Showing papers in "Journal of Non-newtonian Fluid Mechanics in 2005"

Squeeze flow theory and applications to rheometry: A review

Abstract: The deformations and stresses during squeeze flows are evaluated for a wider class of materials than previously covered in articles on this subject. These include generalised Newtonian fluids, yield stress fluids, as well as elastic and viscoelastic materials. Wherever possible, results are given in a compact mathematical form. The effect of different boundary conditions (no slip, perfect slip and partial slip) and how these interact with different types of material behaviour to give a variety of macroscopic responses is also discussed. The significance of this in using squeeze flow as a rheometry method is highlighted and a state-of-the-art view of squeeze flow rheometry is given.

Flow of viscoelastic fluids past a cylinder at high Weissenberg number : stabilized simulations using matrix logarithms

Abstract: The log conformation representation proposed in [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285] has been implemented in a FEM context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and identify the failure of the numerical scheme to balance exponential growth as a possible source for numerical instabilities at high Weissenberg numbers. A different derivation of the log-based evolution equation than in [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285] is also presented. We show numerical results for the flow around a cylinder for an Oldroyd-B and a Giesekus model. With the log conformation representation, we are able to obtain solutions beyond the limiting Weissenberg numbers in the standard scheme. In particular, for the Giesekus model the improvement is rather dramatic: there does not seem to be a limit for the chosen model parameter (α = 0.01). However, it turns out that although in large parts of the flow the solution converges, we have not been able to obtain convergence in localized regions of the flow. Possible reasons include artefacts of the model and unresolved small scales. More work is necessary, including the use of more refined meshes and/or higher order schemes, before any conclusion can be made on the local convergence problems. © 2005 Elsevier B.V. All rights reserved.

The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries

Abstract: The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through micro-fabricated planar abrupt contraction-expansions is investigated. The small lengthscales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. By considering the definition of the elasticity number, El = Wi/Re, we show that the lengthscale of the geometry is key to the generation of strong viscoelastic effects, such that the same flow behaviour cannot be reproduced using the equivalent macro-scale geometry using the same fluid. We observe significant vortex growth upstream of the contraction plane, which is accompanied by an increase of more than 200% in the dimensionless extra pressure drop across the contraction. Streak photography and video-microscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.44 ≤ Re ≤ 64) associated with these high Weissenberg number (0 ≤ Wi ≤ 548) micro-fluidic flows results in the exploration of new regions of the Re-Wi parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in micro-fluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = Wi/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation

Abstract: We present a second-order finite-dierence scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-driven cavity. The scheme is found to be stable at large values of the Weissenberg number. These results support our claim that the high Weissenberg numerical instability may be overcome by the use of logarithmic variables. Remaining issues are rather concerned with accuracy, which degrades with insucient resolution.

On the usage of viscosity regularisation methods for visco-plastic fluid flow computation

Abstract: Viscosity regularisation methods are probably the most popular current method for computing visco-plastic fluid flows. They are however generally used in an ad hoc manner. Here we examine convergence of regularised solutions to those of the corresponding exact models, in both mathematical and physical senses. Mathematically, the aim is to give practical guidance as to the order of error that one might expect for different regularisations and for different types of flow. Our theoretical results are illustrated with a number of computed example flows showing the orders of error predicted. Physically, the question is whether or not the regularised solutions behave in the same way as the exact solutions, qualitatively as well as quantitatively. We show that there are flows for which regularisation methods will generate their maximum errors, e.g. lubrication-type flows. In this context, we also consider the effects of regularisation on problems of hydrodynamic stability. For broad classes of problems, stability characteristics of the flow are incorrectly predicted by the use of viscosity regularisation methods.

