The role of convective constraint release in parallel superposition flows of nearly monodisperse entangled polymer solutions

Recent experiments by Li and Wang (Macromolecules 43:5904–5908, 2010) on parallel superposition flows of nearly monodisperse entangled polymer solutions revealing a flow-induced acceleration of the relaxation dynamics are here analyzed by using a simple differential constitutive equation based on the tube model to examine the role of convective constraint release (CCR) in these situations. Contrary to the expectations of Wang and coworkers, we find that such a flow-induced acceleration is not a CCR effect. Rather, our results suggest that the acceleration is simply due to convection per se (not to be confused with CCR) and to nonlinear orientation effects.     

Fast flow behavior of highly entangled monodisperse polymers

A systematic experimental investigation is carried out to clarify the nature of a well-known capillary flow phenomenon in linear monodisperse polybutadienes (PBd). By varying the surface condition and the die diameter, it is alluded that a spurt-like stick-slip transition actually results from a breakdown of chain entanglement between adsorbed and next-layer unbound chains. In other words, the transition is not a manifestation of any constitutive properties, as previously asserted by Vinogradov and coworkers (1984). The melt viscosity dependence of the transition amplitude agrees with a Navier-de Gennes type analysis of wall slip. A comparison between the capillary flow and dynamic shear behavior of the same monodisperse PBd reveals that the interfacial stick-slip transition occurs at a stress level that is only a third of the plateau stress given by the elastic plateau modulus G _N ⁰=1.0 MPa at 40°C. The molecular weight independence of the critical stress for the transition provides a striking contrast with the transition characteristics observed in linear polyethylenes and suggests a different state of PBd chain adsorption on steel surfaces. Received: 2 April 1998 Accepted: 1 June 1998     

Finite rise time step strain modeling of nearly monodisperse polymer melts and solutions

The step shear strain experiment is one of the fundamental transient tests used to characterize the rheology of viscoelastic polymer melts and solutions. Many melts and solutions exhibit homogeneous deformation and stress relaxation; in these cases the transient dynamics can be modeled by completely ignoring momentum effects and imposing singular kinematics. Recently, however, it has been observed that there are certain classes of nearly monodisperse melts and solutions that exhibit anomalous nonhomogeneous deformation and stress relaxation (Morrison and Larson (1990), Larson, Khan, and Raju (1988), Vrentas and Graessley (1982), and Osaki and Kurata (1980)). We demonstrate that, for these classes, a finite rise time must be incorporated, some source of inhomogeneity must be present, and a small amount of added Newtonian viscosity is necessary. We examine five nonlinear and quasilinear models; the Johnson-Segalman, Phan Thien Tanner, Giesekus, White-Metzner, and Larson models. We determine which mathematical features of the models are necessary and/or sufficient to describe the observed experimental behavior.     

The relaxation time spectrum of nearly monodisperse polybutadiene melts

The relaxation behavior of polymers with long linear flexible chains of uniform length has been investigated by means of dynamic mechanical analysis. The relaxation time spectrum (H()) follows a scaling relationship with two self-similar regions, one for the entanglement and terminal zone, and a second one for the transition to the glass. This can be described in its most general form (termed BSW spectrum) as H() = H _e ^ne + H _g ^– n _g for < _max and H() = 0 for _max < , where H _e , H _g , n _e , n _g are material constants and _max is the molecular weight dependent cut-off of the self-similar behavior. In this study, the dynamic mechanical response has been measured and analyzed for four highly entangled, nearly monodisperse polybutadienes with molecular weights from 20000 to 200000. The data are well represented by the BSW spectrum with scaling exponents of n _e = 0.23 and n _g = 0.67. The values of the exponents obtained in this work are about the same as those found for polystyrene samples in a previous study. This suggests that the two types of polymers have a similar relaxation pattern. However, at this point further refinement of the experiments is needed before being able to draw definite conclusions about the universality of the exponents.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

A convenient way of interpreting steady shear rheo-optical data of semi-dilute polymer solutions

Rheo-mechanical and rheo-optical investigations were carried out with the aim of determining the influence of deformation and orientation or disentangling of polymer coils on the flow behavior in the non-Newtonian region of the flow curve, for a moderately concentrated network solution. To avoid the influence of polydispersity this was done on a series of narrowly distributed polystyrene standards (dissolved in toluene). By using steady state shear flow measurements it was possible to detect qualitatively a reduction in the entanglement density within the non-Newtonian flow region. Birefringence experiments were able to show that deformation of the polymer coils also occurs in the Newtonian flow region, which has no effect on the flow behavior in this range, whereas in the non-Newtonian flow region the increase in deformation is lower than in the Newtonian range. The flow birefringence and its orientation can be described over the whole range of the flow curve with a newly developed equation system (Eq. 8 and 14) derived from the stress states of a sheared solution using the stress-optical rule. Starting from these equations, it could be shown, that in the Newtonian flow region a mastercurve in form of a reduced birefringence Δn′/η₀=f(γ˙) and a reduced orientation φ= f(γ˙/γ˙ _crit) can be plotted, independent from concentration and molar mass. A comparison of the experimentally determined orientation angle and birefringence curve form with theoretical deformations and orientations of polymer coils in a solution state, without intermolecular interactions, was able to demonstrate that the flow behavior of a moderately concentrated network solution is determined decisively (approximately to 85%) by the disentanglement. Received: 8 May 2000 Accepted: 12 September 2000     

Dynamic properties of some polymer solutions subjected to a steady shear superimposed on an oscillatory shear flow

Summary Results of measurements of dynamic moduli in parallel superposition of a steady and oscillatory shear flow were compared with different theories.Most of the rheological models which are based on the assumption that the material properties (spectrum of relaxation times) are unaffected by the presence of the steady rates of shear give results incompatible with our experimental results described earlier. From these models the best fit is given by the WJFLMB-model.A much better fit is given by theories based on the assumption that the relaxation spectrum is cut-off at a critical value of the relaxation time depending on the prescribed steady rate of shear. Under certain conditions these theories explain qualitatively the linear relations between the frequency ₀, at whichG (, ) = 0 and the steady rate of shear , as we found experimentally for several polymer solutions.

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Zusammenfassung Die Ergebnisse von Messungen der dynamischen Moduln bei Superposition einer stationären und einer oszillierenden Scherströmungsk omponente werden mit verschiedenen Theorien verglichen.Die meisten rheologischen Modelle sind auf die Annahme gegründet, daß die Stoffeigenschaften (das Relaxationsspektrum) durch das Vorliegen einer stationären Scherströmung nicht verändert werden. Solche Theorien liefern Ergebnisse, die mit unseren früher beschriebenen Ergebnissen unvereinbar sind. Die beste Übereinstimmung liefert noch das WJFLMB-Modell.Eine wesentlich genauere Anpassung ermöglichen diejenigen Theorien, die auf der Annahme gründen, daß das Relaxationsspektrum bei einem kritischen Wert der Relaxationszeit abgeschnitten wird und daß dieser Wert von der überlagerten stationären Scherströmung abhängt. Unter gewissen Bedingungen erklären diese Theorien zumindest qualitativ die lineare Beziehung zwischen der Frequenz ₀, bei welcherG (, ) = 0 wird, und der zugeordneten Schergeschwindigkeit , wie wir sie bei verschiedenen Experimenten gefunden haben.

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With 4 figures     

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 characterization of commercial highly viscous alginate solutions in shear and extensional flows

The rheological properties of sodium alginate in salt-free solutions were studied by steady shear, dynamic oscillatory and extensional measurements. This biopolymer consists of mannuronic and guluronic acid residues that give a polyelectrolyte character. We applied the scaling theories and checked their accordance with polyelectrolyte behaviour for low concentrations with a shift to neutral polymer behaviour at larger concentrations. This nature was supported by the effect of the concentration on the specific viscosity, the relaxation times from steady shear and the longest relaxation times from small amplitude oscillatory shear (SAOS) measurements. To analyze the extensional behaviour of the samples, we conducted a study of dimensionless numbers and time scales where filament thinning driven by viscous, capillary or elastic forces is at play. We conclude that an exponential filament thinning followed by breakup results in the best regimes that describe the experimental data. Besides, the data pointed out that alginate in salt-free concentrated solutions shows strain thinning of the extensional viscosity and chain rigidity, behaviours that cannot be inferred from the shear rheometry.     

The transition between undiluted and oligomer-diluted states of nearly monodisperse polystyrenes in extensional flow

We have measured the startup and steady extensional viscosity of two narrow molar mass distributed (NMMD) polystyrenes, a 910 kg/mole and a 545 kg/mole, diluted in a NMMD 4.29 kg/mole styrene oligomer, with a wide concentration range from 90 down to 17%. The constant interchain pressure model, proposed by Rasmussen and Huang (Rheol Acta 53(3):199–208 (2014a)), predicts the extensional viscosity well for the dilutions with lower concentrations. However, for the 70 and 90% 545 kg/mole samples which represent the transition between the diluted and undiluted states, the model predictions are less satisfactory. Another concept based on interchain pressure, proposed by Wagner (Rheol Acta 53(10):765–777 (2014)), also shows agreement with the measured data.     

Relations between steady flow and oscillatory shear measurements

Summary Results are given of a comparison between dynamic oscillatory and steady shear flow measurements with some polymer melts. Comparison of the steady shear flow viscosity,, with the absolute value of the dynamic viscosity, ¦¦, at equal values of the shear rate,q, and the circular frequency,, has shown the relation thatCox andHerz had found empirically to be substantially correct.Further, the coefficients of the normal stress differences obtained by streaming birefringence techniques have been compared with 2G () · ^{– 2} in the same range of shear rates as covered by the viscosity measurements (G is the real part of the dynamic shear modulus). Two polystyrenes with narrow molecular weight distribution showed the same shift factor along the orq axis for the normal stress coefficients with respect to 2G () · ^{– 2} and the steady shear flow viscosities with respect to the real part of the dynamic viscosity,. For two polyethylenes the results are not so conclusive owing to the smallness of the shift factor found. An empirical equation is proposed predicting the main normal stress difference from dynamic measurements only.

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Zusammenfassung Die Ergebnisse von Messungen unter erzwungenen Schwingungen und stationärer Scherströmung an einigen Polymerschmelzen werden miteinander verglichen. Der Vergleich der stationären Viskosität mit der absoluten dynamischen Viskosität ¦¦ bei gleichen Werten des Strömungsgradientenq und der Kreisfrequenz zeigt die Gültigkeit der empirischen Beziehung vonCox undHerz.Weiter wurden die Koeffizienten der Normalspannungsdifferenzen, welche durch Messung der Strömungsdoppelbrechung erhalten wurden, mit 2G() · ^–2 verglichen, und zwar wiederum bei gleichen Werten vonq und, wobeiG die Speicherkomponente des dynamischen Schubmoduls ist. Zwei Polystyrole mit enger Molekulargewichtsverteilung zeigen die gleiche Verschiebung entlang der-oderq-Achse für die Normalspannungskoeffizienten in bezug auf2G()· ^–2 und für die stationären Scherviskositäten in bezug auf den Realteil der dynamischen Viskosität. Für zwei Polyäthylene sind die Ergebnisse weniger signifikant, da die entsprechenden Verschiebungen zu klein waren. Eine empirische Beziehung zwischen den Hauptnormalspannungsdifferenzen und den dynamischen Meßwerten wird vorgeschlagen.

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Paper presented at the British Society of Rheology Conference, held at Shrivenham, from 9th–12th September, 1968.     

Superimposed steady and oscillatory shear in dispersed systems

Rheologica Acta - A viscometer has been designed to measure the behaviour of dispersed systems in oscillatory shear. The apparatus permits determination of the dynamic properties within the linear...     

Relation between steady shear flow and dynamic rheology

Summary The relationships between steady shear flow and dynamic rheology are investigated at relatively high shear rates and frequencies. A useful empirical relationship in this region predicts that the magnitude of the complex dynamic viscosity | ^*| should be compared with the shear viscosity at equal values of frequency and shear rate (Cox-Merz-rule). Polystyrenes (PS) and Polyacrylamides (PAAm) have been investigated over a wide range of concentration and molecular weight. Only in case of PAAm/H₂O solutions we have found that the results do not coincide with Cox-Merz-rule. As far as we know this is the first time that deviations from Cox-Merz-rule were observed in a homogeneous system. A molecular interpretation is given.

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Zusammenfassung Die Beziehung zwischen der Scherviskosität und der komplexen (dynamischen) Viskosität bei relativ hohen Schergeschwindigkeiten und Frequenzen wurde untersucht. Eine geeignete empirische Beziehung in diesem Bereich sagt aus, daß der Betrag der komplexen Viskosität | ^*| mit der Scherviskosität bei gleichen Werten von Frequenz und Schergeschwindigkeit vergleichbar ist (Cox-Merz-Regel). Polystyrole (PS) and Polyacrylamide (PAAm) wurden über einen weiten Bereich der Konzentration und des Molekulargewichts untersucht. Nur im Fall der PAAm/H₂O-Lösungen wurden Abweichungen von der Cox-Merz-Regel gefunden. Soweit uns bekannt, ist es das erste Mal, daß Abweichungen von der Cox-Merz-Regel in einem homogenen System gefunden wurden. Eine molekulare Erklärung wird gegeben.

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Presented at the IUPAC 26^th International Symposium on Macromolecules, Mainz, September 17–21, 1979.

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With 4 figures and 1 table     

Interchain tube pressure effect in extensional flows of oligomer diluted nearly monodisperse polystyrene melts

We have derived a constitutive equation to explain the extensional dynamics of oligomer-diluted monodisperse polymers, if the length of the diluent has at least two Kuhn steps. These polymer systems have a flow dynamics which distinguish from pure monodisperse melts and solutions thereof, if the solvent has less than two Kuhn steps, e.g. is not a chain. The constitutive equation is based on a phenomenological tube-based model within the methodology of the molecular stress function approach. The nonlinear dynamics have been explained as a consequence of a constant thermal interchain pressure originating from the short polymer chains (e.g. the oligomers) on the wall of the tube containing the long chains. The nonlinear dynamics are uniquely defined by the Rouse time and the maximal extensibility of the long polymer chains. Both are linked to the entanglement length. The relation between the Rouse times and entanglements have been established based on published extensional experiments on nearly monodisperse polystyrene melts. The constitutive equation has shown agreement with the experimental startup of and steady extension data from Huang et al. (Macromolecules 46:5026–5035, 2013a) based on 285 and 545 kg/mol polystyrenes diluted in styrene oligomers containing 3.3 (1.92 kg/mol) and 7.3 (4.29 kg/mol) Kuhn steps.     

Determination of normal-stress differences in steady shear flow

Rheologica Acta - A new wide-gap concentric cylinder apparatus has been constructed for the measurement of pressures generated in Couette flow; diaphragm-capacitance pressure transducers in the...     

Viscometric properties of viscous theta solutions of monodisperse polystyrene

Theta solvents for polystyrene are prepared from high-viscosity blends of styrene and low-molecular-weight polystyrene, and then used to make dilute solutions with monodisperse polystyrene solutes of high-M = 2.3, 6.0, 9.0, 18.0 · 10⁵. A Weissenberg rheogoniometer is used to measure the non-Newtonian viscosity as a function of shear stress, for low values, and also the complex viscosity components and as functions of frequency. A capillary viscometer is used for high- measurements of(). Viscometric properties, at room temperature, are analyzed as functions of high-molecular-weight solute concentrationc with parameters of constant or to obtain [()], [ ()], and [ ()]. Such a collection of data has apparently not previously been available for polymers in theta solvents (in which Gaussian chain statistics prevail). Also unique is the achievement of high stress ( = 2 10⁴ Pa) at low shear rate, by virtue of high solvent viscosity which is not characteristic of other known theta solvents.     

Superposition of low-amplitude shear vibrations on steady shear flow of an elastic fluid

The previously proposed theory of viscoelastic behavior of polymer fluids is compared with experiments on the superposition of low-amplitude shear vibrations on a steady flow. It is shown that the theory agrees satisfactorily with experiments on a single polymer solution. The superposition of a steady shear flow and low-amplitude vibrations can be used to investigate some nonlinear effects characteristic of elastic fluids by relatively simple methods. The literature devoted to this question is fairly extensive; we cite only investigations in which the main results have been obtained [1–3]. The most common experimental scheme is one-dimensional (parallel superposition), although there is also a two-dimensional scheme of orthogonal superposition of shear vibrations on steady flows. Since almost all the effects in the second scheme are qualitatively similar to the first [3], but are not so clearly manifested, we give the theoretical and experimental results relating to the parallel scheme in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1976.We are grateful to É. Kh. Lipkina for help in the calculations.     

Transient and steady state behaviors of rapid granular shear flows

Rapid granular shear flow is a classical example in granular materials which exhibits fluid-like behavior solely or fluid-like and solid-like behaviors simultaneously. We have performed experiments on annular granular shear flows using monodisperse steel spheres with 2-mm and 3-mm diameters. We discuss some transient (static failure of material due to shear) and steady-state (completely sheared and partially sheared flows) features of rapid granular flows. Our results map out the boundary between overall compaction and dilation that characterizes multiphase behavior of the system. Dimensionless stresses rise as more material is loaded into the system. On the other hand, increasing the compressive force or shear rate is equal to easing the process of shearing by decreasing the ratio of shear to normal stress.     

Non-linear behaviour of asphalts in steady and transient shear flow

Steady-state and transient shear stress and normal stress data were obtained for four asphalts with a modified Weissenberg Rheogoniometer. Interest was specially related to non-linear behaviour at high shear-rates. The time-temperature superposition principle was found to hold in non-linear behaviour. Moreover, steady-state and transient data could be plotted as master curves irrespective of the nature of the asphalts. In particular, the master curve of steady-state viscosity could be extended to results published in the literature. In the nonlinear region the shear stress relaxation after cessation of a steady shear rate becomes a function of t only and is related to the primary normal-stress coefficient, as predicted by the Yamamoto equation. In the shear stress growth experiment an overshoot is obtained at a constant strain close to 1.5, independent of the rate of strain.