Non-Newtonian Rheology

Linear-low-density polyethylene (LLDPE) is steadily gaining importance in a wide variety of applications due to its excellent performance characteristics in the final product. The rheological properties of LLDPE in the dynamic and steady state are of great pragmatic importance and these have been studied in the present work. A correlation between the dynamic and steady-state rheological properties has been attempted and good agreement has been found.

Investigation into the effects of two-step exothermic third-grade chemical reactive
poiseuille fluid flow through fixed walls with exponentially heat dependent viscosity
on the flow and heat transfer rate is carried out. The reactive non-Newtonian fluid is
propelled by constant pressure gradient under Bimolecular kinetic rate law and heat
absorption. The reactive fluid is stimulated by periodic variations in time. The upper
wall of the channel is exposed to coolant convection heat exchange with the
environment and it satisfied the Newton’s cooling law. The dimensionless velocity and
energy balance flow equations are computationally solved by applying a stable and
convergent finite semi-implicit method of an even finer mesh. The response of the flow
fluid and temperature to variational rise in some values of the embedded fluid
parameters are graphically presented. The bifurcation and thermal criticality results
of the reactive fluid under different chemical kinetics are also obtained and conferred
quantitatively.

BaTiO3 thin films have been prepared by inkjet depositing of ceramic inks based on barium titanate nanopowder. Formulated inks had good sedimentation stability. The most significant stabilization of the pigment was observed for samples formulated on ethyl and n-butyl alcohols. All prepared inks had dilatant flow with a pronounced minimum viscosity of Newtonian flow. The printing operation was performed using thermal drop-on-demand inkjet printer. Printed films had dense structure and considerable adhesion to the substrate surface. Optical profilometry of the three layer film showed thickness about 400 nm. Due to strong adhesion printed coatings have not separated from the substrate surface. Special method of forming an intermediate polymer film on the substrate surface has been used to separate printed patterns. Aggres-sively dissolving of an intermediate polymer film has been observed during printing on this intermediate layer. After printing of each subsequent layer substrate thickness has been reduced on average 200 nm and took place rising of surface roughness. However, printed layer has been removed from the substrate surface.

The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article the key aspects of these fluids are reviewed with particular emphasis on single-phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.

The dynamic mechanical properties in terms of the storage modulus E′, loss modulus E″, and the loss tangent δ has been studied for highly filled magnetic polymer composites. The effect of surface treatment on the relaxation spectra has been clearly elucidated and quantitative values indicating the extent of polymer–filler interactions have been given. Various models have been tested for describing the viscoelastic behavior of such highly filled systems. The Wiechert model using a single-arm with a Cole–Cole parameter has been shown to effectively fit the Argand diagram in the case of the present highly filled systems

Presents rheological data on a number of polymers, making use of the master curve approach to determine unified curves for each generic type of polymer. The text offers a step-by-step procedure for developing a speadsheet computer program to obtain accurate thermoplastic rheograms at any tempertature without using sophisticated rheometres. It includes possible correlations of melt flow index with various parameters involved in polymer manufacture, product fabrication and property evaluation.

Review
This book offers an interesting, practical approach to the rheology and processing parameters of thermoplastic materials. . . This book is recommended for engineers and processors who may benefit from the use of the spreadsheet program to predict the behavior of thermoplastic materials as a function of processing parameters.
---Polymer News

The rheology of filled polymer systems is an ever expanding field in the polymer industry today. Using a concise, practical and simple format this comprehensive work explains the concepts behind filled polymer systems and the rheological techniques involved in studying their behaviour. Aware that the readers of the book may come from differing background, the first three chapters familiarize the reader with the basics about polymers, fillers and physicochemical interactions between them, rheology and rheometry. Covering such topics as preparation of filled polymer systems, steady shear viscous properties and extentional flow properties, this book covers the areas of importance from an introductory level through to more complex issues.

