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Showing papers in "Rheologica Acta in 1992"


Journal ArticleDOI
Ronald G. Larson1
TL;DR: In this article, the authors present a review of the latest developments as well as earlier work in this area, organized into the following categories: Taylor-Couette flows, instabilities in cone and plate-and-plate flows, parallel shear flows, extrudate distortions and fracture, Instabilities in shear flow with interfaces, extensional flows, and thermohydrodynamic instabilities.
Abstract: Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

883 citations


Journal ArticleDOI
Ronald G. Larson1
TL;DR: In polymer solutions or blends, flow can strongly influence the degree of mixing of the components as mentioned in this paper, and it can induce ordering transitions in liquid crystals or block copolymers, which can also occur when the two components of the mixture differ greatly in viscoelastic properties.
Abstract: In polymer solutions or blends, flow can strongly influence the degree of mixing of the components. In a shearing flow, droplets in a dispersion can be broken down to sizes comparable to the dimensions of the polymer molecules themselves, thereby inducing molecular-scale mixing. Demixing can also occur when the two components of the mixture differ greatly in viscoelastic properties. Shear or extensional flow can induce polymer migration in nonhomogeneous flows or in flows with curved streamlines, and can render turbid solutions or blends that are otherwise transparent. Flow can also induce polymer gelation, and can induce ordering transitions in liquid crystals or block copolymers. Here, we review these phenomena, discuss proposed mechanisms, and assess the degree to which recent theories can account for the observations. Because the phenomena are complex, multiple experimental probes and theoretical methods are required to study them. Successful theories must incorporate polymer/polymer or polymer/solvent thermodynamics, critical phenomena, and phase transitions, as well as polymer theology and the kinetics of diffusion or crystallization. The experimental techniques used to study these phenomena are equally wide ranging, and include turbidity measurements, light, x-ray, and neutron scattering, fluorescence quenching, microscopy, and theology.

190 citations


Journal ArticleDOI
TL;DR: In this paper, the authors measured and analyzed the dynamic mechanical response of polybutadienes with molecular weights from 20000 to 200000, and the results indicated that the two types of polymers have a similar relaxation pattern.
Abstract: 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(λ)) 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(λ) = H e λne + H g λ− n g for λ < λmax and H(λ) = 0 for λmax < λ, where H e , H g , n e , n g are material constants and λmax 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.

132 citations


Journal ArticleDOI
TL;DR: In this article, a generalized Cole-Cole ansatz is proposed to overcome the related difficulties of complex modulus prediction, and the corresponding constitutive equation with fractional derivatives belonging to the generalizedCole-Cole respondance is stated and the characteristic material functions of the linear viscoelasticity theory are derived.
Abstract: Starting from an analysis of the rheological behavior of the complex modulus predicted by the Cole-Cole formalism, a generalized Cole-Cole ansatz is suggested in order to overcome the related difficulties. The corresponding rheological constitutive equation with fractional derivatives belonging to the generalized Cole-Cole respondance is stated and the characteristic material functions of the linear viscoelasticity theory (like the dynamic modulus and compliance, the relaxation and ratardation functions, the spectra, etc.) are derived. Model predictions of these functions will be compared with experimental results from dynamical measurements and creep data on different polymer systems which show cooperative phenomena (polymeric glasses and gelling systems). One can see that the modified ansatz fits the data very well, in spite of its relative simplicity.

126 citations


Journal ArticleDOI
TL;DR: In this paper, the application of Tikhonov regularization to the determination of relaxation and retardation spectra of viscoelastic fluids is discussed using simulated and real experimental data.
Abstract: The application of Tikhonov regularization to the determination of relaxation and retardation spectra of viscoelastic fluids is discussed using simulated and real experimental data. It is thereby shown that with this method consistent results for relaxation and retardation spectra can be obtained from experimental data for different material functions. Furthermore, the differences between the most frequently used variants of Tikhonov regularization and the maximum entropy method are discussed. For most calculations the program FTIKREG has been used, which is an especially fast and reliable implementation of Tikhonov's regularization method.