The dynamics of single-molecule DNA in flow

Abstract: Within the last decade, fluorescence microscopy of single molecules of DNA in a plethora of flow fields has allowed an unprecedented examination of the dynamics of polymers in flow. As a result, new principles (e.g. “molecular individualism”) have been developed regarding these dynamics and old debates (e.g. conformational hysteresis of polymers in extensional flow) have received a fresh airing. The coupling of the microscopy, employing a spectrum of possible DNA molecules, fragments, and concatemers with dynamic simulation (e.g. Brownian dynamics) has created a tremendous opportunity to both revisit unanswered questions in the field of polymer solution dynamics (particularly in the nonlinear flow regime), as well as to examine new areas surrounding the engineering of flow dynamics of complex fluids in microfluidic devices. The foundation for future studies has been laid by careful experimentation and computer simulation of DNA dynamics in bulk or locally linear flows of many types. Future studies involving collective effects, complex flows, flow-induced reaction, adsorption and so forth are just beginning and again the promise is to develop a new understanding of these polymer processes by examining DNA “one molecule at a time.”

The shear-induced solid–liquid transition in yield stress materials with chemically different structures

Abstract: The shear-induced solid–liquid transition of viscoplastic materials has been studied extensively through various steady-shearing experiments including steady stress sweep, stress ramp, creep and strain recovery. The results are consistent in showing a clear change in behaviour of the materials from solid-like to liquid-like. A transition stress plateau separates the regions of solid behaviour and liquid behaviour. The slope of the plateau reflects the uniformity of the structure, and hence the distribution of bonding strength within this structure. Depending on the structure of the material, the yielding process of viscoplastic materials can occur over a wide or a narrow range of stress, which represents “ductile-type” or “brittle-type” failure. Altering the concentration and extent of particle flocculation (for suspensions) or polymer chain entanglements (for polymer gels) can vary the bonding strength and strength distribution, and therefore change the slope of the stress plateau. The continuous solid structure exhibits creep at stresses well below the yield stress and fails at a critical strain. The yielding of the material seems to be characterised by a critical strain rather than by a critical stress or a critical shear rate. The deformation of viscoplastic materials can be recovered fully or partially in the solid-like region once the stress is removed. This is a significant difference from the behaviour of purely viscoelastic materials. Strain recovery tests result in two characteristic strain values that can be used to define the two commonly used “yield stress” values, the higher one of which is in good agreement with the traditional value of yield stress as measured by vane torsion, for example.

Rheological characterization of melt processed polycarbonate-multiwalled carbon nanotube composites

Abstract: In this study polycarbonate/multiwalled carbon nanotube composites were produced with different compositions by diluting a masterbatch using melt mixing in a DACA-Micro-Compounder. The composites were rheologically characterized using an ARES-rheometer in the dynamic mode under nitrogen atmosphere at 280 °C and frequency varying from 100 to 0.056 rad/s. The results showed that the dynamic moduli and the viscosity increased with increasing MWNT content. At a concentration of 0.5 wt.% MWNT, a significant change in the frequency dependence of the moduli was observed which indicates a transition from a liquid like to a solid like behavior of the nanocomposites. This transition can be related to the formation of a combined network between the nanotubes and the polymer chains.

Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate

Abstract: In this paper, the unsteady magnetohydrodynamic viscous flows of non-Newtonian fluids caused by an impulsively stretching plate are studied by means of an analytic technique, namely the homotopy analysis method We give the analytic series solutions which are accurate and uniformly valid for all dimensionless time in the whole spatial region 0 ≤ η ∞ To the best of authors’ knowledge, such kind of analytic solutions have been never reported Besides, the effects of the integral power-law index ( n = 1 , 2, 3) of the non-Newtonian fluids and the magnetic parameter M = 0 , 1, 2 on the flows are investigated

Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids

Abstract: Drop dynamics plays a central role in defining the interfacial morphology in two-phase complex fluids such as emulsions and polymer blends. In such materials, the components are often microstructured complex fluids themselves. To model and simulate drop behavior in such systems, one has to deal with the dual complexity of non-Newtonian rheology and evolving interfaces. Recently, we developed a diffuse-interface formulation which incorporates complex rheology and interfacial dynamics in a unified framework. This paper uses a twodimensional implementation of the method to simulate drop coalescence after head-on collision and drop retraction from an elongated initial shape in a quiescent matrix. One of the two phases is a viscoelastic fluid modeled by an Oldroyd-B equation and the other is Newtonian. For the parameter values examined here, numerical results show that after drop collision, film drainage is enhanced when either phase is viscoelastic and drop coalescence happens more readily than in a comparable Newtonian system. The last stage of coalescence is dominated by a short-range molecular force in the model that is comparable to van der Waals force. The retraction of drops from an initial state of zero-velocity and zero-stress is hastened at first, but later resisted by viscoelasticity in either component. When retracting from an initial state with pre-existing stress, produced by cessation of steady shearing, viscoelasticity in the matrix hinders retraction from the beginning while that in the drop initially enhances retraction but later resists it. These results and the physical mechanisms that they reveal are consistent with prior experimental observations. © 2005 Elsevier B.V. All rights reserved.

Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel-Bulkley fluids

Abstract: The augmented Lagrangian method is applied to the steady flow problems of Bingham, Casson and Herschel–Bulkley fluids in pipes of circular and square cross-sections. The plug flow velocity, the flow rate, the flow pattern, the velocity profile, the locations of yielded/unyielded surfaces, the stopping criteria and the friction factor are presented and compared with one another. The numerical strategy based on variational inequalities is shown to be realised easily and applicable extensively.

Non-Newtonian fluids with a yield stress

Abstract: A modified Herschel–Bulkley model [E. Mitsoulis, S.S. Abdali, Flow simulation of Herschel–Bulkley fluids through extrusion dies, Can. J. Chem. Eng. 71 (1993) 147–160] predicts an infinite apparent viscosity at vanishing shear rate. Furthermore, the dimensions of one parameter depend on another parameter. In this contribution, we propose a generalized model based on earlier work by De Kee and Turcotte [D. De Kee, G. Turcotte, Viscosity of biomaterials. Chem. Eng. Commun. 6 (1980) 273–282] and on the work of Papanastasiou [T.C. Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987) 385–404] to solve the problems associated with the modified Herschel–Bulkley model. Compared to the responses of the Papanastasiou model and the modified Herschel–Bulkley model, the proposed generalized model provides the expected improvements and is capable of predicting successfully the rheological behavior (viscosity and yield stress) of Carbopol 980 dispersions.

Laminar transitional and turbulent flow of yield stress fluid in a pipe

Abstract: This paper presents an experimental study of the laminar, transitional and turbulent flows in a cylindrical pipe facility (5.5 m length and 30 mm inner diameter). Three fluids are used: a yield stress fluid (aqueous solution of 0.2% Carbopol), a shear thinning fluid (aqueous solution of 2% CMC) without yield stress and a Newtonian fluid (glucose syrup) as a reference fluid. Detailed rheological properties (simple shear viscosity and first normal stress difference) are presented. The flow is monitored using pressure and (laser Doppler) axial velocity measurements. The critical Reynolds numbers from which the experimental results depart from the laminar solution are determined and compared with phenomenological criteria. The results show that the yield stress contribute to stabilize the flow. Concerning the transition for a yield stress fluid it has been observed an increase of the root mean square ( rms ) of the axial velocity outside a region around the axis while it remains at a laminar level inside this region. Then, with increasing the Reynolds number, the fluctuations increase in the whole section because of the apparition of turbulent spots. The time trace of the turbulent spots are presented and compared for the different fluids. Finally, a description of the turbulent flow is presented and shows that the rms axial velocity profile for the Newtonian and non-Newtonian fluids are similar except in the vicinity of the wall where the turbulence intensity is larger for the non-Newtonian fluids.

Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids

Abstract: The effect of viscoelasticity on the deformation of a circular drop suspended in a second liquid in shear is investigated with direct numerical simulations. A numerical algorithm based on the volume-of-fluid method for interface tracking is implemented in two dimensions with the Oldroyd-B constitutive model for viscoelastic liquids. The code is verified against a normal mode analysis for the stability of two-layer flow in a channel; theoretical growth rates are reproduced for the interface height, velocity and stress components. Drop simulations are performed for drop and matrix liquids of different viscosities and elasticities. A new feature is found for the case of equal viscosity, when the matrix liquid is highly elastic and surface tension is low; hook-like structures form at the drop tips. This is due to the growth of first normal stress differences that occur slightly above the front tip and below the back tip as the matrix elasticity increases above a threshold value.

SPH simulations of transient viscoelastic flows at low Reynolds number

Abstract: A numerical study on the transient flow of a viscoelastic fluid is presented. The numerical framework is that of Smoothed Particle Hydrodynamics (SPH) already used by Ellero et al. in previous simulations of Non-Newtonian flows [J. Non-Newtonian Fluid. Mech. 105 (2002) 35–51]. In particular, the start-up flow between parallel plates is simulated for an Oldroyd-B and UCM fluid at low Reynolds number. Results for a Newtonian fluid are also shown for comparison. The numerical results are presented and compared with available theoretical solutions, showing a very good agreement. In particular, the simulations of an Oldroyd-B fluid have been found to be stable and accurate for a wide range of the Weissenberg number. In the case of a UCM fluid, the absence of a viscous term in the momentum equation makes its numerical modelling harder. Namely, the process is characterised by a travelling damped wave, which, if not accurately resolved, can lead to the rapid growth of small oscillations in time eventually causing divergence. On the other hand, if specifically dealing with transient flow problems, stabilising techniques such as BSD, EVSS or AVSS can not be used either; whenever used in conjunction with decoupled solution algorithms, they give an excessive oversmoothing in the results which deteriorates the final accuracy. In this work, we consider an exact SPH discretisation of the hyperbolic equation characterising the UCM model. SPH simulations are finally performed for different Weissenberg numbers showing very promising results. Finally, a discussion on the SPH treatment of the boundary conditions for general hydrodynamics problems is also outlined following the approach of ‘SPH boundary particles’ introduced by Morris for the simulations of low Reynolds number flows.

Shear and extensional rheology of EVA/layered silicate-nanocomposites

Abstract: Nanocomposites of ethylene-vinyl acetate copolymer (EVA) with 28 wt.% vinyl acetate content (EVA28) was prepared by melt intercalation with different loadings of organically-modified bentonite clay. The microstructure and morphology of the nanocomposites were examined by X-ray diffraction (XRD) and electron microscopy. XRD and transmission electron microscopy (TEM) indicated that EVA28 nanocomposites had predominantly exfoliated morphologies. The dynamic and steady shear rheological properties of the nanocomposites showed remarkable differences in comparison to that of pure EVA28 copolymer. Linear viscoelastic parameters were enhanced at all frequencies investigated and indicated the presence of a percolated network structure. Steady shear measurements revealed that the elasticity of EVA28 nanocomposites were dependent on the silicate loading at high shear stresses. Uniaxial extensional viscosities were found to increase with silicate loading and in general exhibited strain hardening behavior. Beyond a critical strain, nanocomposite extensional viscosities were almost identical with that of the unfilled EVA28, suggesting that at high strains, silicates have little effect on the extensional viscosities. An attempt has been made to propose a possible mechanism that describes the influence of clay layers on the uniaxial extensional flow field. Images obtained from transmission electron microscopy (TEM) and an environmental scanning electron microscopy (ESEM) were used to support the proposed mechanism.