Review
`Rheology of Filled Polymer Systems will be of most interest to those involved in injection molding and similar processes. [...]if you are interested in molding processes, and especially in the theoretical background, then this book is for you. [...]The main feature which distinguishes this book from others on polymer rheology is its focus on filled systems. The addition of fillers (particles, fibers, flakes, etc.) makes such systems behave much differently than unfilled polymers. [...]the writing is quite good [...] Shenoy does a good job of presenting data for a variety of systems, explaining the trends intuitively, and then showing how it all fits in with the theories developed earlier in the book.'
Barry Berenberg in Composite.About.com

Demon3 on November 22, 2000Format: Hardcover
Book Review - Rheology of Filled Polymer Systems Aroon V. Shenoy

Kluwer Academic Publishers ISBN 0-412-83100-7

As a researcher in the area of particulate-filled composites I am continually looking for good books on this subject. Such books are hard to find, possibly because the topic is so multi-disciplinary that few authors manage to bring together the knowledge from polymer science (processing, stability, mechanical properties), surface science (dispersion, wetting, surface-treatment) and rheology (compounding and processing).

One area where it is especially difficult to find good information is that of filled polymer rheology. This topic is vital to understanding the behaviour of a filled polymer melt. For example, extruder throughput and mould filling during injection moulding are critical factors that must be understood when formulating a good particulate-filled polymer composite. I have found it hard to understand most texts on filled polymer rheology and therefore I was relieved when I read this book. The author must be congratulated on having presented such a complex field in a focussed and interesting way. All aspects of rheological measurement techniques are covered. First of all is an introduction to the rheological behaviour of un-filled polymers. Basic rheological concepts are presented followed by a comparison of the different measurement techniques. Steady shear and unsteady shear are both treated in detail where the author highlights the trends such as the influence of particle size, shape, distribution, concentration and surface treatment. Another chapter discusses the different types of polymer processing equipment and their relative merits and drawbacks for preparing polymer composites.

One especially intriguing section shows that even MFI data, which is simple and inexpensive to obtain, can be used as a powerful tool for estimating the rheological response of a filled polymer melt. The author shows that just by knowing the MFI and the Tg of the polymer, it is possible to calculate an approximate rheological response of the filled polymer melt. This estimation has sufficient accuracy to be of use in predicting the flow behaviour of the filled polymer melt during processing. Thus, even the humble MFI technique is shown to be a powerful tool and I expect that Shenoy's Unification approach will prove useful for many people, including myself.

I highly recommend this book to anyone interested in filled polymers. It is clearly written by someone with an excellent grasp of the subject. The text is concise and easy to read whilst the content is well organized and interesting.

This study concluded the results of a research on the features of cement based permeation grout, based on some important grout parameters, such as the rheological properties (yield stress and viscosity), coefficient of permeability to grout (kG) and the inject ability of cement grout (N and Nc assessment), which govern the performance of cement based permeation grouting in porous media. Due to the limited knowledge of these important grout parameters and other influencing factors (filtration pressure, rate and time of injection and the grout volume) used in the field work, the application of cement based permeation grouting is still largely a trial and error process in the current practice, especially in the local construction industry. It is seen possible to use simple formulas in order to select the injection parameters and to evaluate their inter-relationship, as well as to optimize injection spacing and times with respect to injection source dimensions and in-situ permeability. The validity of spherical and cylindrical flow model was not verified by any past research works covered in the literature review. Therefore, a theoretical investigation including grout flow models and significant grout parameters for the design of permeation grouting was conducted in this study. This two grout flow models were applied for three grout mixes prepared for w/c=0.75, w/c=1.00 and w/c=1.25 in this study. The relations between injection times, radius, pump pressure and flow rate for both flow models were investigated and the results were presented. Furthermore, in order to investigate these two flow model, some rheological properties of the grout mixes, particle size distribution of the cement used in this study and some geotechnical properties of the sand used in this work were defined and presented.