87 citations


Journal ArticleDOI
TL;DR: In this paper, the rheological behavior of a styrene butadiene rubber (SBR) compound was studied with three different rheometers, i.e., biconical rotational, capillary and slit die, to define the true viscous behavior of the compound.
Abstract: Rubber compounds are known to exhibit slip at the wall in particular flow conditions. The slip velocity is usually determined by using the classical Mooney method. The rheological behavior of a styrene butadiene rubber (SBR) compound was studied with three different rheometers. Biconical rotational, capillary and slit die rheometers were used to define the true viscous behavior of the compound and the slip velocity. It was shown that it was impossible to apply the Mooney method to our experimental data. New characterizations were thus developed for both capillary and slit die experiments. They were based on the dependency of the slip velocity on the local flow gap. Contrarily to the Mooney method, they provided physically acceptable results and led to a power-law relationship between wall slip, wall shear stress and local geometry of the flow.

72 citations


Journal ArticleDOI
TL;DR: In this paper, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined visco-elastic difference is made based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.
Abstract: Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries

62 citations


Journal ArticleDOI
TL;DR: In this paper, a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations, and new results with suspensions of magnetic and non-magnetic α-Fe2O3 particles in mineral oil are interpreted with the model.
Abstract: Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic γ-Fe2O3 and non-magnetic α-Fe2O3 particles in mineral oil are interpreted with the model proposed.

60 citations


Journal ArticleDOI
TL;DR: In this paper, a sample placed between quartz windows of a modified parallel plate fixture of a Rheometrics Mechanical Spectrometer is radiated from a collimated UV source using a liquid light guide and a mirror.
Abstract: Ultraviolet-radiation-cured cross-linked systems are used extensively in optoelectronic applications. We describe a new in situ technique for doing controlled curing of photosensitive materials and monitoring the gelation through dynamic theological measurements. In this method, a sample placed between quartz windows of a modified parallel plate fixture of a Rheometrics Mechanical Spectrometer is radiated from a collimated UV source using a liquid light guide and a mirror. By varying the sample exposure to UV radiation, the degree of cross-linking can be precisely controlled to observe the material behavior in the pre, post, and critical gel state. Time-dependent measurements on urethane based materials show the gelation behavior to have an “induction” period with no change in dynamic moduli (G′, G″), followed by their sharp increase as the materials develop a network structure. The critical gel point is characterized by a power-law dependence of the dynamic moduli on frequency. The gelation kinetics scales with sample thickness and radiation intensity, the scaling factor in both cases being the critical gelation time. The rheological measurements correlate with differential photocalorimetric studies.

51 citations


Journal ArticleDOI
TL;DR: In this article, the Tanner-Keentok model was used to predict the onset of edge fracture in a cone-and-plate rheometer with six elastic polymer solutions.
Abstract: The “edge fracture” instability which occurs at the air/liquid interface in a cone-and-plate rheometer is studied for six elastic polymer solutions. Theoretical models for the onset of edge fracture are evaluated in light of the experimental data. The data are well-described by the Tanner-Keentok model, which predicts that fracture will occur whenever a critical value of the second normal stress difference is exceeded in magnitude.

43 citations


Journal ArticleDOI
TL;DR: In this article, a general one-particle constitutive equation for the stress tensor is modified to include diffusion and migration effects, and a balance equation is formulated for the polymer mass density in order to describe the nonhomogeneous composition of the polymer solution resulting from migration.
Abstract: Given a general one-particle constitutive equation for the stress tensor, we discuss how to incorporate the additional effects of polymer diffusivity and migration into that constitutive equation within the framework of continuum mechanics. For the example of an upper-convected Maxwell model representing the polymer contribution to the stress tensor of a dilute polymer solution, we describe i) how to modify the constitutive equation for the stress tensor to include diffusion and migration effects, ii) how to formulate a balance equation for the polymer mass density in order to describe the nonhomogeneous composition of the polymer solution resulting from migration, and iii) how to close the extended set of coupled equations by means of further constitutive equations for the migration velocity and the diffusion tensor. In order to guarantee the material objectivity for all equations, we formulate them in the body tensor formulation of continuum mechanics (and then translate them into Cartesian space). The proposed equations are compared to results of a recent kinetic-theory approach.

