Transient Elongational Flow Research Articles

Polymer solutions under elongational flow: 1. Birefringence characterization of transient and stagnation point elongational flows

Birefringence measurements are reported in transient and stagnation point elongational flows created by forcing a polymer solution through a narrow contraction. A strongly molecular weight dependent birefringence was observed and attributed to segmental orientation caused by individual chain extension. The birefringence was also found to depend on the position within the flow field, the solvent type, thermodynamic quality and viscosity, the polymer composition, and the type of flow field. Two distinct concentration regimes, corresponding to the dilute and semi-dilute polymer regions, were observed. The transition was marked by a dynamic critical overlap concentration which was lower than that observed under quiescent conditions. In the dilute regime, a laminar flow profile was observed and intermolecular interactions were negligible. The modest local orientation and overall chain deformation however indicate that intramolecular hindrances to extension exist. Transient elongational flows were characterized by a ‘tube-like’ birefringence which had a diameter equal to that of the orifice and extended several orifice diameters into the solution. In contrast, stagnation point elongation flows possessed both the tube-like birefringence and the classical highly localized birefringent ‘lines’. The transition between the tubular and linear birefringent zones is a function of the viscous coupling between the polymer coil and the deforming fluid element. This coupling is itself a complex function of temperature, molecular parameters and the flow conditions. Measurements in stagnation point elongational flows have also indicated that the maximum degree of local orientation does not occur at the stagnation point, and data indicate that chains continue to accelerate until a region very close to the orifice. In transient elongational flow the polymer dynamics follow a coil-to-deformed coil transition with birefringence saturation not observed.

Simulation of Fracture of Flexible Polymer Chains in Transient Elongational Flow

Using the Brownian dynamics technique, we have simulated the fracture process of flexible polymer chains subjected to convergent (sink) flow, where the elongational rate is strongly position dependent. The system studied has been a very dilute solution of polystyrene with molecular weight 2 x 10 6 in cyclohexane at a temperature of 35 °C. The polymer was modeled as a bead-spring chain, adequately parametrized as to reproduce real polymer/solvent conditions. The fracture yield varies with the flow rate and is seen to depend to a high degree on the instrumental setup. The distribution of fragments at the end of the convergent flow region is found to be centered around half the initial molecular weight, and we find that there is no fracture below a certain critical flow rate. These results are in qualitative agreement with the experimental results of Reese and Zimm 1 on DNA and Nguyen and Kausch 2 on polystyrene, a finding that confirms the applicability of the Brownian dynamics simulation technique for studying polymer chain fracture.

Simulation of deformation and fracture of polymer chains in flowing solutions

Simulation studies are reviewed that employ the Brownian dynamics technique to characterize conformational and dynamic aspects of polymers in solutions that are subjected to different types of flow. Thus, the polymer deformation is considered in a shear flow, comparing the simulation results with other experimental and theoretical findings. The stretching of the chains in steady elongational flow and their eventual fracture is simulated and the critical rates required for such phenomena are evaluated. Finally, simulations for polymer fracture in transient elongational flows produced by the passage of the solution through a small orifice are reviewed. The degradation yield and the size distribution of the fragments are simulated and compared with experiments.