Rheological data of unmodified and polymer-modified asphalts are conventionally obtained from dynamic mechanical characterization and expressed in terms of sets of curves showing the variation of viscoelastic properties with frequency. Using the conventional melt flow indexer, the material's volumetric-flow rate MVR (in cm3 / 10 minutes) through a predefined die under conditions of constant temperature and stress when obtained for the same asphalts, shows a direct relationship with the dynamic data. The MVR value helps in unifying the sets of dynamic data curves of |G*|, G" and |G* |/sin d versus frequency in the case of unmodified asphalts, poly- mer-modified asphalts and asphalt mastics. The unification technique has a sound theoretical basis and the uni- fied curves have far-reaching implications. Since MVR is so simple to determine quite accurately on a relatively inexpensive, easy-to-use flow measurement device (FMD), this parameter can be generated on paving sites or at refineries, if needed, rather than in research laboratories as is the case with the fundamental rheological parameters. The MVR can then be used as an excellent indicator of the fundamental rheological parameters through the use of the unified curves. The MVR can be utilized to accurately determine the currently used high temperature performance grade specification of paving asphalt. On account of the simplicity in obtaining this specification value from the MVR, it may be routinely used for quality control / quality assurance purposes. It can also be used as a rapid product development / formulation tool.
Zusammenfassung Die rheologische Daten von unmodifizierten und durch Polymere modifizierte Asphalte werden üblicherweise mittels dynamisch-mechanischer Charakterisierung erhalten und dann als Kurvenschar, welche die Änderung der viskoelastischen Eigenschaften bei verschiedenen Frequenzen zeigen, dargestellt. Für die gleichen Asphal- te kann aber auch die volumetrische Fliessrate (MVR), welche in einem konventionellen Melt Flow Indexer mit definierter Düse bei konstanter Temperatur und Schubspannung gemessen wird, mit den dynamischen Daten korreliert werden. Der MVR-Wert wird hierbei benutzt, um die frequenzabhängigen dynamischen Daten für |G*|, G" und |G*|/sin d für modifizierte und unmodifizierte Asphalte und Asphaltharze zu normieren. Diese Normie- rungstechnik basiert auf einen theoretischen Hintergrund und die normierten Kurven haben weitreichende prak- tische Konsequenzen. Der MVR-Wert kann sehr einfach und genau mit preiswerten und einfach zu bedienen- den Flow Measurement Devices (FMD) vor Ort oder in Raffinerien bestimmt werden, anstatt in Forschungslabors durch aufwendige rheologische Versuche. Der MVR-Wert kann sodann mittels der normierten Kurven als ein hervorragender Indikator für fundamentale rheologische Parameter herangezogen werden. Zudem kann er benutzt werden um die gegenwärtig verwendete "High Temperature Performance Grade" Anforderungen von Strassenasphalt präzise zu bestimmen. In Anbetracht der Einfachheit, mit welcher diese Spezifikation anhand des MVR-Wertes bestimmt werden kann, könnte dieses Verfahren routinemässig zur Qualitätskontrolle und Qualitätsbürgschaft ebenso zur schnellen Produktentwicklung verwendet werden.

Polymer blends have received a lot of attention in recent years due to the possibility of getting compounds with novel and/or different properties through proper marriage of the properties of the respective mono-components. The flow behaviour of blends when subjected to stresses is complex and is often found not to vary monotonically with composition. Mixing rules and mixture theories have been used for estimating melt viscosity of a blend at zero shear rate. However a knowledge of the entire rheogram is desirable for process optimization, process design and trouble shooting.In the present paper a method proposed earlier to estimate the rheograms of polymer melts through the use of the melt flow index has been extended to polyblends. A method for obtaining the melt flow index of the polymer blends at various compositions from the melt flow index of the individual components and the blend ratio has been suggested based on the altered free volume state model. Curves that are coalesced using the melt flow index of the blend at different blend ratios have been presented for a polypropylene-high density polyethylene blend, a high density polyethylene-polymethyl methacrylate blend, a polystyrene-polymethyl-methacrylate blend, a polystyrene-polyacetal blend and a polymethylmethacrylate-polyacetal blend.

The present analysis deals with the study of time-dependent flow of a second-order fluid on a rotating cone in the presence of chemical reaction and heat generation or absorption effects under prescribed heat flux conditions. The boundary-layer nonlinear partial differential equations of second grade fluid are first reduced into a system of ordinary differential equations with the help of transformations and nondimensional similar and nonsimilar quantities, and then solved analytically by optimal homotopy analysis method (OHAM). The effects of relevant parameters such as chemical reaction, heat generation, or absorption on local skin friction coefficients, local Nusselt number, and local Sherwood number are discussed. These effects are illustrated graphically as well as in tabular form to describe special features of the solutions.

Polymers filled with extending fillers, such as calcium carbonate or talc, or with reinforcing fillers, such as glass fibers or mica, are increasingly being used in a number of applications. The addition of fillers to a polymer changes the melt rheological behavior of the polymer. A knowledge of the viscosity vs. shear-rate flow curves of the filled system at various temperatures and as a function of filler parameters (such as filler type, shape, and amount) is necessary for process design, optimization, and trouble shooting. The generation of such rheological data is ezpensive and cumbersome in view of the broad range of fillers and the large numbers of filler parameters. In the present article, a unifying approach is proposed that coalesces the flow curves of filled systems of a polymer at various temperatures into a master curve that is independent of the filler parameters. An effective methods is presented to estimate the rheograms of filled systems with the use of a master curve, characteristic of a genetic resin type, knowing the melt-flow index and glass-transition temperature of the system. Master curves have been reported for filled system of low-density polyethylene, high-density polyethylene, poly-propylene polystyrene, nylons, poly(ethylene terephthalate), and polycarbonate.

