominant mode of cooling. The material thermal conductivity is found to have a small but definite influence on the filament profiles. Two-dimensionsl effects of the kinematic field are only significant up to a distance of about two orifice radii from the nozzle exit.
TL;DR: In this article, Approximationsgleichungen f den Durchsatz, the Leistung, the Geschwindigkeit, and the Schergeschwindigekeit vorgestellt.
Abstract: Die Auslegung von Extrudern fur Schmelzen mit Potenzgesetzverhalten ist unter Einbeziehung des Querstromungseinflusses bisher nur mit numerischen Verfahren moglich. In diesem Beitrag werden Approximationsgleichungen fur den Durchsatz, die Leistung, die Geschwindigkeit und Schergeschwindigkeit vorgestellt, die eine Auslegung ohne aufwendige numerische Verfahren gestattet. Innerhalb bestimmter Grenzen sind die Ergebnisse der Approximationsgleichungen weitgehend identisch mit denen der numerischen Verfahren. Es werden sowohl Ein- als auch Mehrzonenschnecken isotherm und nicht-isotherm behandelt.
TL;DR: In this article, it is shown that Tirrell's diffusion flux can be deduced from a macroscopic modelling which involves second-order gradients and a vectorial internal variable related to the microstructure.
Abstract: The present study concerns the phenomenon of flow-induced polymer migration. It is shown that Tirrell's diffusion flux can be deduced from a macroscopic modelling which involves second-order gradients and a vectorial internal variable related to the microstructure. In contrast to Tirrell's model, however, a migration may also occur across straight streamlines. The flow down an inclined plane is examined by way of example. The roles played by the microstructure and the second gradients, respectively, are thus exhibited.
TL;DR: In this article, the rheological behavior of three types of HDPE/LDPE blends at several compositions (various weight percentages of LDPE) was studied with the aid of a capillary rheometer and three different capillaries.
Abstract: The rheological behaviour of three types of HDPE/LDPE blends at several compositions (various weight percentages of LDPE) has been studied with the aid of a capillary rheometer and three different capillaries.
TL;DR: In this article, the authors defined relative viscosity as the ratio of suspension visco-solutions to solution viscosities at the same shear stress rather than shear rate, which reached asymptotic values for all concentrations of dissolved polymer and for all particle loadings.
Abstract: Viscosities of suspended particles in polymeric solutions depend upon dissolved polymer concentration, volume fraction of particles and shear rate. In this analysis of viscosity data, relative viscosity was defined as the ratio of suspension viscosity to solution viscosity at the same shear stress rather than shear rate. These relative viscosities reached asymptotic values at high shear stress for all concentrations of dissolved polymer and for all particle loadings. At a given particle loading, the asymptotic values of relative viscosity were nearly independent of the concentration of dissolved polymer. Realtive viscosities were correlated with volume fraction by the one-constant equation of Maron and Pierce.
TL;DR: In this paper, the viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) stress growth rate at constant speed and (iii) the elastic recovery in elongational flow.
Abstract: The viscoelastic behavior of polymeric systems based upon the Leonov model has been examined for (i) the stress growth at constant strain rate, (ii) the stress growth at constant speed and (iii) the elastic recovery in elongational flow. The model parameters have been determined from the available rheological data obtained either in steady shear flow (shear viscosity and first normal-stress difference as a function of shear rate) or oscillatory flow (storage and loss moduli as a function of frequency in the linear region) or from extensional flow at very small strain rates (time-dependent elongation viscosity in the linear viscoelastic limit). In addition, the effect of the parameter characterizing the strain-hardening of the material during elongation has also been studied. The estimation of this parameter has been based upon the structural characteristics of the polymer chain which include the critical molecular weight and molecular weight of an independent segment. Five different polymer melts have been considered with varying number of modes (maximum four modes). Resulting predictions are in fair agreement with corresponding experimental data in the literature.
TL;DR: In this paper, the influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed separately for the low Reynolds number and the high Reynolds number regions.
Abstract: The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions In the former, we make use of the two-concentric-sphere model It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids
TL;DR: In this paper, the properties of six high-density polyethylene (HDPE) samples with known average molecular weight and molecular weight distribution have been determined with the aid of two capillary viscometers over a wide range of temperatures and shear rates.
Abstract: Rheological properties of six high-density-polyethylene (HDPE) samples with known average molecular weight and molecular weight distribution have been determined with the aid of two capillary viscometers over a wide range of temperatures and shear rates. Generalized relationships have been found for the entrance correction, the zero-shear viscosity and the shift factors of the whole viscosity curve.
TL;DR: In this article, the dynamic shear moduli as functions of circular frequency are measured first for the melts of a series of polystyrenes of narrow molecular mass distributions, after careful preparation of mixtures the same moduli are also determined for these mixtures.
Abstract: A mixing rule as suggested by the Doi-Edwards theory is checked experimentally. For this purpose, the dynamic shear moduli as functions of circular frequency are measured first for the melts of a series of polystyrenes of narrow molecular mass distributions. After the careful preparation of mixtures the same moduli are also determined for these mixtures. A discussion is given of the remarkable but limited validity of the additivity of contributions by the single macromolecules to the mentioned moduli.