Journal ArticleDOI
TL;DR: In this paper, three biopolymer systems which are commonly believed to yield physical gels are compared and contrasted in light of Winter's criterion for chemical gelation (tan (loss angle) becomes frequency independent).
Abstract: Three biopolymer systems which are commonly believed to yield physical gels are compared and contrasted in light of Winter's criterion for chemical gelation (tan (loss angle) becomes frequency independent). Biopolymer concentration is taken as the natural variable in the gelation process. The Xanthan gum system is found to yield a sol state up to a concentration of 3% with the gel-like symptoms arising as a result of separation of an anisotropic phase. Gelatin at 20 °C shows a gel point at 0.75% by the above criterion and otherwise behaves analogously to a chemically crosslinked network. Guar gum gelled with borate fails the gel criterion on our instrumental time scale because of the finite lifetime of the guar/borate linkage, here estimated to be in the range 10–100 s. On shorter time scales, however, this system appears to behave as a rubbery network.

Journal ArticleDOI
TL;DR: In this article, the rheological properties of a series of lightly crosslinked carboxy copolymers in aqueous solutions have been evaluated in steady shear and dynamic oscillatory modes.
Abstract: The rheological properties of a series of lightly crosslinked carboxy copolymers in aqueous solutions have been evaluated in steady shear and dynamic oscillatory modes. Viscosity profiles and the behavior of storage modulus are related to the chemical composition of the copolymers and their crosslinking density. A maximum in viscosity and in storage modulus which depends on the type of crosslinking agent used is explained by a combination of a chain entanglement mechanism and a closely-packed spheres model. The recovery of viscosity and storage modulus after shearing is very fast and is related to the very fast rearrangement of the microgel structure as a function of time.

Journal ArticleDOI
TL;DR: In this paper, the Galerkin method of weighted residuals is employed to solve the differential equation for the particle orientation distribution function, and the steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations.
Abstract: Suspensions of small nonspherical particles having dipolar moments exhibit non-Newtonian behavior under the influence of shear and external fields. Numerical methods are presented for calculating the rheological and rheo-optical properties of dilute suspensions of Brownian particles having permanent dipoles subject to time-dependent shear and external fields. The numerical methods employ the Galerkin method of weighted residuals to solve the differential equation for the particle orientation distribution function. The steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations. These numerical results provide valuable insight into the coupling which occurs between the effects of rotary Brownian motion, the hydrodynamic resistance of nonspherical particles, and the external torque exerted on dipolar particles. The results are applicable to both suspensions of magnetic particles and electrically dipolar particles.

Journal ArticleDOI
TL;DR: In this article, the authors show that filtering, present in most rheometers, will eliminate the stress jump and not allow its measurement, while the torque head inertia for a spring-type torque measuring system is found to greatly influence the measurements and a stress jump is not seen.
Abstract: Stress jumps occur in fluids that possess a viscous contribution to their total stress. On cessation of shear, such a fluid will show an instantaneous loss of stress, while some of the stress will remain and subsequently decay in some manner, either exponential or otherwise. The results in this paper show that filtering, present in most rheometers, will eliminate the stress jump and not allow its measurement. The torque head inertia for a spring-type torque measuring system is found to greatly influence the measurements and a stress jump is not seen. In fact, the material's true stress relaxation behaviour is far from that measured. The force rebalance torque measuring system is found to accurately measure stress jumps.