Numerical simulation of non-isothermal viscoplastic waxy crude oil flows

Abstract: This paper examines the numerical simulation of transient non-isothermal flows of a viscoplastic fluid in a pipe. The situation considered refers to the waxy crude oils transportation in a pipeline, where the flowing oil is cooled down due to extreme external temperature conditions. The rheological model used is an extension of the classical Bingham model in which plastic viscosity and yield stress are allowed to be temperature-dependent parameters. To solve the governing equations, we propose a decoupled transient solution algorithm. At each time step, the velocity–pressure problem and the temperature problem are solved sequentially. Particular attention is devoted to the velocity–pressure problem in which the “true” (without regularization procedure) Bingham model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum, constitutive and energy equations are discretized using a Finite Volume method on a staggered grid with a TVD scheme for the convective term. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the steady-state solution underline the influence of the temperature changes on the flow pattern, especially in terms of yielded/unyielded regions. In particular, in a pipe flow, as soon as the temperature field varies in the mean flow direction, the fluid is yielded.

Analytical solutions for fully developed laminar flow of some viscoelastic liquids with a newtonian solvent contribution

Abstract: We present analytical solutions for fully developed pipe and channel flows of two viscoelastic fluids possessing a Newtonian solvent, where the polymer contribution is either described by the Phan-Thien–Tanner (PTT) or FENE-P models. We derive in detail the pipe flow solution for the PTT fluid, and present the final solutions for the remaining three cases. This constitutes an important addition to existing results where the presence of a solvent with Newtonian characteristics has been consistently overlooked, as it posed considerable difficulties to the task of obtaining a closed form solution. In addition, interesting aspects of the solutions are discussed. © 2005 Elsevier B.V. All rights reserved.

A theory of die-swell revisited

Abstract: The swelling of an extrudate initially performing a fully-developed tube flow is reconsidered for a wide class of constitutive equations, including PTT, pom–pom and general network type models. The results confirm and extend the original analysis; the limitations are also discussed.

Prediction of linear viscoelastic properties for polydisperse mixtures of entangled star and linear polymers: Modified tube-based model and comparison with experimental results

Abstract: We have developed and tested a new model suitable for the prediction of linear viscoelasticity (LVE) from knowledge of molecular structure for arbitrary mixtures of polydisperse star and linear entangled molecules. The model is based on key ingredients of tube models: reptation, fluctuations and constraint release. We impose no artificial time scale separation between fluctuations and reptation but rather allow both relaxation processes to proceed simultaneously. Early fluctuations are treated in a new and simple way, based on thermal energy threshold considerations. Because the modelled systems are arbitrary mixtures of linear and star molecules, we cannot obtain analytical solutions but have to resort to a time-marching algorithm to predict the relaxation modulus. The model has been tested on a wide range of literature data. Excellent predictions are obtained if the constraint release solvent influence on relaxation processes is treated consistently by using an extension of the "Graessley criterion". The solvent must be included only if the corresponding constraint release characteristic time is short compared to the considered relaxation process. (c) 2005 Elsevier B.V. All rights reserved.

Thixotropic investigation on cement paste: Experimental and numerical approach

Abstract: Cement paste is a suspension of cement particles in water. In this manuscript, a new rheological equation is presented to simulate thixotropic behavior of cement paste. This new material model is based on the previous work done by Hattori and Izumi. More precisely, the coagulation rate and dispersion rate of the cement particles are assumed to play the dominating role in generating thixotropic behavior. This is a so-called microstructural approach. The current work introduces ‘memory’ into the relevant shear viscosity equation (i.e. into the apparent viscosity). Two types of memory functions are used. One is the memory of recent coagulation rate and the other is of recent shear rate. Model evaluation is carried out by comparing experimental data with model prediction. The experimental data is obtained using the ConTec Viscometer 4. The model prediction is calculated with the software Viscometric-ViscoPlastic-Flow.

