Elastic stresses in capillary jets of dilute polymer solutions

The elastic longitudinal stresses associated with the flow of jets of dilute polymer solutions from a short nozzle and their effect on the stability of the free jet are investigated theoretically and experimentally. The results obtained make it possible to take a fresh look at the ways in which a polymer additive affects the stability of high-velocity capillary jets.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–9, Marc–April, 1985.     

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.     

Coarse-grained model of entangled polymer melts in non-equilibrium

A coarse-grained model developed for entangled polymeric systems and calibrated to represent melts in equilibrium (Rakshit, Picu, J Chem Phys 125:164907(1)–(10), 2006) is used to model shear flows. The model is a hybrid between multimode and mean-field representations: chain inner blobs are constrained to move along the chain backbone and the end blobs are free to move in 3D and continuously redefine the diffusion path for the inner blobs. Therefore, contour length fluctuations and reptation are captured. Constraint release is implemented by tracing the position of chain ends and performing a local relaxation of the chain backbones once end retraction is detected. This algorithm takes advantage of the multi-body nature of the model and requires no phenomenological parameters other than the length of an entanglement segment. The model is used to study start-up and step strain shear flows and reproduces features observed experimentally such as the overshoot during start-up shear flow, the Lodge–Meissner law, the monotonicity of the steady state shear stress with the strain rate, and shear thinning at large . These simulations are performed in conditions in which using a fully refined model of the same system would have been extremely computationally demanding or simply impossible with the current methods.     

A rheo-optical study of shear-thickening and structure formation in polymer solutions. Part I: Experimental

Simultaneous measurements of the optical and theological response of solutions of highly fractionated polystyrenes have been made, in-situ, to ascertain the connection between flow-induced structure formation and the phenomenon of shear-thickening. Transient and steady state viscosity, dichroism, birefringence and the associated orientation angles were measured in decalin and bromobenzene in the semi-dilute region using a couette device capable of shear rates up to 8,000 s^–1. A one-to-one correlation has been found between the occurrence of maxima in the dichroism and minima in the viscosity. While the size and shape of the shear-thickening structures could not be directly determined, results suggest they are intermediate in size between a cluster of entangled chains and a completely phase-separated liquid. For solutions exhibiting shear-thinning alone, no maximum in dichroism was observed, the signal instead showed a saturation behavior at high shear rates. Birefringence was found to be insensitive to the structure formation and attributable to that of the dissolved chains or entanglement regions. The kinetics of the structuring process leading to shear-thickening are instantaneous and completely reversible and there is a concentration window, above and below which only shear-thinning occurs.     

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites

The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.     

Influence of polymer conformation on the entrance length in capillary flow

An analysis of the flow of polymer solutions through capillaries by means of pressure profiles was performed in this work. The experiments were carried out with aqueous solutions of flexible and semirigid macromolecules, Polyox and Xanthan respectively. The influence of the macromolecules' conformation on the flow field development is reflected on the different magnitudes of the entry length, being of the order of 60 diameters for the solutions of rigid macromolecules, and of the order of 10 diameters for flexible ones. In addition, the calculated end effects were larger for the rigid macromolecules than for the flexible ones. From these results, it is found that an increase in the entrance length is observed when the pseudoplastic behavior of the polymer solutions is increased.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

A modified tube dilatation theory for the relaxation of entangled linear polymer melts

In this paper, the “tube dilatation” or “tube Enlargement” concept introduced by Marrucci, is revisited in the case of broad entangled linear polymer melts. Using the tube fluctuation relaxation function of Doi and a linear mixing rule, the model implicitly contains both the features of double reptation and time modification by tube renewal. It has been shown that theoretical arguments of both double reptation with tube renewal and tube dilatation can be used to take into account the effect of polydispersity on the distribution of relaxation times. The model has been tested for some polymers with various N/Ne values. However, experiments indicate that the loss of only one entanglement does not systematically induce a change of the relaxation times through a constraint release and tube renewal process. The freeing of a critical volume, larger than the volume of a tube segment, is required to induce an efficient dilution effect on relaxation times.     

Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid

The capillary thinning of a filament of viscoelastic liquid, which is the basis of a microrheometer, is analyzed in terms of a multi-mode FENE fluid. After a short time of viscous adjustment, the stress becomes dominated by the elastic contribution and the strain-rate takes on a value equal to two-thirds the rate at which the stress would relax at fixed strain. This strain-rate decreases as the dominant mode changes. At late times, modes reach their finite extension limit. The fluid then behaves like a suspension of rigid rods with a large extensional viscosity, and the liquid filament breaks. Predictions are compared with the experiments of Liang and Mackley (1994).     

