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Nov 2001

Volume 45, Issue 6, pp. 1261-1491


Experimental observation and numerical simulation of transient “stress fangs” within flowing molten polyethylene

K. Lee, M. R. Mackley, T. C. B. McLeish, T. M. Nicholson, and O. G. Harlen

J. Rheol. 45, 1261 (2001); http://dx.doi.org/10.1122/1.1389316 (17 pages) | Cited 9 times

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We report experimental observations and matching numerical simulation for the time-dependent start-up flow of two molten polyethylenes (PEs) within a slit entry and exit geometry. For the case of a low density polyethylene (LDPE), an unexpected transient, birefringence “stress fang” was observed downstream of the slit exit. The stress fang consisted of a localized region of stress concentration. The stress fang, however, was not observed for a linear low density polyethylene (LLDPE) sample subjected to the same processing condition. A matching time-dependent numerical simulation of the flow is also presented. Using a split Lagrangian–Eulerian method for simulating transient viscoelastic flow with the multimode pom–pom constitutive equation, the general features of the stress fangs were predicted for the LDPE. In addition, the simulation did not predict stress fangs for the LLDPE. The paper demonstrates that for this particular case the pom–pom model can successfully discriminate the complex flow behavior of different PEs, and shows that the presence (or otherwise) of a stress fang is sensitive to the particular rheology of the polymer that arises from long chain branching. © 2001 The Society of Rheology.
Show PACS
47.11.-j Computational methods in fluid dynamics
83.80.Sg Polymer melts
78.20.Fm Birefringence
61.25.H- Macromolecular and polymers solutions; polymer melts

Finite element analysis of axisymmetric creeping motion of a deformable non-Newtonian drop in the entrance region of a cylindrical tube

See Jo Kim and Chang Dae Han

J. Rheol. 45, 1279 (2001); http://dx.doi.org/10.1122/1.1402659 (25 pages) | Cited 1 time

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The finite-element method was employed to analyze axisymmetric creeping motion of a deformable drop in the entrance region of a cylindrical tube. In the present study a non-Newtonian drop suspended in a non-Newtonian medium was considered, for which a truncated power-law model was employed. The penalty function method was used to eliminate the pressure variables from the system equations, considerably reducing the computational time required. In solving the system equations an unstructured mesh generator and auto-remeshing technique were used to describe the shapes of highly deformed drops. The results are in good agreement with experiments of Chin and Han [J. Rheol. 23, 557–590 (1979); 24, 1–37 (1980)] describing the deformation as the drop approaches the inlet from the reservoir section and recoil after it enters the tube. The present study demonstrates the effects of the capillary number and viscosity ratio on the deformation of non-Newtonian drops suspended in non-Newtonian liquids in the entrance region of a cylindrical tube. © 2001 The Society of Rheology.
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83.85.Tz Creep and/or creep recoil
47.50.-d Non-Newtonian fluid flows
83.50.Ha Flow in channels
02.70.Dh Finite-element and Galerkin methods
83.60.Fg Shear rate dependent viscosity

A simple constitutive equation for entangled polymers with chain stretch

Giovanni Ianniruberto and Giuseppe Marrucci

J. Rheol. 45, 1305 (2001); http://dx.doi.org/10.1122/1.1402661 (14 pages) | Cited 21 times

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We propose a simple way of including chain stretch effects in convective constraint release theories for entangled polymers. The main idea is that the characteristic time of orientational relaxation depends in a series-parallel way on all three relevant mechanisms, i.e., reptation, constraint release (thermal and convective), and Rouse relaxation. As usual, a separate equation describes chain stretch, which however is assumed not to be affected by constraint release. The model is further simplified by writing the orientational equation in differential form. For step strains, the successful damping function of the Doi–Edwards theory is exactly preserved. Predictions in steady shear also favorably compare with typical data of nearly monodisperse polymers. © 2001 The Society of Rheology.
Show PACS
83.50.Ax Steady shear flows, viscometric flow
83.80.Sg Polymer melts
83.80.Rs Polymer solutions
83.10.Bb Kinematics of deformation and flow