A knowledge of the complete flow curve, or rheogram, of a PVC formulation depicting the variation of the melt viscosity over industrially relevant ranges of shear rate and temperature is essential in the design of polymer-processing equipment, process optimization, and troubleshooting. These data are generated on sophisticated rheometers that are beyond the financial and technical means of most PVC processors. The only flow parameter that can be readily measured on an inexpensive apparatus is the melt flow index of the resin-mix. In the present work, a method has been proposed to estimate the rheograms of a PVC formulation 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 formulation. A master curve that coalesces rheograms of different PVC formulations at various temperatures has been generated and proposed as a tool for estimating the flow curve.

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of Computational Fluid Dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

This paper reports the results of an experimental investigation to determine the climbing constants of viscoelastic liquids in the rotating rod geometry with two layers of viscoelastic liquids
and the results of an investigation which describes the effects of eccentricity on the free surface shape of a non-Newtonian liquid in motion between eccentric cylinders. The former set of results shows the rotating rod geometry with a layered medium of viscoelastic liquids may be used as a free surface viscometer yielding reliable and reproducible values for the sequentially determined climbing constants of those liquids. The latter set of results indicates that the concentric cylinder geometry is not
a good free surface viscometer. Very small eccentricities generate large circumferential pressure gradients which overwhelm small normal stress effects. There is good agreement between experimental and second order predictions for small eccentricities and rotational speeds and fluids which display large normal stress effects.

A tribo-dynamics model, predicting the conjunctional inefficiency and dynamic response of automotive hypoid gear pairs is presented. A dynamics model is coupled with an analytical friction model (viscous and boundary). The temperature rise at the centre of the conjunction is accounted for through use of thermal network model and Time Temperature Superposition (TTS) method, as well as the time varying geometry of the meshing gear teeth. Newtonian and non-Newtonian lubricant shear behaviour are both considered Surface topography measurements of a run-in pinions are obtained. Inefficiency calculations are performed for typical automotive drive cycle snapshots. Precisely measured lubricant shear characterstics for lubricants different blended viscosity modifiers and evolving surface topography are used in the study of transmission inefficiency. The integrated thermal-tribodynamic analysis is shown to distinguish between different viscosity modifier types, an approach not hitherto reported in literature.

The nature of transition from ordinary micelles (of nanometer length scale) of surface active ionic liquid 1-Hexadecyl-3-methylimidazolium chloride, to wormlike micelles (WLM) (micrometer length scale), mediated by hydroxy aromatic π-electron systems 1-Naphthol, 2-Naphthol and 2,3-Dihydroxynaphthalene (2,3-DHN) in salt free condition have been studied under Newtonian as well as non-Newtonian flow regimes. Conductance and tensiometry show that the additives lower the CMC of the ionic liquid. The interaction parameter (β) of the systems at different mole fraction evaluated on basis of Rubingh’s Regular solution approach were negative at all SAIL/Additive compositions. UV-Vis spectroscopy showed that micelle-bound additives formed hydrogen bonds with interfacial water molecules. Increase in steady state fluorescence anisotropic measurements revealed that the additives increasingly partitioned within the micelles. 1H-NMR study confirmed that although the additives reside at the palisade layer, they perturb the micellar core as well. At higher concentration (100mM, 1:1), systems formed transparent viscoelastic gel. Rheological study of the viscoelastic gels showed that their zero shear viscosity is a function of temperature. 2,3-DHN interacted most strongly with the SAIL micelles, both in Newtonian and non-Newtonian regimes. This was corroborated by DFT study of binding energy.  Hydrogen bonding of the hydroxy functionality along with strong cation-π interaction between the aromatic moieties and the imidazolium ring are considered as the main driving forces behind the morphology change. The viscosity of C16-3-MeImCl/1-Naphthol increased as function of salt concentration unlike C16-3-MeImCl/NaSal system. A possible mechanism is suggested and discussed. The present study sheds light on understanding the molecular interactions behind the structural change from spherical to elongated micelles, in both microscopic and macroscopic scale, triggered by hydroxy naphthalenes under salt-free condition. The metal tolerance of the gels has huge application prospects as fractured fluids in oil-mining industry.

