Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

Solutions of xanthan gum/guar gum mixtures: shear rheology,porous media flow,and solids transport in annular flow

Mixtures of xanthan and guar gum in aqueous solution were studied in two flow situations: simple shear and porous media. In addition, solids transport in vertical annular flow of sand suspensions was explored. The zero shear rate viscosity of the solutions displayed a pronounced synergy: the viscosity of the mixture is higher than that of the polymer solutions in a wide range of relative concentrations of the two polymers, in agreement with previous literature. However, at relatively high shear rates, the viscosity approaches the value of the more viscous xanthan gum solutions at mass fractions of xanthan gum between 0.1 and 0.15, and the degree of synergy substantially decreases. Stress relaxation experiments in simple shear indicate that the polymer mixtures exhibit a well-defined yield stress after relaxation that is absent in solutions of pure polymers. In porous media flow experiments, a synergistic behavior mimicking the shear flow results was obtained for the polymer mixtures at low shear rates. However, at a critical shear rate, the apparent viscosity in porous media flows exceeds the shear viscosity due to the elongational nature of flow in the pores. The solids transport capacity in annular flows is well-represented by trends in shear viscosity and stress relaxation behavior. However, the lack of viscosity synergy at high shear rates limits the applicability of the mixtures as a way to improve solids suspension capacity in annular flows.     

Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Drag reduction in the turbulent pipe flow of polymers

The paper concerns an experimental study of the fully developed turbulent pipe flow of several different aqueous polymer solutions: 0.25%, 0.3% and 0.4% carboxymethylcellulose (CMC), 0.2% xanthan gum (XG), a 0.09%/0.09% CMC/XG blend, 0.125% and 0.2% polyacrylamide (PAA). The flow data include friction factor vs. Reynolds number, mean velocity and near-wall shear rate distributions, and axial velocity fluctuation intensity u′ at a fixed radial location as a laminar/turbulent transition indicator. For each fluid we also include measurements of shear viscosity, first normal-stress difference and extensional viscosity. At high shear rates we find that the degree of viscoelasticity increases with concentration (0.3% CMC is an exception) for a given polymer, and in the sequence XG, CMC/XG, CMC, PAA, whilst at low shear rates the ranking changes to CMC, CMC/XG, XG, PAA. The extensional viscosity ranking is XG/CMC, XG, CMC, PAA at high strain rates and the same as that for the viscoelasticity at low shear rates. We find that the observed drag-reduction behaviour is consistent for most part with the viscoelastic and extensional-viscosity behaviour at the low shear and strain rates typical of those occurring in the outer zone of the buffer region.Although laminar/turbulent transition is practically indiscernible from the friction factor vs. Reynolds number plots, particularly for PAA and XG, the u′ level provides a very clear indicator and it is found that the transition delay follows much the same trend with elasticity/extensional viscosity as the drag reduction.     

Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (M _w 1.8 10⁶). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Matheson's theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.     

The effect of parallel combined steady and oscillatory shear flows on blood and polymer solutions

Human blood at physiological volume concentration exhibits non-Newtonian and thixotropic properties. The blood flow in the microcirculation is pulsatile, initiated from the heart pulse and can be considered as superposition of two partial flows: a) a steady shear, and b) an oscillatory shear. Until now steady and viscoelastic behavior were separately investigated. Here we present the response to the combination of steady and oscillatory shear for human blood, a high molecular weight aqueous polymer solution (polyacrylamide AP 273E) and an aqueous xanthan gum solution. The polyacrylamide and xanthan solutions are fluids that model the rheological properties of human blood. In general, parameters describing blood viscoelasticity became less pronounced as superimposed steady shear increased, especially at low shear region and by elasticity, associated with reduction in RBC aggregation. The response of polymer solutions to superposition shows qualitative similarities with blood by elasticity, but their quantitative response differed from that of blood. By viscosity another behavior was observed. The superposition effect on viscous component was described by a modified Carreau equation and for the elastic component by an exponential equation.Paper in part presented at the Symposium on Rheology and Computational Fluid Mechanics dedicated to the memory of Prof. A. C. Papanastasiou, University of Cyprus, Nicosia, July 4–5, 1996     