TL;DR: In this paper, the effect of inertia in three popular impulse experiments in shear flows of viscoelastic liquids is considered and the difference between experimental observables and a theory based on the assumption of ignorable inertia could be quite substantial.
Abstract: The effect of inertia in three popular impulse experiments in shear flows of viscoelastic liquids is considered. Dynamics of the flow is used to evaluate the stress observables such as the shear stress and the first normal stress difference at the walls. In particular we find that for many linear viscoelastic models with slowly fading memory, the difference between experimental observables and a theory based on the assumption of ignorable inertia could be quite substantial.
TL;DR: In this paper, a parallel-plate rheometer was constructed for use with the Materials Test System (MTS) for the measurement of fast transient and steady-state responses of polymeric liquids.
Abstract: A parallel-plate rheometer (PPR) has been constructed for use with the Materials Test System (MTS) for the measurement of fast transient and steady-state responses of polymeric liquids. This particular combination exploits the versatility and capability of the MTS programmable drive system, while the design of the PPR ensures the ideal simple shearing configuration. Instrument compliance, material inertia and mechanical lag in both the input and output components of the system are minimal, thus avoiding defects of most existing rheometers. Reproducible data on a 20% polyisobutylene-in-decalin solution have been obtained for various complicated flow programs. This test system is thus suitable for extensive rheological characterization of complex viscous liquids.
TL;DR: In this article, the elongational behaviour of polyethylene samples having different molecular structure has been tested using the isothermal melt spinning technique and the extensional behaviour of the different samples is analyzed as a function of total strain.
Abstract: The elongational behaviour of polyethylene samples having different molecular structure has been tested. Elongational viscosity measurements have been carried out using the isothermal melt spinning technique. The extensional behaviour of the different samples is analysed as a function of total strain. The effect of long-chain branching on elongational viscosities is described. A comparison is presented between elongational viscosity and melt strength data.
TL;DR: In this article, the authors reported the generation of excess thermal noise induced by capillary flow of aqueous solutions of poly(ethylene oxide) (PEO) are supplemented by measurements on the following solutions: PEO/DMF, PS/THF, PVAC/cyclohexanone, and poly(acrylamide)/water.
Abstract: The previously reported results concerning the generation of excess thermal noise induced by capillary flow of aqueous solutions of poly(ethylene oxide) (PEO) are supplemented by measurements on the following solutions: PEO/DMF, PEO/i-PrOH, PS/THF, PVAC/cyclohexanone, and poly(acrylamide)/water. Similarly to the previous findings, a noise level increasing with the flow rate is recorded, the noise exhibiting a l/fα-frequency spectrum. Within a certain flow range, distinct peaks are recorded in the spectrum (harmonics of a fundamental frequency,f0). Thef0-values of the various solutions under varying flow conditions arrange themselves along a commonf0-shear rate curve. They appear to be associated with transversal oscillations of the solution upstream the capillary entrance.
TL;DR: In this article, a theory of a two-point rheometrical method of determination of the weight-average molecular weightM w of polyamide-6 is presented, based on the measurement of the instantaneous values of zero-shear-rate viscosity of the degrading polymer melt, and a formula is derived which enables the calculation of the initial value ofM w (i.e. at zero-residence-time in molten state) of the investigated sample.
Abstract: A theory of a two-point rheometrical method of determination of the weight-average molecular weightM w of polyamide-6 is presented. The method is based on the measurement of the instantaneous values of zero-shear-rate viscosity of the degrading polymer melt, and a formula is derived which enables the calculation of the initial value ofM w (i.e. at zero-residence-time in molten state) of the investigated sample. The experimental verification of the method proves its applicability. The considerations carried out may be regarded as a first step towards developing a theory of an in-line rheometer for a continuous determination ofM w .
TL;DR: The second moment of the finite cluster statistics exhibits a maximum for a 2-D concentration ΦS near 0.67 without measurable anomaly in the viscosity as discussed by the authors, and the results of the cluster statistics are compared to those obtained in percolation.
Abstract: We study the cluster statistics and the viscosity of a two-dimensional suspension of passive macroscopic spheres undergoing shear. The second moment of the finite cluster statistics exhibits a maximum for a 2-D concentrationΦS near 0.67 without measurable anomaly in the viscosity. The results of the cluster statistics are compared to those obtained in percolation.
TL;DR: In this article, the normal-stress difference between six high-density polyethylene (HDPE) samples was calculated by using Tanner's approach and an analytical expression has been found correlating the normal stress difference with the shear-stress taking into account the molecular characteristics.
Abstract: Die-swell data have been obtained for six high-density-polyethylene (HDPE) samples. The data are presented in the form of generalized relationships taking into account both molecular and operational parameters.Data obtained from annealed samples have been used to calculate the first normal-stress difference by using Tanner's approach. An analytical expression has been found correlating the normal-stress difference with the shear-stress taking into account the molecular characteristics.