Chain extension and degradation in convergent flow

Rheology and birefringence measurements showed conclusively that quasi-full chain extension could be achieved in stagnant extensional flow above some critical strain rate of the order of the reciprocal of the chain characteristic time. Degradation in this highly expanded state could be rationalized with a model of chain scission through frictional loading in which the fracture event is controlled by the force balance between polymer solvent viscous friction and the breaking strength of the bond under consideration. In contrast to the process of chain extension, which could be observed only under rather restrictive conditions of flow, polymer degradation is ubiquitous and is readily detected in situations as diverse as convergent flow, ultrasonic irradiation, solution crystallization, turbulence and flow across porous media. Although some extensional flow component was always present in these types of degradation, the residence time in the high strain-rate region is so short that only a limited degree of coil expansion could be expected. Degradation in transient elongational flow indicated a behaviour definitely distinct from the degradation of fully extended chains under stagnant conditions. In particular, the following experimental facts cannot be explained by the model of fully extended frictionally loaded chains: dot ε f ≊ M −1 (where dot ε is the critical strain rate for chain fracture); dot ε f ≊ η s −0.25 (where η s, is the solvent viscosity); degradation yield is a fairly unique function of average fluid velocity or entrance pressure drop and is almost independent of differences in elongational strain rate introduced by nozzle geometry. These facts lead us to the conclusion that the fundamental parameter which governs the rate of degradation of partly deformed coils is not the magnitude of the local stress, but rather the deformation energy accumulated by the coil up to the moment of rupture.

Molecular coils and their deformation

The study of stress-effects on chain conformation has always been a fruitful - and sometimes highly controversial - issue in macromolecular science. In this paper chain scission in transient elongational flow is investigated. Particular attention is given to the possible nature of stress transfer from the deforming highly dilute polymer solution to the embedded molecular (PS) chain. The dependencies of the measured degradation efficiency on molecular weight, solvent viscosity, nozzle geometry and flow rate exclude the classical mechanism of chain loading through strain-rate dependent viscous friction. On the basis of their findings the authors propose a model where the loading of hairpin-like segments in almost static friction works against the internal relaxation of these structures.

Effects of solvent viscosity on polystyrene degradation in transient elongational flow

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTEffects of solvent viscosity on polystyrene degradation in transient elongational flowTuan Q. Nguyen and Henning H. KauschCite this: Macromolecules 1990, 23, 24, 5137–5145Publication Date (Print):November 1, 1990Publication History Published online1 May 2002Published inissue 1 November 1990https://doi.org/10.1021/ma00226a017RIGHTS & PERMISSIONSArticle Views325Altmetric-Citations47LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts

Fractional Exponential Form of Relaxation Modulus and Transient Elongational Flow

Williams and Watts have shown that a fractional exponential form for the decay function is able to describe dielectric relaxation in polymeric systems. The possible use of the fractional exponential form for the relaxation modulus in rheology is discussed. The elongational stress growth function and the complex viscosity function are simulated via the defect‐diffusion model.

Kinetics of polymer degradation in transient elongational flow

AbstractAn expression of the kinetics describing the rate of bond scission under stress is proposed and applied to the case of degradation of polymers in transient elongational flow. The new equation permits to take into account the existence of critical values, either for molecular weight or strainrate, below which no chain scission occurs. Compared with the other types of mechano‐chemical degradation, depolymerization in transient elongational flow is characterized by a short residence time and an inhomogeneous flow field in which the scission rate constants change drastically with the spatial coordinates. The evolution of molecular size distribution during the degradation process has been investigated using a general polymer fragmentation scheme. The set of differential equations was solved exactly with a matrix technique. Excellent concordance between calculations and experimental results from dilute polystyrene solutions was obtained, providing the spatial distribution of the strain‐rate was properly incorporated into the degradation kinetics.

Birefringence of polyethylene melt in transient elongational flow at constant strain rate

AbstractSimultaneous birefringence and elongational viscosity measurements were carried out on molten commercial grade, low‐density polyethylenes during simple elongational flow at constant strain rate and constant temperature. The birefringence increased with time during constant strain rate elongation. The increase in birefringence was a linear function of elongational stress throughout whole elongation, but the elongational viscosity increased in two stages. The increase in elongational viscosity can be divided into linear viscoelastic and nonlnear viscoelastic regions. The linear region appeared at small strain and the nonlinear region appeared at strain greater than 0.7. The elongational viscosity in the nonlinear region increased much more rapidly than that in the linear region. The Gaussian approximation, which is commonly used in molecular models, could be used for the transient elongational flow. A constant stress‐optical coefficient C = 1.3 × 10−10 cm2/dyn was obtained for all the elongational experiments, independent of strain rate (0.002‐0.2s−1). The stress‐optical coefficients were weakly dependent on temperature, as predicted by the theory of rubber elasticity.