Rheological and drag reduction characteristics of xanthan gum solutions

The rheological and turbulent drag reducing characteristics of commercial and purified xanthan gum solutions of concentrations 50–500 ppm have been studied with and without addition of 100 ppm NaCl. The purification by soxlet extraction of xanthan gum using 95% ethanol is effective in removing low-molecular-weight impurities from xanthan. The increased content of higher molecular-weight xanthan in purified xanthan is evident from rheological and drag reduction behavior. The addition of 100 ppm salt to dilute solutions introduces semi-flexibility in xanthan gum solution without occurrence of self-association. The change in molecular behavior in the presence of salt is evident from rheological normal-stress and turbulent drag reduction behaviors.     

Molecular interpretation of the behaviour of polyisobutylene in different solvents

The effects of solvent environment on the behaviour of a high molecular weight polyisobutylene dissolved in kerosene and various grades of poly-1-butene solvent mixtures are investigated. The dependence of various molecular parameters such as zero-shear viscosity, intrinsic viscosity, specific viscosity, relaxation time and molecular expansion factor, on the polymer concentration, type of solvent and solvent viscosity is studied in the vicinity of dilute and semidilute regions (near the critical concentrationc ^*). The dependence of these parameters on solvent environment follows qualitatively Zimm's molecular model. The dependence on the polymer concentration deviates from this dilute solution theory. The effects of temperature on the zero-shear viscosity and the Maxwell relaxation time are also presented for two PIB solutions.     

The triple jet: influence of shear history on the stretching of polymer solutions

A kerosene-based aircraft safety fuel and aqueous solutions of poly (ethylene oxide) and polyacrylamide are examined using the “triple jet” system. This device allows the solution to be stretched as it flows from a capillary tube and the axial stress, strain and strain rate in the liquid are measured.The shear history of the solution is altered by placing cylindrical inserts in the capillary tube. This is shown to have a large effect on the extensional behaviour of aircraft safety fuel, a moderate effect on the extensional behaviour of poly (ethylene oxide) solution and little effect on the behaviour of polyacrylamide solution. The extensional viscosity of the aircraft fuel is raised by an order of magnitude when a long period of high shear is used; the effects last for periods of up to one second, though traditional methods suggest a relaxation time of the order of 10^?3 seconds. A liquid of shear viscosity 4 centipoise may have an extensional viscosity of over 100 poise.Plots of the extensional modulus of the jet as a function of distance along the jet emphasize the importance of shear history for the first two types of solution and suggest that the latter stages of the stretching process are elastic in character. Typical extensional moduli for the solutions tested are in the range 1.3–5.0 × 10⁴ dyn.cm^?2.The relevance of the interplay between shearing and stretching flow to the phenomena of lubrication and turbulence suppression is mentioned.     

On the use of flow through a contraction in estimating the extensional viscosity of mobile polymer solutions

We consider the use of pressure measurements in contraction flows in the determination of the extensional viscosity behaviour of polymer solutions. The experimental data are interpreted on the basis of the recent theory of Binding. The resulting extensional viscosities are compared with those obtained from a commercial Spin Line Rheometer.We conclude that contraction flows provide a convenient means of determining the extensional viscosity of shear-thinning polymer solutions. The case is not so clear for constant viscosity Boger fluids.In the course of the experiments, it is shown that excess pressure losses in the contractions can be brought about by two distinct flow mechanisms in the case of Boger fluids. In the axisymmetric case, both vortex enhancement and excess pressure loss are observed, although there is not a strict one-to-one correlation between these phenomena. In the planar case, vortex enhancement is not conspicuously present, although there is still a substantial excess pressure loss at high flow rates. This excess must be associated with the ‘bulb’ flow field which essentially replaces the vortex-enhancement regime of the axisymmetric case.     

