The role of elongational viscosity in the mechanism of drag reduction by polymer additives

The role of elongational viscosity in the mechanism of drag reduction by polymer additives is investigated qualitatively by means of direct numerical simulations of a turbulent pipe flow. For the polymer solution, a generalised Newtonian constitutive model is utilised in which the viscosity depends on the second and third invariant of the rate-of-strain tensor via an elongation parameter. This elongation parameter is capable of identifying elongational type of regions within the flow. The simulations show that complementary to stretching of the polymers, also compression must be incorporated to have drag reduction, contrary to many suggestions done in the literature on the mechanism which assume that stretching of the polymers is most important.     

The rheology of a smectic main-chain polymer

The rheology of a smectic main-chain polymer shows that the activation energy is high (275 kJ mol^–1) and that the viscosity is more than two orders of magnitude higher than in the isotropic phase. The recoverable strain in the smectic phase is largely due to the reformation of the smectic layers after cessation of shear.     

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.     

The rheology of polymer solution elastic strands in extensional flow

We apply micro-oscillatory cross-slot extensional flow to a semi-dilute poly(ethylene oxide) solution. Micro-particle image velocimetry (μPIV) is used to probe the real local flow field. Extreme flow perturbation is observed, where birefringent strands of extended polymer originate from the stagnation point. This coincides with a large increase in the extensional viscosity. The combination of stagnation point flow and μPIV enables us to investigate directly the stress and strain rates in the strand and so determine the true extensional viscosity of the localised strand alone. The Trouton ratio in the strand is found to be ~4000, amongst the highest values of Trouton ratio ever reported. Consideration of the flow in the exit channels surrounding the highly elastic strand suggests a maximum limit for the pressure drop across the device and the apparent extensional viscosity. This has implications for the understanding of high Deborah number extensional thinning reported in other stagnation point flow situations.     

The role of transient rheology in polymeric sintering

The initial theory of Frenkel and Eshelby for the coalescence of drops in air (or sintering) of Newtonian fluids, which equated the work of surface tension to the work done by viscous stresses while assuming biaxial extensional flow kinematics, was extended to the case of time-dependent material functions using the Upper Convected Maxwell (UCM) model. A numerical scheme was developed to solve the ordinary differential equations (ODE) for the stresses, which are embedded in the ODE based on the mechanical energy balance. Initial conditions required to solve the set of non-linear ODEs were obtained from visualization experiments of the coalescing drops as the theory for elastic contact gave unrealistically high values of the initial neck radius. The transient model predicted that coalescence was accelerated by increasing the relaxation time, the opposite relationship of what was predicted by the steady-state UCM formulation, and was capable of quantitatively predicting the experimental coalescence rates at times when viscoelasticity was important.     

The rheology of suspensions of porous zeolite particles in polymer solutions

We present data and predictive models for the shear rheology of suspended zeolite particles in polymer solutions. It was found experimentally that suspensions of zeolite particles in polymer solutions have relative viscosities that dramatically exceed the Krieger–Dougherty predictions for hard sphere suspensions. Our investigations show that the major origin of this discrepancy is due to the selective absorption of solvent molecules from the suspending polymer solution into zeolite pores. The effect raises both the polymer concentration in the suspending medium and the particle volume fraction in the suspension. Consequently, both the viscosity of the polymer solution and the particle contribution to the suspension viscosity are increased. We propose a predictive model for the viscosity of porous zeolite suspensions by incorporating a solvent absorption parameter, α, into the Krieger–Dougherty model. We experimentally determined the solvent absorption parameter by comparing viscosity data for suspensions of porous and nonporous MFI zeolite particles. Our results are in good agreement with the theoretical pore volume of MFI particles.     

The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

Non-Newtonian viscosity of concentrated polymer solutions

Summary The results of investigations of Newtonian and Non-Newtonian viscosity of solutions of various polymers in wide range of concentrations, temperatures, molecular weight of polymers in different solvents are presented here.These results show that the nature of solvent has a much greater effect on the viscosity of polar polymer solutions with very strong specific interaction than on the viscosity of non-polar polymer solutions.The nature of solvent affects not only the absolute value of viscosity, which as a rule, in the whole range of investigated shear stress is greater in poor solvent solutions than in good ones, but also determines the type of the flow curves.Solutions of flexible polymer (polyisobutylene) are characterized by complete flow curves regardless of the solvent nature. Solutions of rigid-chain polymer (acetyl-cellulose) are characterized by complete flow curves, both in good and in poor solvents. For the polystyrene solutions in good solvents incomplete flow curves and in poor solvents complete flow curves are observed.All these observations show that the anomaly of viscosity of polymer solutions is caused by two processes which occur simultaneously: the process of desintegration of structures and the process of orientation of chains and elements of the desintegrated structures.The structures presented in the solution dissociate under heat motion and activation heat and its changes with temperature and shear stress reflect very well the changes in the structure of solutions.The nature of solvent influences the value of critical molecular weight which in the case of good solvent is greater than in a poor one.