Two-dimensional Fourier transform rheology

Dagmar van Dusschoten, Manfred Wilhelm, and Hans W. Spiess

J. Rheol. 45, 1319 (2001); http://dx.doi.org/10.1122/1.1402660 (21 pages) | Cited 3 times

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A two-dimensional Fourier transformation (FT) rheology experiment is presented that separates the relaxation dynamics of different contributions to the stress relaxation, here specifically for entangled polymers. This experiment has the overall form of discrete large amplitude oscillations and consists of multiple step shear experiments. It is called large amplitude step shear oscillations, LASSO. The time-dependent nonlinear material response follows the discrete periodic excitation and can therefore be Fourier transformed, which results in a spectrum of harmonics for each delay time between the steps. The FT is used here to correlate the different step shear experiments. The method was applied to a slightly entangled, polydisperse polyisobutylene solution where a small deviation of the time strain separation is detected, even at times exceeding the Rouse time by orders of magnitude. On the other hand, the time temperature superposition seems to work for all the harmonic decays within the spectrum. When the time window between the shear steps is reduced such that slow relaxation processes still possess memory of prior steps, an increase of the nonlinear contributions of the fast, completely relaxed, relaxation modes is observed. This is in qualitative agreement with reptation models where polymer stretching and orienting are considered coupled processes. © 2001 The Society of Rheology.
Show PACS
83.60.Df Nonlinear viscoelasticity
83.80.Rs Polymer solutions
83.85.St Stress relaxation

The effect of droplet extension on the rheology of emulsions of water in alkyd resin

M. J. Thompson, J. R. A. Pearson, and M. R. Mackley

J. Rheol. 45, 1341 (2001); http://dx.doi.org/10.1122/1.1410371 (18 pages)

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We present experimental findings and matching modeling concerning the effect of water droplets on the rheology of a high viscosity alkyd resin. In the flow regime where significant droplet deformation occurs, the shear viscosity of the fluid containing highly extended filaments was found to be lower than that of the alkyd resin on its own. A theoretical mechanism for this high shear rate viscosity reduction is proposed, and reasonable agreement is established with experimental observation. At intermediate shear rates a crossover between viscosity enhancement and viscosity reduction correlates with a capillary number close to 1. At low shear rates classic viscosity enhancement was observed. © 2001 The Society of Rheology.
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83.80.Iz Emulsions and foams
83.80.Rs Polymer solutions
47.55.D- Drops and bubbles
47.50.-d Non-Newtonian fluid flows
82.70.Kj Emulsions and suspensions
83.50.Jf Extensional flow and combined shear and extension
83.60.Fg Shear rate dependent viscosity
66.20.-d Viscosity of liquids; diffusive momentum transport

Viscosity of surfactant stabilized emulsions

K. M. B. Jansen, W. G. M. Agterof, and J. Mellema

J. Rheol. 45, 1359 (2001); http://dx.doi.org/10.1122/1.1410372 (13 pages)

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A new scaling parameter for the viscosity of surfactant stabilized emulsions is proposed. We suggest that the attractive force between emulsion droplets is caused by the small surfactant micelles in the continuous phase of an emulsion. The new scaling parameter will be referred to as the depletion flow number, Fld=4πηsmatha2am/kTϕm, and is defined as the ratio between the viscous energy needed to separate the droplets and the depletion energy that opposes this separation. Here ηs, a, am, and ϕm are the solvent viscosity, dispersed phase droplet radius, micelle radius, and micelle volume fraction, respectively. Fld is of the order of unity at the onset of shear thinning and is capable of explaining all previously observed effects of drop size, solvent viscosity, and surfactant concentration. With master curves which are obtained by using Fld as the running parameter, a relatively simple empirical model is constructed which can reproduce the viscosity curves of many previously reported in the literature. © 2001 The Society of Rheology.
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83.80.Iz Emulsions and foams
82.70.Uv Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)
82.70.Kj Emulsions and suspensions
66.20.-d Viscosity of liquids; diffusive momentum transport
83.60.Fg Shear rate dependent viscosity

Assessment of the Doi–Ohta theory for co-continuous blends under oscillatory flow

I. Vinckier and H. M. Laun

J. Rheol. 45, 1373 (2001); http://dx.doi.org/10.1122/1.1410373 (13 pages) | Cited 3 times

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Predictions of the semiphenomenological Doi–Ohta theory for the rheology and morphology of immiscible blends are compared to experimental data of a 40/60 blend of PMMA/PαMSAN with a co-continuous structure. Since the Doi–Ohta theory actually was developed for co-continuous blends, published comparisons on droplet–matrix blends are not considered as adequate. It is verified how the polymeric constituents contribute to the blend response and it is shown how the phenomenological parameters of the Doi–Ohta theory can be determined. Subsequently, these parameters are used to predict the morphology evolution and rheological response of the blend under oscillatory flow. The evolution of the storage modulus clearly reflects the changes in morphology of the blend over time and strain amplitude in agreement with the theoretical predictions. Below a critical strain amplitude the co-continuous structure will coarsen until a droplet–matrix morphology is generated but large strain amplitudes are effective enough to stop domain growth. © 2001 The Society of Rheology.
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83.80.Tc Polymer blends
82.35.Jk Copolymers, phase transitions, structure
61.41.+e Polymers, elastomers, and plastics
47.35.-i Hydrodynamic waves

The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release

M. H. Wagner, P. Rubio, and H. Bastian

J. Rheol. 45, 1387 (2001); http://dx.doi.org/10.1122/1.1413503 (26 pages) | Cited 17 times

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The molecular stress function theory for polymer melts is extended to include a new, dissipative convective constraint release process. First the Helmholtz free energy of tube segments with strain-dependent tube diameter is established neglecting constraint release, and it is demonstrated that the molecular stress is a function of the average logarithmic stretch under these conditions. Then convective constraint release is introduced as a dissipative process in the energy balance of tube deformation, which leads to a strain-dependent evolution equation for the molecular stress function. Constraint release is considered to be the consequence of different convection mechanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasizes that tube kinematics are fundamentally different for rotational and nonrotational flows, and therefore distinguishes explicitly between simple shear and pure shear (planar extension). For the startup of simple shear and extensional flows, the predictions of our set of constitutive equations consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress function with only two nonlinear material parameters are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, stress relaxation after step-shear strain is described for both the HDPE and the LDPE melt. © 2001 The Society of Rheology.
Show PACS
83.80.Sg Polymer melts
47.50.-d Non-Newtonian fluid flows
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
47.55.Kf Particle-laden flows
83.85.St Stress relaxation
47.27.T- Turbulent transport processes
47.60.-i Flow phenomena in quasi-one-dimensional systems
83.50.Ha Flow in channels
47.32.-y Vortex dynamics; rotating fluids

Design of an orifice die to measure entrance pressure drop

Seungoh Kim and John M. Dealy

J. Rheol. 45, 1413 (2001); http://dx.doi.org/10.1122/1.1410374 (7 pages) | Cited 1 time

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The entrance pressure drop (ΔPent) associated with the flow from a cylindrical reservoir into a capillary is of great importance in melt rheology. First, it is required in order to determine the true wall shear stress in a capillary rheometer when only the overall pressure drop is measured. In addition, it is used to calculate an average extensional viscosity at strain rates that are not accessible using a true extensional rheometer. We recommend the use of a specially designed orifice die, in place of a Bagley plot, for the determination of this entrance pressure drop. This orifice has the following characteristics: its length to diameter (L/D) ratio is no more than 0.5, its entrance angle is greater than 90°, and the exit of the orifice is designed to prevent melt from touching the die wall. © 2001 The Society of Rheology.
Show PACS
66.20.-d Viscosity of liquids; diffusive momentum transport
83.60.Fg Shear rate dependent viscosity
47.80.-v Instrumentation and measurement methods in fluid dynamics
83.85.Rx Extensional flow measurement

Role of lubricated contacts in concentrated polydisperse suspensions

Christophe Ancey

J. Rheol. 45, 1421 (2001); http://dx.doi.org/10.1122/1.1413504 (19 pages) | Cited 8 times

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In this article experimental results of the bulk behavior of concentrated suspensions of coarse and fine (colloidal) particles in a Newtonian fluid (water) are presented. Different rheological behaviors can be observed depending on both the solid concentrations in fine and coarse particles and the shear velocity. For suspensions concentrated in coarse particles that are poor in fine particles, the bulk behavior is frictional for low shear velocities and viscous for sufficiently large shear velocities. In the converse case, for mixtures rich in fine particles, the bulk behavior is viscoplastic. A more complex time-dependent behavior can be observed when the viscoplastic force exerted by the dispersion on coarse particles roughly balances the force of gravity. The diversity in bulk behavior is explained by the specific role played by the contact between coarse particles. © 2001 The Society of Rheology.
Show PACS
82.70.Kj Emulsions and suspensions
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.50.Ax Steady shear flows, viscometric flow
83.60.La Viscoplasticity; yield stress
47.55.Kf Particle-laden flows
46.55.+d Tribology and mechanical contacts

Time-strain nonseparability in viscoelastic constitutive equations

Youngdon Kwon and Kwang Soo Cho

J. Rheol. 45, 1441 (2001); http://dx.doi.org/10.1122/1.1413505 (12 pages) | Cited 3 times

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The time-strain separability in viscoelastic systems is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation for long times. The violation of separability in the short-time response just after step strain is also well understood [L. A. Archer, J. Rheol. 43, 1555 (1999)]. In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency from the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard type unstable or dissipative unstable. It is shown that the Hadamard-type instabilities of the Wagner, Luo–Tanner, Papanastasiou, and Kaye–Bernstein–Kearsley–Zapas models with Larson–Monroe or Mooney potential, as well as the dissipative instability of the Lodge model (all proven previously) [Y. Kwon and A. I. Leonov, Rheol. Acta 33, 398 (1995)] are all caused by the separability hypothesis inherent in their equations. The conclusion drawn in this study is shown to be applicable to the Doi–Edwards model (with independent alignment approximation). Hence, the Hadamard-type instability of the Doi–Edwards model results from the time-strain separability in its formulation and its remedy may lie in the transition mechanism from Rouse to reptational relaxation suggested by Doi and Edwards. © 2001 The Society of Rheology.
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83.85.St Stress relaxation
83.60.Wc Flow instabilities
83.60.Df Nonlinear viscoelasticity
02.60.Nm Integral and integrodifferential equations
46.35.+z Viscoelasticity, plasticity, viscoplasticity
02.30.Hq Ordinary differential equations

Determination of viscosity from drop deformation

Y. T. Hu and A. Lips

J. Rheol. 45, 1453 (2001); http://dx.doi.org/10.1122/1.1413506 (11 pages) | Cited 4 times

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A novel technique for measuring viscosities of droplets is described. This technique uses the transient and steady state deformation of a droplet suspended in an immiscible fluid. Drop viscosities are derived from small deformation theory as ηd=(−5math/2Dsα−1.5)ηs for hyperbolic flow, and ηd=(−5math/4Dsα−1.5)ηs for shear flow. Here math is the flow rate, Ds is the steady state deformation, α is the exponent obtained from deformation growth or relaxation, and ηs is the suspending fluid viscosity. Drop viscosities measured using this technique, implemented on a four-roll mill apparatus, are compared with bulk viscosities measured using a conventional rheometer. The measurement scope of the new technique, with respect to capillary number, drop size, and viscosity ratio, is defined. © 2001 The Society of Rheology.
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47.55.D- Drops and bubbles
47.80.-v Instrumentation and measurement methods in fluid dynamics
68.03.Cd Surface tension and related phenomena
83.85.Jn Viscosity measurements
83.50.Ax Steady shear flows, viscometric flow

Unstable flow and nonmonotonic flow curves of transient networks

Eric Michel, Jacqueline Appell, François Molino, Jean Kieffer, and Grégoire Porte

J. Rheol. 45, 1465 (2001); http://dx.doi.org/10.1122/1.1413507 (13 pages) | Cited 8 times

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We have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated. The phase behavior which comprises a liquid–gas phase separation and a percolation threshold is characterized. The rheological measurements are performed in the one phase region above the percolation line. Shear thinning is observed for all samples, leading in most cases to an unstable stress response at intermediate shear rates. We built up a very simple mean field model which involves the reduction of the residence time of the stickers in the droplets due to chain tensions at high shear. The computed flow curves are nonmonotonic with a range where the stress is a decreasing function of the rate, a feature that indeed makes homogeneous flows unstable. The computed the flow curves compare well to the experiments. © 2001 The Society of Rheology.
Show PACS
82.70.Kj Emulsions and suspensions
83.80.Iz Emulsions and foams
83.50.Ax Steady shear flows, viscometric flow
47.55.D- Drops and bubbles
68.05.Gh Interfacial properties of microemulsions
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
64.60.A- Specific approaches applied to studies of phase transitions

Electrorheological properties of a mixture of two immiscible fluids having the same viscosity

Hiroshi Orihara, Akio Taki, Masao Doi, and Akio Inoue

J. Rheol. 45, 1479 (2001); http://dx.doi.org/10.1122/1.1413508 (9 pages) | Cited 1 time

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We investigated the electrorheological (ER) properties of a mixture of two immiscible fluids having the same viscosity, but different permittivity and conductivity. In this mixture droplets were dispersed; when subjected to an electric field they became elongated. We observed an ER effect, i.e., an increase in the apparent viscosity following application of an electric field. It was seen from microscopic observation that the ER effect in the mixture is brought about by a morphological change, with the interfacial tension between the two fluids playing a crucial role. © 2001 The Society of Rheology.
Show PACS
66.20.-d Viscosity of liquids; diffusive momentum transport
47.55.D- Drops and bubbles
83.60.Np Effects of electric and magnetic fields
83.80.Gv Electro- and magnetorheological fluids
77.22.Ch Permittivity (dielectric function)
83.60.Fg Shear rate dependent viscosity
68.03.Cd Surface tension and related phenomena
64.75.-g Phase equilibria

Erratum: “Differential constitutive equations for polymer melts: The extended Pom–Pom model” [J. Rheol. 45, 823–843 (2001)]

Wilco M. H. Verbeeten, Gerrit W. M. Peters, and Frank P. T. Baaijens

J. Rheol. 45, 1489 (2001); http://dx.doi.org/10.1122/1.1406999 (1 page)

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Abstract Unavailable
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99.10.Cd Errata
83.80.Sg Polymer melts
83.10.Gr Constitutive relations
83.60.Df Nonlinear viscoelasticity
83.50.Jf Extensional flow and combined shear and extension
61.25.H- Macromolecular and polymers solutions; polymer melts

Erratum: “Electrorheology of filled silicone elastomers” [J. Rheol. 45, 641–657 (2001)]

Bo Liu and Montgomery T. Shaw

J. Rheol. 45, 1491 (2001); http://dx.doi.org/10.1122/1.1410375 (1 page)

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Abstract Unavailable
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99.10.Cd Errata
83.80.Gv Electro- and magnetorheological fluids
83.60.Np Effects of electric and magnetic fields
83.80.Wx Filled elastomers
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