We have studied the rheological properties of some magnetorheological fluids (MRF). MRF are known to exhibit original rheological properties when an external magnetic field is applied, useful in many applications such as clutches, damping devices, pumps, antiseismic protections, etc. While exploiting parameters such as magnetic field intensity, particle concentration and the viscosity of the suspending fluid, we highlighted the importance of each one of these parameters on rheology in the presence of a magnetic field. We made this study by conducting rheological experiments in dynamic mode at very low strain which facilitates the comprehension of the influence of the structure on MRF rheology. Our results confirmed the link between the magnetic forces which ensure the cohesion of the particles in aggregates, and the elastic modulus. Moreover, we found that the loss modulus varies with the frequency in a similar manner than the elastic modulus. The system, even with the smallest deformations, was thus not purely elastic but dissipates also much energy. Moreover, we demonstrated that this dissipation of energy was not due to the matrix viscosity. Actually, we attributed viscous losses to particle movements within aggregates.

Rheological modelling of drilling fluids in oil fields is usually described by Bingham plastic and Ostwald-deWaele models. These models gain popularity because their specific descriptive parameters are fairly easy to estimate. Standard methods use Fann VG meter dial reading at 600 and 300 rpm to determine these rheological parameters. Unfortunately, these points correspond to higher shear rates which seldom prevail during particle settling. Recently, many researchers pointed out that the non-Newtonian behavior of drilling fluids can be described well by the three parameters Herschle-Bulkley model. Again, the determination of its parameters using the standard API method make use of dial readings at 6 & 3 rpm to determine yield stress and 600 and 300 rpm to determine the other two parameters. Furthermore, the use of non-linear regression techniques to determine these parameters though deemed more accurate, sometimes give meaningless negative yield stress values. This work aims to investigate different techniques and shear rates to derive rheological parameters and show their influence on the magnitude of effective viscosity and hence settling velocity. It is demonstrated that very small differences among the values of the model parameters determined by different techniques/dial readings can lead to substantial differences in predicted settling velocities. Results of this work shows that the use of Herschle-Bulkley rheological parameters was by far the most accurate for representing the example muds rheograms as well as predicting the settling velocities, particularly when using non-linear regression values.

The importance of linear low density polyethylene (LLDPE) is being rapidly felt. The combination of favourable production economics and excellent product performance characteristics has enabled this new plastic to gain acceptance for a wide variety of applications. No studies on the rheological properties of LLDPE exist to date. The viscous and elastic properties of this new polymer has now been investigated and unified curves for viscosity and normal stress differences are given. The temperature dependence of the rheological properties of LLDPE has also been studied.

Mediums are a combination of drying oils and other materials such as varnish, wax, gums and dryers, used to modify the texture of the oil paint. The aim of this work was to analyse the rheological properties of some artists' oil based mediums (labelled as thixotropic) created by two modern brands with different scale manufacturing: Winsor and Newton with Liquin Original, Liquin Light Gel and Liquin Impasto, based on alkyd resin and Natural Pigments that sells Oleogel, Oleoresgel and Impasto Medium, based on linseed oil and different thickening silica. Rheological characterization of the mediums was carried out at 20ºC with a RS1 Rheostress (TermoHaake, Germany). All mediums presented high shear thinning behaviour and important yield stresses, with different zero shear viscosities. They also showed a predominant elastic behaviour. Some differences were observed in time evolution of viscosity and the recovery of elastic modulus, which is related to the supposed thixotropy of these mediums.

A method has been proposed earlier by Shenoy et al. to estimate complete flow curves depicting the variation of melt viscosity over industrially relevant range of shear rate and temperature through the use of unified curves characteristic of each generic type of polymer. In the present paper, the unified curves have been fitted through modified forms of already known generalized Newtonian models. The advantage of fitting such rheological models to unified curves lies in the fact that calculations involving entrance length estimates, heat transfer, die design, mold design, etc. are greatly simplified. Knowing the model parameters, one needs to know only the melt flow index, which is a relatively easy parameter to obtain, to make any engineering design calculations. The modified generalized Newtonian models have been fitted to a number of polymers covering one or more from each group of olefinics, styrenics, cellulosics, vinyls and engineering thermoplastics.