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Zusammenfassung Es werden die Untersuchungsergebnisse der Newtonschen und Nicht-Newtonschen Viskosität von konzentrierten Polymerlösungen in verschiedenen Lösungsmitteln innerhalb eines weiten Bereichs von Konzentration, Temperatur und Molekulargewicht der Polymeren mitgeteilt. Diese Resultate zeigen, daß die Art des Lösungsmittels einen wesentlich größeren Einfluß auf die Viskosität polarer Polymerlösungen mit starker spezifischer Wechselwirkung hat als auf die Viskosität nichtpolarer Polymerlösungen.Die Natur des Lösungsmittels beeinflußt nicht nur den Absolutwert der Viskosität, der üblicherweise im gesamten untersuchten Schubspannungsgebiet für schlechte Lösungsmittel größer ist als für gute, sondern auch den Fließkurvenverlauf. Unabhängig vom Lösungsmittel sind Lösungen von Polymeren mit flexiblen Ketten (Polyisobutylen) durch unvollständige Fließkurven gekennzeichnet. Die Lösungen von Polymeren mit steifen Ketten (Acetylcellulose) sind durch geschlossene Fließkurven sowohl in schlechten als auch in guten Lösungsmitteln charakterisiert. Die Polystyrollösungen ergeben bei guten Lösungsmitteln offene und bei schlechten Lösungsmitteln geschlossene Fließkurven.Diese Ergebnisse zeigen, daß die Viskositätsanomalie von Polymerlösungen von zwei gleichzeitig auftretenden Prozessen abhängig ist; dem Prozeß des Strukturzerfalls und dem Prozeß der Orientierung von Ketten und Elementen der zerfallenen Strukturen. Die in der Lösung existierenden Strukturen zerfallen durch die Wärmebewegung. Die Aktivierungswärme und ihre Änderungen in Abhängigkeit von Temperatur und Schubspannung geben die Strukturänderung der Lösungen sehr gut wieder. Die Art des Lösungsmittels beeinflußt die Größe des kritischen Molekulargewichts, das bei guten Lösungsmitteln größer ist als bei schlechten.

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Paper presented at the Conference on Advances in Rheology, Glasgow, September 16–18, 1969.     

Free volume dependence of polymer viscosity

The Simha–Somcynsky (S–S) equation of state (eos) was used to compute the free volume parameter, h, from the pressure–volume–temperature (PVT) dependencies of eight molten polymers. The predicted by eos variation of h with T and P was confirmed by the positron annihilation lifetime spectroscopy; good agreement was found for h(P = constant) = h(T) as well as for h(T = constant) = h(P). Capillary shear viscosity (η) data of the same polymers (measured at three temperatures and six pressures up to 700 bars), were plotted as logη vs 1/h, the latter computed for T and P at which η was measured. In previous works, such a plot for solvents and silicone oils resulted in a “master curve” for the liquid, in a wide range of T and P. However, for molten polymers, no superposition of data onto a “master curve” could be found. The superposition could be obtained allowing the characteristic pressure reducing parameter, P*, to vary. The necessity for using a “rheological” characteristic pressure reducing parameter, P*_R = κP*, with κ = 1 to 2.1 indicates that the free volume parameter extracted from the thermodynamic equilibrium data may not fully describe the dynamic behavior. After eliminating possibility of other sources for the deviation, the most likely culprit seems to be the presence of structures in polymer melts at temperatures above the glass transition, T _g. For example, it was observed that for amorphous polymers at T ≅ 1.52T _g the factor κ = 1, and the deviation vanish.     

The role of particle interactions in the rheology of dispersed systems

Summary Certain aspects of the rheological behaviour of dispersions cannot be understood unless attractive forces between the particles are assumed, resulting in the building-up of a network structure.A network model is postulated in which the particles are arranged in chains. During deformation these chains are stretched resulting in breakage of bonds between the particles. In this process and especially in what happens after that, an important question is whether the relative motion of a single particle with respect to the surrounding network is noticeable to only a few particles in the immediate vicinity or to a large number of particles over relatively large distances. The necessary information about the changing network structure during a large deformation at constant shear rate was derived from dielectric measurements in the case of water in oil emulsions and from super-imposed oscillatory shear experiments in the case of fat crystal dispersions.It is shown that the rheologieal behaviour of the water in oil emulsions may be characterized by motion of single particles, whereas in the fat-dispersions in oil collective displacements of large numbers of particles (aggregates) have to be taken into account.In the fat dispersions the magnitude of the forces acting in the network chains is explained in terms ofvan der Waals interaction. In the emulsions such forces determine the behaviour only at sufficiently low rates of shear. At higher shear rates the hydrodynamic interaction between single particles has to be taken into account.Among the quantities, which emerge from these network considerations is the characteristic time related with the motions of the particles or agglomerates. Therefore, time effects in dispersed systems are discussed more extensively.

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Zusammenfassung Bestimmte Aspekte des rheologischen Verhaltens von Dispersionen lassen sich nur unter der Voraussetzung von Anziehungskräften zwischen den Teilchen, die zur Bildung einer Netzwerkstruktur führen, erklären.Es wird ein Netzwerkmodell postuliert, in welchem die Teilchen kettenförmig angeordnet sind. Während der Deformation werden diese Ketten gedehnt, was zum Bruch der Bindungen zwischen den Teilchen führt. In bezug auf diesen Vorgang und besonders auf das, was nachher geschieht, erhebt sich die wichtige Frage, ob die relative Bewegung eines einzelnen Teilchens sich hinsichtlich des umgebenden Netzwerks nur auf einige benachbarte Teilchen auswirkt oder sich auf eine größere Anzahl weiter entfernter Teilchen erstreckt. Die benötigte Information über die Änderungen der Netzwerkstruktur während größerer Deformationen bei konstanter Schergeschwindigkeit wurde an Hand von dielektrischen Messungen für Wasser-in-Öl-Emulsionen und im Falle von Fettkristalldispersionen mit Hilfe von Versuchen mit überlagerter oszillierender Scherung ermittelt. Es zeigt sich, daß das rheologische Verhalten von Wasser-in-Öl-Emulsionen sich durch die Bewegung einzelner Teilchen charakterisieren läßt, während bei Dispersionen in Öl kollektive Bewegungen einer größeren Zahl von Teilchen (Aggregaten) berücksichtigt werden müssen. In den Fettdispersionen wird die Größe der in den Ketten des Netzwerkes ausgeübten Kräfte durchvan derWaalssche Wechselwirkungen erklärt. In den Emulsionen bestimmen derartige Kräfte das Verhalten nur bei genügend niedrigen Schergeschwindigkeiten. Bei höheren Schergeschwindigkeiten ist mit einer hydrodynamischen Wechselwirkung zwischen den einzelnen Teilchen zu rechnen.Unter den Größen, die sich aus diesen Betrachtungen der Netzwerkstruktur ableiten lassen, ist die mit den Bewegungen der Teilchen oder Agglomerate verbundene charakteristische Zeit. Aus diesem Grunde werden die Zeiteffekte in dispersen Systemen ausführlich besprochen.

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Kinetic theory and rheology of dilute polymer solutions

Summary A summary is given of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results.With 1 table     

Characterization of polymer dispersions by Fourier transform rheology

Fourier transform rheology is a very sensitive technique to characterize non-linear rheological fluid properties. It has been applied here for the first time to polymer dispersions in water and the results are compared to those from conventional rheology, namely steady and small amplitude oscillatory shear experiments. The investigated systems are mainly based on styrene and n-butylacrylate. A first attempt was made to evaluate how far colloidal parameters like particle volume fraction and ionic strength as well as chemical composition and surface characteristics of the dispersed particles are reflected in FT-rheology spectra. Significantly different non-linearities are observed for highly concentrated dispersions of particles with different T_g. These differences are not detected in linear oscillatory shear and show up in steady shear only at significantly higher shear rates. Particle surface characteristics influence the non-linear response in oscillatory shear significantly and the intensity of the overtones is found to be higher for a dispersion of particles with a “hairy” swollen surface layer as compared to a system of smooth particles, although the solids content was adjusted to match the steady shear viscosity. The intensity of the overtones in FT-rheology strongly decrease upon dilution. At a solid content below 35% no differences are observed in the FT-experiments for the systems investigated here, whereas the differences in steady shear are very pronounced in this concentration range. A significant influence of added salt onto the non-linear response is detected for some systems, which might be correlated to the stability of these systems. The observed phenomena certainly cannot be explained in terms of constitutive equations or microstructural statistical mechanical models at present. Thus, FT-rheology yields information complementary to classical steady or linear oscillatory shear experiments. Received: 11 December 2000 Accepted: 8 April 2001     

The role of viscoelasticity in polymer sintering

An experimental study for polymer sintering has been carried out using pairs of powder particles. Although in many cases Newtonian sintering models successfully describe polymer sintering, they predict a faster coalescence rate than that observed with the polypropylene copolymer resins used in this study, indicating that factors other than the surface tension and the viscosity play a role in polymer sintering. Observations of coalescence under the microscope and rotational molding experiments suggest that melt elasticity slows down the process. Based on these findings, a mathematical model describing the complete polymer sintering process for viscoelastic fluids has been developed. The approach was similar to that of Frenkel (1945) and the convected Maxwell constitutive equations were used together with the quasi-steady state approximation. The proposed viscoelastic sintering model is capable of predicting the sintering rate slowdown observed in this study. Received: 18 August 1997 Accepted: 30 March 1998