Polymer fracture in steady and transient elongational flows

The scaling of the critical strain rate for fracture of polymers, observed in cross-slot-type elongational flow devices and predicted by recent models, differs from that obtained in flows through sudden contractions. We argue that while the former experiments are performed under quasi-steady-state conditions that lead to full stretching of the polymers, the transient nature of the latter results in a partial, nonuniform stretching of the chains. An expression for the scaling of the critical strain-rate for fracture of such partially stretched chains is derived and is shown to agree with experiments on elongational flows through contractions. Further experimental tests of the above model are proposed.

Degradation of a polymer solution in transient elongational flow: effect of temperature

The effect of temperature on the mechanical degradation of diluted polystyrene solutions, in dioxan and dekalin, has been studied in elongational flow created by forcing the fluid through a steep contraction. Thermal activation has little influence on the yield for chain scission in this system due to the short residence time and transient strain rate inherent to this type of flow. Chain scission in both solvents showed a weak negative activation energy which could only be partially accounted for by a change in solvent viscosity with temperature. Below the θ-temperature in dekalin solutions an abrupt decrease in chain scission is recorded after phase separation. Formation of interchain aggregates below the θ-point gives rise to a transient topological network. These physical crosslinks prevented the macromolecule from being fully stretched under flow and exerted a protective effect by lowering the local axial stress acting on the chain.

A new elongational rheometer for polymer solutions

Design and operation of a new elongational rheometer for low elastic polymer solutions are described. The free jet elongational rheometer is easy to operate and for suitable operating conditions a transient elongational flow with an approximately constant rate of strain can be realized. In any case, convenient comparative parameters can be obtained. The method of rheological curve fitting leads to a deformation dependent ralaxation time parameter of a modified upper convected Jeffreys-law.

Constitutive equation for polymer liquids: application to shear flow

A constitutive equation for describing the nolinear viscoelastic behaviour of polymer systems is proposed. It is based on the concept of structural kinetics. The suggested model is a modification of the one presented by Acierno et al. It differs from the latter by the kinetic equation.The model is applied to various types of equilibrium and transient shear flows. Transient elongational flow will be dealt with in a separate paper. The equilibrium experiments include viscosity and first normal stress difference, linear dynamic moduli, parallel and orthogonal superposition moduli. Three transient experiments are included. Two of them have been used before: relaxation of shear stress upon cessation of flow and shear stress overshoot as a function of rest time. The third technique is a new one and consists of superimposing orthogonally a vibration on relaxation after cessation of flow. The transient experiments prove the necessity to introduce a new kinetic equation in Acierno's model.In the experiments two fluids are used: a polyisobutylene solution in decaline and a polyacrylamide solution in a mixture of glycerine and water. For one system the kinetic model parameter is derived from shear flow data. For the other this parameter is derived from elongatinal flow data. The purpose is to develop a model where a single set of material parameters describes both shear flow and elongational flow data.

Some limitations on the detection of high elongational stress effects in dilute polymer solutions

AbstractThe elongational flow behavior of dilute polymer solutions is of great current interest because it has been suggested that elongational viscosity effects may be involved in a number of phenomena such as turbulent drag reduction and flow cavitation suppression. Unfortunately, recent experiments, in trying to investigate elongational effects, have produced widely varying results. In this paper, an attempt is made to analyze one of the factors that contribute to this diversity. By using a generalized convected Maxwell model, it is shown that in a transient elongational flow, both stretching rate and flow time must reach the proper values before high stress levels can be observed. This is true for both accelerating flows such as through a cone or wedge and decelerating flows such as in a free jet. Since most previous experiments have not considered flow time, consistent results cannot be expected. Consequently, the proper control of all flow conditions is an essential requirement when trying to observe high stress levels. The results presented here provide valuable guidelines in this regard.