Journal ArticleDOI
L. Berger1, J. Meissner1
TL;DR: In this article, simple and planar elongations have been performed with anionically polymerized polybutadienes (PB) and their blends at room temperature, and the crossover G′(ω) = G″(ω), obtained from oscillatory measurements shows correlations with molecular parameters.
Abstract: Shear oscillations, simple and planar elongations have been performed with anionically polymerized polybutadienes (PB) and their blends at room temperature. The PB components were of different molar mass averages and of narrow molar mass distributions; the blends had bimodal molar mass distributions and are represented by the weight ratio w of the high molecular component. The crossover G′(ω) = G″(ω) obtained from oscillatory measurements shows correlations with molecular parameters. For the zero shear viscosity the well-known relation η0 ∞ Mw3.4is found. The recoverable equilibrium shear compliance Je0 is nearly the same for the components; for the blends it strongly depends on w with a pronounced maximum at small w. In elongation outside the linear region strain hardening is found; its magnitude depends on Mw of the components, the composition w of the blend, the mode of elongation (simple or planar), and the elongational strain rate. The hardening revealed in the increase of the elongational viscosity above the linear viscoelastic limit increases as a function of w up to a maximum similar to Je0 such that, for both properties, the molecular processes may be the same. The elongational viscosity µ2 (from the lateral stress in planar elongation) is above the linear viscoelastic limit for bimodal and below this limit for conventional broad molar mass distributions. In general, it can be stated that with a more narrow molar mass distribution of linear polymers the elongational behavior of the melts comes closer to the linear viscoelastic limit.

Journal ArticleDOI
TL;DR: In this article, a numerical solution for the three-dimensional flow of an upper-convected Maxwell model in a journal bearing, operating under static loading conditions, is provided.
Abstract: A numerical solution is provided for the three-dimensional flow of an upper-convected Maxwell model in a journal bearing, operating under static loading conditions. Realistic values are taken for the material parameters and the geometrical and flow variables. It is concluded that a relaxation time of the order of 10−4 s is required before viscoelasticity results in a practically-important increase in load-bearing capacity. This conclusion is unchanged if fluid inertia is included in the analysis; it is also effectively independent of the L/D ratio of the bearing.

Journal ArticleDOI
TL;DR: In this article, the cone-and-plate distance method is modified by assuming that the ratio ψ* of the second normal stress difference to the first is independent of shear rate.
Abstract: In the present work the measurement and description of the second normal stress difference in pure viscoelastic fluids and in suspensions of these fluids is discussed The various measurement methods implemented to date are described briefly Following this, the cone-and-plate distance method, which was introduced by Jackson and Kaye, is discussed The analysis method of this experimentally relative simply implemented technique is modified This is done by assuming that the ratio ψ* of the second normal stress difference to the first is independent of shear rate This permits the precalculation of the measured function with ψ* as a curve parameter The best possible fit of the measurement leads to the determination of ψ* This method is used to measure the normal stress ratio of pure polyisobutene and of a 345% suspension of the same fluid The result for the pure fluid matches literature values; ψ* of the suspension was found to have negative sign, as for the pure fluid, but to be of much greater magnitude

Journal ArticleDOI
TL;DR: In this paper, the constitutive equations of temporary slip-link networks are derived, and the stress tensor is determined by three material functions, namely, the time-dependent linear-viscoelastic memory function, and two strain-dependent functions describing slip and disentanglement of network strands.
Abstract: Allowing for flow-dependent slip in the junctions of a temporary junction network, we derive the constitutive equations of temporary slip-link networks. The stress tensor is determined by three material functions, namely, the time-dependent linear-viscoelastic memory function, and two strain-dependent functions describing slip and disentanglement of network strands. Slip and disentanglement are related via a mass balance for network strands.

Journal ArticleDOI
TL;DR: In this paper, a boundary element method is used to simulate the unsteady motion of a sphere falling under gravity along the centreline of a cylindrical tube containing a viscoelastic fluid.
Abstract: A boundary element method is used to simulate the unsteady motion of a sphere falling under gravity along the centreline of a cylindrical tube containing a viscoelastic fluid. The fluid is modelled by the upper-convected Maxwell constitutive equation. Results show that the viscoelasticity of the liquid leads to a damped oscillation in sphere velocity about its terminal value. The maximum sphere velocity, which occurs in the first overshoot, is approximately proportional to the square root of the Weissenberg number when the ratio of the sphere radius to the tube radius is sufficiently small. Particular attention is also paid to the wall effects. It is shown that a closer wall reduces the oscillatory amplitude of the sphere velocity but increases its frequency. The results suggest that the falling-ball technique, which is now widely used for viscosity measurement, might also be used for the determination of a relaxation time for a viscoelastic fluid.

Journal ArticleDOI
TL;DR: In this paper, a simple constitutive framework is used to review some phenomenological models for solid-fluid mixtures, including compressibility effects and a scalar measure of particle interactions.
Abstract: A simple constitutive framework is used to review some phenomenological models for solid-fluid mixtures. Several successful descriptions of viscoplasticity assume that stress is proportional to a normalized deformation rate. The modulus in this constitutive equation evolves with time for thixotropic materials. This approach is used in most models based on scalar measures of structure. Such measures are determined by an evolution equation that is insensitive to rate reversals during shear flow. This behavior appears to be characteristic of inelastic materials such as an aqueous solution of bentonite. However, the same solution with guargum does not exhibit this response due to elasticity induced by the polymer. Models for granular media extend this constitutive framework by including compressibility effects and a scalar measure of particle interactions. The effect of fluid viscosity on particle interactions is incorporated using a mixture theory approach. Pipe flow of viscoplastic materials and shear flow of granular media are analyzed using boundary conditions that allow slip at solid surfaces.

Journal ArticleDOI
TL;DR: Imbedded fiber retraction (IFR) has been applied to study the compatibility of high polymers in their molten states as mentioned in this paper, where the interfacial tension between two immiscible high-viscosity thermoplastic resins was measured.
Abstract: Imbedded-fiber retraction (IFR) has been applied to study the compatibility of high polymers. IFR measures the interfacial tension between two immiscible high-viscosity thermoplastic resins in their molten states. Ten nonreactive blend pairs were studied. One blend component was a poly(styrene-co-acrylonitrile-co-fumaronitrile) terpolymer resin (S/AN/FN). The other component was one of a set of ten S/AN resins with an AN level between 0 and 51%. These high-molecular-weight resins were particularly challenging for IFR since they were nearly isorefractive, had high melt viscosities (103–105 Pa s), and could chemically age when molten. Interfacial tensions γ12 ranged from 0.00 to 5.5 dyn/cm at 200 °C. Miscible bends had γ12 = 0 and a single Tg.Immiscible blends had γ12 > 0 and two Tgs. Compatibility was quantitatively assessed from the monotonic rise in γ12 as compatibility decreases. The results demonstrate that IFR can rank the compatibility of high polymers. It is expected that IFR can also rank the compatibility of polymers with similar Tgs,and rank the ability of additives to enhance blend compatibility.

Journal ArticleDOI
TL;DR: In this paper, a series of SAN (styrene-co-acrylonitrile) random copolymers were studied by means of oscillatory rheometry in the rubbery plateau zone and in the terminal zone.
Abstract: A series of polydisperse SAN (styrene-co-acrylonitrile) random copolymers was studied by means of oscillatory rheometry in the rubbery plateau zone and in the terminal zone. The plateau modulus, the Newtonian viscosity, and the critical frequencies for the onset of non-Newtonian behavior were extracted from the experimental data. All these viscoelastic quantities consistently indicate that the tail of molecular weights below approximately Me (the entanglement spacing) acts as a solvent for the rest of the polymer with M>Me.

Journal ArticleDOI
TL;DR: In this paper, stress-optical measurements are used to quantitatively determine the third normal stress difference (N3 = N1 + N2) in three entangled polymer melts during small amplitude (<15%) oscillatory shear over a wide dynamic range.
Abstract: Stress-optical measurements are used to quantitatively determine the third-normal stress difference (N3 = N1 + N2) in three entangled polymer melts during small amplitude (<15%) oscillatory shear over a wide dynamic range. The results are presented in terms of the three material functions that describe N3 in oscillatory shear: the real and imaginary parts of its complex amplitude ψ 3 * = ψ 3 ′ - iψ 3 ″ , and its displacement ψ 3 d . The results confirm that these functions are related to the dynamic modulus by ω2ψ 3 * (ω)=(1-β)[G*(ω))−\(\frac{1}{2}\)G*(2ω)] and ω2ψ 3 d (ω)=(1- β)G′(ω) as predicted by many constitutive equations, where β = −N2/N1. The value of (1-β) is found to be 0.69±0.07 for poly(ethylene-propylene) and 0.76±0.07 for polyisoprene. This corresponds to −N2/N1 = 0.31 and 0.24±0.07, close to the prediction of the reptation model when the independent alignment approximation is used, i.e., −N2/N1 = 2/7 − 0.28.

Journal ArticleDOI
TL;DR: In this paper, the Boundary Element Method (BEM) was used to simulate spherical particle sedimenting in circular, triangular and square conduits containing a viscous, inertialess, Newtonian fluid.
Abstract: Numerical simulations of a spherical particle sedimenting in circular, triangular and square conduits containing a viscous, inertialess, Newtonian fluid were investigated using the Boundary Element Method (BEM). Settling velocities and pressure drops for spheres falling along the centre-lines of the conduits were computed for a definitive range of sphere sizes. The numerical simulations for the settling velocities showed good agreement with existing experimental data. The most accurate analytic solution for a sphere settling along the axis of a circular conduit produced results which were almost indistinguishable from the present BEM calculations. For a sphere falling along the centre-line of a square conduit, the BEM calculations for small spheres agreed well with analytic results. No analytic results for a sphere falling along the axis of a triangular conduit were available for comparison. Extrapolation of the BEM predictions for the pressure drops, to infinitely small spheres, showed remarkable agreement with analytic results. For the circular conduit, the sphere's settling velocity and angular velocity were computed as a function of drop position for small, medium and large spheres. Excellent agreement with a reflection solution was achieved for the small sphere. In addition, end effects were investigated for centre-line drops and compared where possible with available experimental data and analytic results.

Journal ArticleDOI
TL;DR: It was found that slip is a function of L/D as well as shear stress, i.e., slip develops during flow, thus inducing spatial anisotropy in the fluid until a stable state is reached, and the stiffness of xanthan increases with the increase of the ionic strength.
Abstract: Flow experiments through capillaries with 0.2% xanthan in aqueous solution and 0.1 N NaCl brine were carried out to study the influence of the molecular conformation on the flow development at relatively low shear rates, from 20s−1 to 400s−1. Capillaries with a wide range of length-to-diameter ratios, L/D = 4.5 to 1015 were used. The apparent viscosity as a function of L/D at a constant shear rate shows a continuous decrement of the viscosity as L/D increases, until an asymptotic value is reached. The decrement in the apparent viscosity is partially explained in terms of slip. It was found that slip is a function of L/D as well as shear stress, i.e., slip develops during flow, thus inducing spatial anisotropy in the fluid until a stable state is reached. However, the substantial difference in apparent viscosity between short capillaries and capillaries longer than 300 D may be attributed to dominant elongational flow due to the contraction in the small capillaries and slip in long capillaries. The flow in a sufficiently long capillary can be divided in four regions rather than three, as is usually assumed. In the first region, which corresponds to the entry, elongational and shear flow coexist and elongational flow dominant. In the second region, end effects and slip development are coupled. In the third region the flow is fully developed and end effects are negligible. However, the fluid shows physical characteristics different from those of the fluid at rest, as a consequence of prior slip development. The fourth zone is the exit region in which the velocity rearranges due to the change of boundary conditions. The length of each region depends on the conformation of the macromolecules and shear rate. In addition, it was found that the stiffness of xanthan increases with the increase of the ionic strength. Finally, a performance of Bagley's analysis in the whole range of L/D studied showed that the use of the Bagley correction is not a reliable way to correct for end effects when the flow is not fully developed and/or in the presence of slip.

Journal ArticleDOI
TL;DR: In this article, the authors provide an assessment of the current understanding of the hole-pressure effect and the role it plays in the field of viscometry, which is interesting to see.
Abstract: This paper provides an assessment of our current understanding of the hole-pressure effect and the role it plays in the field of viscometry. The discovery in 1968 by Broadbent, Kaye, Lodge and Vale that the use of pressure taps to measure the normal stress exerted on a boundary by a non-Newtonian material can lead to significant errors has opened up interesting new avenues for making viscometric measurements. The kinematical theory developed by Higashitani and Pritchard (1972) to estimate the hole pressure, to which a deeper understanding has recently been supplied by Yao and Malkus (1990), has formed the basis of many new developments in viscometry. It is interesting that such a simplistic theory for the hole pressure apparently has a rather wide range of applicability.

Journal ArticleDOI
TL;DR: In this paper, an analytical solution for the stationary temperature profile in a polymeric melt flowing into a cold cavity, which also takes into account viscous heating effects, was obtained for the injection stage of the molding process.
Abstract: An analytical solution is obtained for the stationary temperature profile in a polymeric melt flowing into a cold cavity, which also takes into account viscous heating effects. The solution is valid for the injection stage of the molding process. Although the analytical solution is only possible after making several (at first sight) rather stringent assumptions, the calculated temperature field turns out to give a fair agreement with a numerical, more realistic approach. Approximate functions were derived for both the dissipation-independent and the dissipation-dependent parts which greatly facilitate the temperature calculations. In particular, a closed-form expression is derived for the position where the maximum temperature occurs and for the thickness of the solidified layer.

Journal ArticleDOI
TL;DR: In this paper, the stability of the Couette flow with the power law viscosity in a wide annular gap has been investigated theoretically in this work with the aid of the method of small disturbances.
Abstract: The stability of the Couette flow of the liquid with the power law viscosity in a wide annular gap has been investigated theoretically in this work with the aid of the method of small disturbances. The Taylor number, being a criterion of the stability, has been defined using the mean apparent viscosity value in the main flow. In the whole range of the radius ratio, R i /R o and the flow index, n, considered (R i /R o ≥ 0.5, n = 0.25–1.75 ), the critical value of the Taylor number Ta c is an increasing function of the flow index, i.e., shear thinning has destabilizing influence on the rotational flow, and dilatancy exhibits an opposite tendency. In the wide ranges of the flow index, n > 0.5, and the radius ratio, R i /R o > 0.5, the wide-gap effect on the stability limit is predicted to be almost the same for non-Newtonian fluids as for Newtonian ones. The ratio on the critical Taylor numbers for non-Newtonian and Newtonian fluids: Ta c (n) and Ta c (n = 1) obey a generalized functional dependence: Ta c (n)/Ta c (n = 1) = g(n), where g(n) is a function corresponding to the solution for the narrow gap approximation. Theoretical predictions have been compared with experimental results for pseudoplastic liquids. In the range of the radius ratio R i /R o > 0.6 the theoretical stability limit is in good agreement with the experiments, however, for R i /R o < 0.6, the critical Taylor number is considerably lower than predicted by theory.