A finite difference study of the stretching and break-up of filaments of polymer solutions

The stretching and break-up of a viscoelastic filament pulled by a constant weight is studied numerically by a finite difference method. The results show the following tendencies:(1) Newtonian filaments, even in the absence of surface tension, show a rapid increase in elongation at one particular point (they “break” there).(2) The addition of a viscoelastic polymer prevents, or at least delays, the break-up, even if it makes only a small difference to shear viscosity.(3) Surface tension accelerates break-up, but even in the presence of surface tension elasticity has a stabilizing effect.     

Viscoelastic properties of polymer solutions

Summary Measurements were taken of the thrust of liquid jets ejecting from a long capillary into air for aqueous solutions of polyacrylamide (ET 597) of various concentrations. The measurements were then used to determine axial normal stresses for two capillary diameters: 1.52 mm (L/D = 201.5) and 2.44 mm (L/D = 207.2). The results show that the calculated values of the axial normal stress are higher for the larger capillary diameter than for the smaller, as recently reported byPowell andMiddleman. It has been further found that this diameter effect becomes more pronounced as the concentration of solute is increased. For the same materials, we also measured the primary normal stress difference by means of aWeissenberg rheogoniometer. Comparison between the two kinds of measurements shows that the magnitude of axial normal stresses is much smaller than that of normal stress differences over the range of shear rates studied (200 20,000 sec^–1) for the materials investigated. This result seems to point out the necessity of measuring the wall normal stresses, which are believed to depend not only on the capillary diameter, but also on the concentration. The authors therefore contend that, in general, the measurement of axial normal stresses alone is not sufficient to completely determine the elastic properties of viscoelastic solutions.     

Normal stress measurements on drag-reducing polymer solutions

Summary The elastic properties of very dilute solutions of a number of drag-reducing polymers differing either in chemical nature or molecular weight were investigated over a range of values of shear stress using the jet thrust method. Parallel drag reduction measurements were also made with the solutions. The results indicate a general relationship between the value of the first normal stress difference at the wall, (p ₁₁-p ₂₂, and the dragreducing ability.The data tends to confirm the generality of the correlation between the value of theWeissenberg number and the drag reduction reported byMetzner for a single polymer sample.     

Dynamic measurements on polymer solutions and melts

Summary An apparatus for the measurement of the dynamic viscosity is described. In a coaxial cylinder geometry forced vibrations are executed in the frequency region from 2·10^–4 to 50 cycles/sec. Fluids with a wide range of viscosities (10^–1 to 10⁷ poise) can be measured. A number of experimental results obtained on dilute solutions and melts of polymers are given and compared with results of the molecular theories.

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Zusammenfassung Es wird ein Gerät für die Messung der dynamischen Viskosität beschrieben. Innerhalb eines koaxialen Zylindersystems werden im Frequenzgebiet von 2 · 10^–4 bis 50 Hz erzwungene Schwingungen ausgeführt. Messungen an Flüssigkeiten sind in einem weiten Viskositätsbereich (10^–1 bis 10⁷ Poise) möglich. Einige Messungen an verdünnten Lösungen oder Schmelzen von Hochpolymeren werden mitgeteilt und mit Voraussagen molekularer Theorien verglichen.

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Paper read at the Annual Meeting of the German Rheologits, Berlin-Dahlem, May 20–21, 1968).     

Unstable capillary flow of reinforced polymer melts

The injection capillary flow of various unfilled and glass fibre or calcium carbonate filled polypropylene and nylon 6.6 melts is studied using either a single capillary of five capillaries in series, separated by small reservoirs. Only unfilled nylon 6.6 yields instability during flow through a single capillary due to mechanochemical degradation in the capillary at extremely high shear rates above 5 × 10⁵ s^?1. It is found that only short glass fibre reinforced polypropylene yields high frequency oscillations in the reservoir pressure and extrudate diameter and has discontinuity in the flow curve when the apparent shear rate is above 4 × 10⁵ s^?1 and the flow is through multiple capillaries. Further increase in the shear rate restores the stable flow. The intensity of the oscillations and the range of shear rate during which unstable flow occurs are increased with increasing melt temperature. The mechanism of this unstable flow is investigated by studying fibre orientation at the capillary entrance and exit using mouldings simulating capillary entry-exit flows.