Zum Einfluß von Füllstoffen auf das rheologische Verhalten von hochmolekularen Polyethylenschmelzen I. Das Fließverhalten in Scher- und Dehnströmungen

Zusammenfassung Das Fließverhalten von Polymersuspensionen in verschiedenen Strömungsformen wird anhand von mit isotropen und anisotropen Partikeln (Glaskugeln bzw. Glasfasern) gefüllten hochmolekularen Schmelzen untersucht. Zur Anwendung kommen dabei sowohl lineare als auch verzweigte Polymere, nämlich Polyethylene mit hoher Dichte (HDPE) und mit niedriger Dichte (LDPE).Alle untersuchten Systeme zeigen in der Scherströmung im Rotationsrheometer bei Zugabe von Füllstoff eine Verringerung der elastischen Eigenschaften. Solches Verhalten ist für Suspensionen isotroper Teilchen zu erwarten, bei Fasersuspensionen wird jedoch gewöhnlich ein verstärktes Anwachsen der ersten Normalspannungsdifferenz mit zunehmender Füllung gefunden. Bei höheren Schergeschwindigkeiten (Messungen im Kapillarviskosimeter) wird die durch die Füllstoffe bewirkte Viskositätserhöhung zunehmend geringer, die Suspensionen verhalten sich also mit zunehmendem Füllgrad stärker scherentzähend. Das Einsetzen der für das lineare HDPE typischen Instabilitäten (stick-slip, Wandgleiten) läßt sich durch den Ersatz von (elastischem) Polymer durch (starre) Kugeln nicht beeinflussen, diese Form des Schmelzenbruchs setzt bei gleichen Schubspannungen ein und ist so wegen der höheren Viskosität der Suspension sogar zu niedrigeren Durchsätzen hin verschoben.Um die Lücke zwischen den Messungen im Rotations- und im Kapillarviskosimeter (niedrige bzw. hohe Schergeschwindigkeiten) zu schließen, wurden Experimente bei oszillatorischer Scherbeanspruchung durchgeführt. Die bekannte Cox-Merz-Beziehung vermag das Verhalten der ungefüllten Schmelzen zwar recht gut zu beschreiben, versagt jedoch bei den Suspensionen gerade im Bereich niedriger Schergeschwindigkeiten, ebenso wie andere vorgeschlagene Korrelationen zwischen dynamischen und stationären Kenngrößen.Zur Bestimmung des Materialverhaltens bei uniaxialer Dehnbeanspruchung wurde ein Rotationsrheometer in geeigneter Weise modifiziert, so daß für die verwendeten sehr hochviskosen Stoffsysteme eine Messung möglich wurde. Die verschiedenen reinen Schmelzen zeigen ein wenig unterschiedliches Dehnverhalten mit ausgeprägten Verfestigungserscheinungen. Eine stationäre Dehnviskosität konnte in keinem Fall gemessen werden. Die Zugabe von Glaskugeln ändert die Dehnviskosität nicht wesentlich, der Zusatz von Glasfasern jedoch bewirkt eine merkliche Erhöhung der instationären Dehnviskosität im Anlaufbereich.

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The flow behaviour of suspensions is examined in different flow geometries using linear and branched high-molecular-weight polyethylene melts as suspension media containing isotropic (glass beads) and anisotropic (glass fibre) particles.In shear flow in a rotational rheometer, all suspensions show a decrease of the elastic properties with increasing filler content. While this behaviour has to be expected with suspensions of isotropic particles, fibre-filled polymer fluids usually show increasing normal stress differences with increasing fibre content. At higher shear rates (in a capillary viscometer) the particle-induced viscosity increase deminishes, hence the suspensions tend to be more shear thinning with increased filler content.The onset point of instabilities typically found with the linear HDPE is not shifted towards higher volumetric flow rates by replacement of elastic polymer by inelastic fillers as might be expected; on the contrary, the so-called stick-slip behaviour is initiated at constant values of shear stress and hence — because of the higher viscosity of the suspensions — at lower flow rates.Additionally, experiments were carried out with oscillating shear strain. Neither the well-known Cox-Merz relation nor similar relations, discussed in the literature, could properly correlate oscillatory and steady-state fluid behaviour of the suspensions, especially in the low shear rate range, whereas the former worked rather well for the unfilled melts.To allow for measurements of extensional properties, a rotational rheometer was slightly modified, thus being capable of determining the extensional viscosity of highly viscous polymeric materials. The pure melts showed only a slightly different behaviour with pronounced strain hardening. No stationary values of the Trouton viscosity could be obtained. While addition of glass beads was of little influence on material behaviour, addition of glass fibres showed remarkable increase of the extensional viscosity in the start-up region.