Rheological properties of long glass fiber filled polypropylene

Abstract: Long glass fiber-filled polypropylene (PP) composites are produced by pultrusion, and the extrudate is cut at different lengths producing composites containing long fibers of controlled length. The rheological properties of such composites in the molten state have been studied using different rheometers. A capillary rheometer has been constructed and mounted on a molding-injection machine. The shear viscosity of filled PP determined from the capillary rheometer, after corrections for entrance effects, was found to be very close to that of unfilled PP. However, large excess pressure losses at the capillary entrance were observed and these data have been used to obtain an apparent elongational viscosity. The apparent elongational viscosity was shown to be considerably larger than the shear viscosity for PP and filled PP, and it increased markedly with fiber length and fiber content. Rotational rheometers with a parallel-plate geometry were used to investigate the viscoelastic properties of these composites and their behavior was found to be non-linear, exhibiting a yield stress. A model is proposed to describe the shear viscosity from a solid-like behavior at low stresses to fluid-like behavior at high shear stresses taking into account fiber content and orientation. A modified model, proposed for elongational flow, describes relatively well the apparent elongational data.

Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids

Abstract: The purpose of this brief paper is to report mean velocity profile data for fully developed pipe flow of a wide range of shear-thinning liquids together with two Newtonian control liquids. Although most of the data reported are for the laminar–turbulent transition regime, data are also included for laminar and turbulent flow. The experimental data were obtained in unrelated research programmes in UK, France and Australia, all using laser Doppler anemometry (LDA) as the measurement technique. In the majority of cases, axisymmetric flow is observed for the laminar and turbulent flow conditions, although asymmetry due to the Earth's rotation is evident for the laminar flow of a Newtonian fluid of low viscosity (i.e. low Ekman number). The key point, however, is that for certain fluids, both yield-stress and viscoelastic (all fluids in this study are shear-thinning), asymmetry to varying degrees is apparent at all stages of transition from laminar to turbulent flow, i.e. from the first indications to almost fully developed turbulence. The fact that symmetrical velocity profiles are obtained for both laminar and turbulent flow of all the non-Newtonian fluids in all three laboratories leads to the conclusion that the asymmetry must be a consequence of a fluid-dynamic mechanism, as yet not identified, rather than imperfections in the flow facilities.

Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times

Abstract: We solve the one-dimensional cessation Couette and Poiseuille flows of a Bingham plastic using the regularized constitutive equation proposed by Papanastasiou and employing finite elements in space and a fully implicit scheme in time. The numerical calculations confirm previous theoretical findings that the stopping times are finite when the yield stress is nonzero. The decay of the volumetric flow rate, which is exponential in the Newtonian case, is accelerated and eventually becomes linear as the yield stress is increased. In all flows studied, the calculated stopping times are just below the theoretical upper bounds, which indicates that the latter are tight.

High-resolution finite element simulation of 4:1 planar contraction flow of viscoelastic fluid

Abstract: In this work, we present high-resolution solutions for viscoelastic 4:1 planar contraction flow problems using a transient finite element method based on the fractional step method (FSM) and stabilization techniques (DEVSS-G/DG) with linear equal-order interpolation function. The Oldroyd-B model was used as the constitutive equation. A parallel multi-frontal algorithm was implemented to enhance computational speed and all solutions were obtained on a parallel machine. The vortex intensity and the re-attachment length of corner vortex show good mesh-convergent behavior and are compared with previous results from the literature. In particular, the present results are in good agreement with the predictions of the high-resolution finite volume method of Alves et al. [15]. This may be the first case that quantitative agreement is obtained between studies using different numerical methods for the benchmark problem of 4:1 planar contraction flow. As there has been little quantitative agreement in the previous investigations and only few simulation results with highly refined meshes exit, this study may well be regarded as accurate and meaningful in the sense that reasonable convergence is achieved for prediction of 4:1 planar contraction flow using transient finite element methods.