The support pressure of a slurry shield corresponds to the in situ earth and groundwater pressure to ensure the stability of the tunnel face. The support fluid (bentonite suspension) penetrates from the excavation chamber into the pore space and transfers the support pressure to the granular structure of the soil within this zone. At the same time, the cutting tools rotate periodically with the cutting wheel and remove the penetrated soil up to a certain cutting depth at the face. Shortly after the tool passing, the penetration process starts again. Both, the support pressure and the soil excavation, act in the same direction at the tunnel face, but they are subject to different cyclic intervals. This relationship between the time needed for the transient penetration process and the interval of the cyclic passage of the cutting tools at a local point at the face is examined and the impact onto the global face stability is discussed.

The steady motion of a simple fluid between vertical cylinders which rotate about non-concentric axes is solved by means of domain perturbations. The theory is developed as a perturbation of the rest state in powers of the angular frequency (omega) of the inner cylinder, and the solution is carried out to and including the second order in (omega). The stress is expanded in a series of Rivlin-Ericksen tensors. At
the second order only one material parameter, the climbing constant, enters the analysis. A procedure is developed for predicting the shape of the free surface on the fluid. Secondary motions generated by the eccentricity are shown to appear at the second order.

The need for recycling of polymeric waste has been well recogmized as a result of the escalating prices of the petrochemical feedstocks and the growing awareness to curtail solid waste that causes environmental pollution. During processing, the molecular weight of the polymer is reduced due to thermal and shear degradation. Since the melt rheology of the processed material is sensitive to the changes in molecular structure, knowledge of the complete flow curve depicting the variation of melt viscosity with shear rate at processing temperatures is a useful tool for assessing the reprocessibility of waste material and for specifying the conditions of reprocessing. In the present paper, an effective method is proposed to generate the melt flow curves of polymer waste from knowledge of its melt flow index. The method makes use of a master curve that can be obtained by plotting the available viscosity data in terms of modified functions based on the melt flow index. The master curves characteristic of the particular generic resin type are presented for low-density polyethylene, polypropylene and polystyrene.

A residual-based lubrication method is used in this paper to find the flow rate and pressure field in converging-diverging rigid tubes for the flow of time-independent category of non-Newtonian fluids. Five converging-diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel-Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging-diverging tubes, convergence to analytical solutions found earlier for the flow in converging-diverging tubes of Newtonian fluids as special cases for non-Newtonian, and convergence to analytical solutions found earlier for the flow of power-law fluids in converging-diverging tubes. A brief investigation was also conducted on a sample of diverging-converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically-symmetric converging-diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range.

Extensional flow behaviour is very important in polymer processing operations such as fiber spinning and film blowing but there is scanty experimental data in the literature due to inherent difficulties in measurement of the relevant flow parameters. In the present paper, an attempt has been made to correlate the existing available data on the extensional flow of three generic types of polymer melts through a logarithmic plot of modified extensional viscosity function, ηE · MFI, and a modified extension rate, (ε/MFI)2. The method may be extended to other polymeric systems.
Das Dehnfließverhalten ist sehr wichtig bei polymeren Herstellungsprozessen wie Faserspinnen und Filmblasen, doch es gibt nur spärliche experimentelle Daten in der Literatur wegen der inhärenten Schwierigkeiten bei der Messung der entsprechenden Fließparameter. In dieser Arbeit ist der Versuch gemacht worden, die vorhandenen zugänglichen Daten des Dehnfließens von drei verwandten Typen von Polymerschmelzen durch eine logarithmische Auftragung der modifizierten Dehnviskositätsfunktion ηE · MFI und einer modifizierten Dehngeschwindigkeit (ε/MFI)2, zu korrelieren. Diese Methode kann auf andere Polymersysteme übertragen werden.

Since the realization that the Superpave specification parameter |G*/sin δ is not adequate in rating polymer-modified binders for high temperature performance grading of paving asphalts, researchers have been seeking ways to refine this parameter to make it more sensitive to pavement performance and also find other possible parameters that may better relate to rutting resistance. Most of these efforts have led to positive results in the right direction, but each has its own set of limitations that is preventing immediate implementation of the suggested ideas. From among the various suggestions, the one that has the highest merit for possible use is the refinement of the Superpave specification parameter, namely, the term |G*|/(1 - (1/tan δ sin δ)) that evolved through a theoretical derivation based on fundamental concepts. This performance-based specification term was shown to be more sensitive to the variations in the phase angle δ than the original Superpave specification parameter and thus described the unrecovered strain in the binders more accurately. Though this refinement led to better discrimination between rutting resistance of various asphalts, not all asphalts with the same performance-grade based on the new parameter behaved identically in their rutting performance in laboratory mixture test evaluations. By model fitting the master curve formed from |G*|/(1-(1/tan δ sin δ)) versus frequency data at various temperatures for each binder, a rut-controlling term was extracted that correctly graded the binders in terms of the mixture performance. However, this approach is not appropriate for routine use as it requires large sets of data generation at various temperatures to form the master curve before determination of the model parameters for the rut-controlling term. The present work proposes an alternative method of using the term |G*|/(1-(1/tan δ sin δ)) such that it can be easily adopted as a high temperature performance grading specification for asphalts and evaluates its efficacy through actual field performance data.

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.

Recent research on the stability of entanglements of polymer melts and on the correlation between viscosity improvement during processing and entanglement stability led to the discovery of a new property of the liquid state of polymers which is not explained by the current models in polymer physics: it is called " sustained orientation ". In simple terms, by manipulation of the stability of entanglements, it is possible to create and maintain quasi-stable at high temperature in an amorphous polymeric melt (say 120 o C above T g) a certain state of orientation that was induced by a mechanical deformation. The manipulation of entanglements was done by Rheo-Fluidification. In our experiments, the viscosity of a melt (e.g. PMMA) was measured at the exit of a Rheo-Fluidification treatment where the melt was submitted to a combination of shear-thinning and strain-softening via the use of cross-lateral shear vibration superposed on pressure flow (originated by an extruder feed). The exiting melt was frozen into pellets and the rheological properties of those pellets were studied. Under certain Rheo-Fluidification processing conditions, the viscosity reduction of the melt induced by the combination of shear-thinning and strain softening could be preserved in the pellets granulated at the exit of the disentangling processor. These " treated " pellets displayed sustained-orientation, i.e. a lower viscosity when they were reheated in a melt flow indexer, or in a dynamic rheometer after they had been compressed into disks. Yet, the molecular weight, M w , was hardly changed (~3%) to justify the viscosity reduction, and it was also observed that the viscosity only gradually (sometimes over periods of hours) returned to the value it should have at the corresponding temperature (the Newtonian value), indicating that the changes were reversible. These results suggest that the classical concept of M e to describe entanglements is too simplistic and its usefulness is probably limited to the linear range of viscoelasticity. We suggest that these type of experimental results, recently presented, have resonance in our fundamental understanding of the interactions between the macromolecules, inviting us to redefine the nature of entanglements, the nature of molecular motions and flow, and reformulate the equations underlying rheology, crystallization, glass formation, and the stability of the interactions at different temperatures and under stress. The whole description

Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration.

The deformation behavior of poly (vinylidene fluoride) has been analyzed in both the melt state and solid state in order to develop unified grade and temperature invariant curves through the use of simple and appropriate normalizing factors. The advantage of such master curves lies in their ability to provide quick estimates of shear viscosity and normal stress difference as well as long-term mechanical behavior with reasonable accuracy useful for design purpose.

The fully developed thermal field in constant pressure gradient driven laminar flow of viscoelastic fluids in straight pipes of arbitrary contour ∂D is investigated. The non-linear fluids considered are constitutively represented by a class of single mode, non-affine constitutive equations. The driving forces can be large and inertial effects are accounted for. Asymptotic series in terms of the Weissenberg number Wi are employed to represent the field variables. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is the result of secondary flows in the cross-section. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its  Newtonian counterpart. Large enhancements are possible even with dilute fluids. Isotherms for the temperature field are  presented and discussed for several non-circular contours such as the ellipse and the equilateral triangle together with heat transfer behavior in terms of the Nusselt number Nu.

Addition of metal halides to nylons has been shown to be advantageous in a number of ways. The decrease in melting temperature, increase in glass transition temperature and melt viscosity by such additions have allowed more convenient processing of low molecular weight polymers and thermally unstable polymers. Rheological data depicting the variation of melt viscosity with shear rate at temperatures relevant to processing are necessary in optimizing and trouble-shooting plastics processing operations. In the present paper, a method has been proposed to estimate, complete flow curves or rheograms of nylon—metal halide systems with the use of a master curve knowing the melt flow index and glass transition temperature of the system. The validity of the approach has been verified for the nylon 6—lithium chloride system and shown to hold good for any nylon—metal halide combination.