Erster Teil einer vom Fachbereich Chemietechnik der Universität Dortmund genehmigten Dissertation     

Ermittlung des dehnrheologischen Verhaltens thermoplastischer Kautschuke

Zusammenfassung Mit Hilfe eines einfachen Dehnrheometers wurden Dehnfließversuche mit thermoplastischen Kautschukblends (Ibuflex-SEH und Santoprene) durchgeführt. Die auf diese Weise erhaltenen Dehnviskositätsdaten wurden mit den von kautschukmodifizierten Thermoplasten (PVC, PE und PS) verglichen. Nach der Anlaufphase zeigt Ibuflex-SEH ein stationäres Fließverhalten, während die Dehnviskosität von Santoprene als Funktion der Zeit monoton ansteigt, ohne einen stationären Zustand zu erreichen. Die Ursachen des Unterschieds im Fließverhalten der untersuchten Polymermaterialien wurden diskutiert.

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Extensional flow experiments were carried out on a simple extensional rheometer with the thermoplastic elastomer blends: Ibuflex-SEH and Santoprene. The extensional viscosity data obtained were comparable with those of elastomer modified PVC, PE and PS. After the transient stage Ibuflex-SEH shows a steady-state flow behaviour, whereas the extensional viscosity of Santoprene as a function of time increases monotonically without reaching a stationary state. The causes for these differences were discussed.

Erweiterte Fassung eines Vortrags anläßlich der Jahrestagung der Deutschen Rheologischen Gesellschaft vom 13.–15. Mai 1985 in Berlin     

Extensional flow —a mathematical perspective

Extensional flow has been studied extensively for less than half the lifetime of the word rheology, although measurement of viscosity from extensional flow experiments can be traced back to the beginning of this century. In recent years extensional flow has, however, attracted a great deal of attention in conferences, workshops and special issues of journals. This has coincided with interest, both scientific and industrial, in elasticoviscous fluids, notably polymer solutions and molten polymers. The particular success of specialized, carefully targetted or focussed, workshops is highlighted.A personal reflection is offered here on some of the issues in extensional flow from the point of view of an applied mathematician. The state of the art, as far as extensional viscosity is concerned, is briefly surveyed. Both theoretical and practical aspects of the task of obtaining useful extensional flow properties are outlined, drawing heavily on a recent review by James and Walters. Particular attention is paid to spinning experiments, drawing heavily on recent theoretical investigations by the author. The merits of defining a spinning viscosity, in addition to the formally defined tensile viscosity, are advanced. The idea of general approximations for extensional flows is reviewed and some aspects of this are highlighted, particularly in connection with Metzner's idea of extensional primary field (EPF) approximations. Finally qualitative investigations of the behaviour of model fluids (in model flows) are illustrated and a new result on the boundedness of solutions for unsteady uniaxial extension of a FENS-P dumbbell model is presented.Presented as a keynote lecture at the 4the European Rheology Conference, September 4–9, 1994, Seville, Spain     

Generation of inkjet droplet of non-Newtonian fluid

In this study, the generation of inkjet droplets of xanthan gum solutions in water–glycerin mixtures was investigated experimentally to understand the jetting and drop generation mechanisms of rheologically complex fluids using a drop-on-demand inkjet system based on a piezoelectric nozzle head. The ejected volume and velocity of droplet were measured while varying the wave form of bipolar shape to the piezoelectric inkjet head, and the effects of the rheological properties were examined. The shear properties of xanthan gum solutions were characterized for wide ranges of shear rate and frequency by using the diffusive wave spectroscopy microrheological method as well as the conventional rotational rheometry. The extensional properties were measured with the capillary breakup method. The result shows that drop generation process consists of two independent processes of ejection and detachment. The ejection process is found to be controlled primarily by high or infinite shear viscosity. Elasticity can affect the flow through the converging section of inkjet nozzle even though the effect may not be strong. The detachment process is controlled by extensional viscosity. Due to the strain hardening of polymers, the extensional viscosity becomes orders of magnitude larger than the Trouton viscosities based on the zero and infinite shear viscosities. The large extensional stress retards the extension of ligament, and hence the stress lowers the flight speed of the ligament head. The viscoelastic properties at the high-frequency regime do not appear to be directly related to the drop generation process even though it can affect the extensional properties.     

A novel geometry for rheological characterization of viscoelastic materials

A novel geometry for generating a viscometric flow presents advantages of both cone and plate and parallel plate geometries, regarding uniform shear field and adjustable range of measurement. Kinematics and dynamics of the generated flow have been described mathematically utilizing an orthogonal curvilinear coordinate system based on the shapes of the shearing surfaces which are similar to the surface that generates the flow. Simple equations that allow the calculation of quantities of experimental interest in the rheological characterization of liquid materials, namely, shear rate, shear stress and two normal stress differences, have also been derived.The geometry, called pseudosphere, was tested with two types of fluids (Newtonian and pseudoplastic). Results show that the geometry can be used with low viscosity liquids (Newtonian liquids) by only adjusting the gapH. The behavior of pseudoplastic fluids for both low and moderately high viscosity could also be studied with this geometry. Very reproducible results were obtained when compared with those obtained with cone and plate geometry. Regions of lower shear rate could be studied using only the pseudosphere geometry.     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

The unraveling of a polymer chain in a strong extensional flow

By assuming that in a strong extensional flow a polymer molecule in dilute solution is quickly driven into a folded or kinked state in which drag and entropic elastic forces dominate over the Brownian force, we derive kink dynamics equations that describe the unraveling of the molecule in the extensional flow. Solving these equations numerically, we find that although the ends of the chain move, on average, affinely in the flow field until the chain is unfolded to about 1/3 of its fully extended length, large viscous stresses are produced because the solvent must flow around nonextending strands of polymer that lie between neighboring kinks. These predictions are compared with available experimental data and with other theoretical models.     

Elongational flow and rheology of monodisperse polymers in solution

We describe the utilization of idealized stagnation point extensional flows, produced by opposed jets, for birefringence visualization of induced molecular strain and flow resistance measurements. We identify rheological changes associated with the coil---stretch transition which occurs beyond a critical strain-rate in elongational flow-fields. In dilute solutions of monodisperse atactic polystyrene, increases in extensional viscosity are observed as isolated molecules become stretched. The largest increases in extensional viscosity, however, are found only beyond a critical concentration and strain rate, and are associated with the stretching of transient networks of interacting molecules. These results parallel similar effects seen in porous media flow and capillary entrance experiments. We determine the molecular weight dependence of the critical concentration which scales as M^−0.55 in agreement with pairwise interaction of coils, but is much lower than conventional values of the critical polymer concentration, c^*. We believed that polydispersity may play an important role in the development of such transient networks, and in controlling the degradation behaviour during flow.     

Rapid conical flows of viscoelastic solutions

Several examples of conical, stretching flows of viscoelastic solutions are described. Two cases are then examined in more detail, the rapidly stretching free jet and an internally pressurised sheet of liquid in which extension takes place in a circumferential direction.It is shown that both the stress and strain rate may readily be calculated at different positions, provided certain assumptions are made. The changes of extensional viscosity necessary to produce the specified flow geometries are then shown to be anomalous and inconsistent. If, however, a solid-like model based on the Green measure of strain is used, a more satisfactory interpretation of the behaviour is achieved.It is emphasised that these are high-speed, high Deborah number flows and that such a flow pattern is not a general one.An example is also given in which the stretching of rubber is shown to be consistent with the same solid-like model, and values of the extensional moduli of elasticity are quoted for both liquids and rubber.     

Rheology of concentrated microgel solutions

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.