Re-examination of the approximate methods for interconversion between frequency- and time-dependent material functions

Abstract: The paper examines the correctness of the best-known approximate methods of interconversion between the frequency- and the time-dependent material functions. Approximate interconversions are compared to the close-form viscoelastic interrelations through the relaxation and/or retardation spectra. The analysis showed that the simple method, G(t) ≃ G′(ω)|ω=1/t, should be avoided. The most successful was the method of Schwarzl yielding results with maximum relative error within 2%. The magnitude of the error of interconversion is related to the magnitude of the response function first derivative. When the first derivative ψ = |d(log G′(ω))/d(log(ω))|

Rheological measuring techniques and their relevance for the molecular characterization of polymers

Abstract: The zero shear viscosity η0, the linear steady-state compliance and the elongational viscosity are rheological quantities, which can preferably be used for a molecular characterization of polymers. The techniques applied to obtain reliable results are described. It is demonstrated that linear polyethylenes of high-density fulfill the relationship η0 ∼ M w 3.6 independently of the polydispersity. Mw is the absolute mass-average molar mass. Long-chain branched polyethylenes significantly deviate from this relation. The results from polyethylenes are used to characterize electron beam irradiated polypropylenes. It is clearly shown that long-chain branches are introduced by irradiation the topography of which changes with the dose. Measurements of the elongational viscosities support the conclusions from shear experiments. Creep tests in extension show the existence of steady-state elongational viscosities for the irradiated polypropylenes. The viscosities run through a maximum as a function of the elongational rates reached at steady state. The shape of the curves depends on the dose indicating once more a change in molecular structure by irradiation.

A numerical study of steady and unsteady viscoelastic flow past bounded cylinders

Abstract: We consider two-dimensional, inertia-free, flow of a constant-viscosity viscoelastic fluid obeying the FENE-CR equation past a cylinder placed symmetrically in a channel, with a blockage ratio of 0.5. Through numerical simulations we show that the flow becomes unsteady when the Deborah number (using the usual definition) is greater than De ≈ 1.3, for an extensibility parameter of the model of L 2 = 144. The transition from steady to unsteady flow is characterised by a small pulsating recirculation zone of size approximately equal to 0.15 cylinder radius attached to the downstream face of the cylinder. There is also a rise in drag coefficient, which shows a sinusoidal variation with time. The results suggest a possible triggering mechanism leading to the steady three-dimensional Gortler-type vortical structures, which have been observed in experiments of the flow of a viscoelastic fluid around cylinders. The results reveal that the reason for failure of the search for steady numerical solutions at relatively high Deborah numbers is that the two-dimensional flow separates and eventually becomes unsteady. For a lower extensibility parameter, L 2 = 100, a similar recirculation is formed given rise to a small standing eddy behind the cylinder which becomes unsteady and pulsates in time for Deborah numbers larger than De ≈ 4.0–4.5.

The effect of die exit curvature, die surface roughness and a fluoropolymer additive on sharkskin extrusion instabilities in polyethylene processing

Abstract: This paper reports experimental observations and numerical simulations relating to sharkskin extrusion instabilities for two different types of polyethylene, a metallocene high-density polyethylene (HDPE) and a linear low-density polyethylene (LLDPE). Experimental results are presented for both the effect of die exit curvature and die surface roughness for slit die geometry. Matching polyflow numerical simulations are also reported and are shown to be qualitatively consistent with experimental observations. The onset of the sharkskin instability is correlated with the magnitude of the stress concentration at the die exit, and is found to be sensitive to both the melt/wall separation point for a curved exit die, and the level of partial slip at the die wall. Additional observations on the effect of a fluoropolymer additive also support the sensitivity of the sharkskin instability to partial slip at the wall.

Constitutive equations for extensional flow of wormlike micelles: stability analysis of the Bautista–Manero model

Abstract: We carry out a stability analysis of the Bautista–Manero (B–M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity η E are unstable when the elongational rates ɛ ˙ exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s−1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B–M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time λ J . We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases.