Showing papers in "Rheologica Acta in 1985"

The yield stress myth

Abstract: New experimental data obtained from constant stress rheometers are used to show that the yield stress concept is an idealization, and that, given accurate measurements, no yield stress exists. The simple Cross model is shown to be a useful empiricism for many non-Newtonian fluids, including those which have hitherto been thought to possess a yield stress.

On the viscosity of a concentrated suspension of solid spheres

Abstract: Explanations of the very high viscosities of concentrated suspensions of spheres based on the dissipation in squeezing flow between particles pairs are shown to be in error. The dissipation in pair interactions is always of the order of that generated by shearing motions, and this dissipation is of too low an order in concentration for single pair interactions to explain the observed viscosities.

A new interpretation of viscosity and yield stress in dense slurries: Coal and other irregular particles

Abstract: Illinois coal was ground and wet-sieved to prepare three powder stocks whose particle-size distributions were characterized. Three suspending fluids were used (glycerin, bromonaphthalene, Aroclor), with viscositiesη s that differed by a factor of 100 and with very different chemistries, but whose densities matched that of the coal. Suspensions were prepared under vacuum, with coal volume fractionsφ that ranged up to 0.46. Viscosities were measured in a cone-and-plate over a shear rate $$(\dot \gamma )$$ range 10−3−102 s−1. Reduced viscosityη r = η/ηs is correlated in the high-shear limit (η ∞) withφ/φ M∞, whereφ M∞ is the maximum packing fraction for the high-shear microstructure, to reveal the roles of size distribution and suspending fluid character. A new model that invokes the stress-dependence ofφ M is found to correlateη r well under non-Newtonian conditions with simultaneous prediction of yield stress at sufficiently highφ; a critical result is that stress and not $$\dot \gamma $$ governs the microstructure and rheology. Numerous experimental anomalies provide insight into suspension behavior.

Thixotropic behaviour of concentrated bauxite residue suspensions

Abstract: An experimental study on the time-dependent rheology of highly concentrated and flocculated suspensions of bauxite residue (red mud) is presented. Both the thixotropic breakdown with shear and recovery at rest have been quantitatively examined using a vane-shear instrument and a capillary rheometer. It is demonstrated that both the yield stress and the apparent viscosity of the material can be drastically reduced, by orders of magnitude, by shear-induced agitation with a simple anchor impeller. The rate of thixotropic decay is a function of solids concentration, agitation time and speed. With prolonged agitation, the flow properties are brought to an equilibrium level characterized by a finite yield stress and a shear rate-dependent (shear-thinning) viscosity. In the absence of shear, the yield stress gradually increases with time but at a rate considerably slower than the rate of decay in the shear field. Even after an extended rest period of several months, only a fraction of the initial yield stress can be regained. The observed behaviour has been interpreted in terms of a time-dependent but non-reversible transformation of a network structure of flocculated particles initially developed in the red mud. Using a structural kinetic approach, models have been developed for correlating the experimental kinetic data. The paper concludes with a discussion on the practical consequences of the work.

Linear elastico-viscous properties of molten standard polystyrenes

Abstract: This paper contains an extensive presentation of dynamic mechanical data (complex moduli), as obtained on the melts of a series of standard polystyrenes of narrow molar mass distributions. It also shows the way of obtaining structural parameters (plateau modulus and friction factor) which are needed for an interpretation of these data in terms of simple theoretical models (Maxwell elements, Doi-Edwards model). A linear mixing rule is used for taking into account the finite width of the molar mass distributions.

Constitutive relationships for polymeric materials with power-law distributions of relaxation times

Abstract: The linear relaxation modulus of polydisperse polymer melts and solutions can often be approximated by a power law,ct −m over some range of time,t. If, in addition, the nonlinear rheology is given by a separable integral equation, with a strain-dependent factor typical of those observed experimentally, then some commonly observed empirical rules and equations can be readily derived as approximations, namely the Cox-Merz relationship between complex viscosity and steady-state shear viscosity, Bersted's predictions of steady shear stress and first normal-stress difference from a truncated spectrum of linear relaxation times, and the observation of Koyama and coworkers that the ratio of the nonlinear to the linear time-dependent elongational viscosity is independent of strain rate, over a range of strain rates outside the linear regime.

Viscoelastic effects in non-Newtonian flows through porous media

Abstract: An analysis is presented for the flow of polymer solutions through a tube having a periodically varying diameter; this geometry is often used to represent a porous medium. It is found that if the stretch rate is assumed constant, the stress depends not only upon the Deborah number, but also on the ratio of the maximum to the minimum diameter. If the latter dimensionless group is not too large, no shear thickening is predicted to arise irrespective of the value of the Deborah number. These results explain the observed lack of superposition of curves of the product of the friction factor with the Reynolds number plotted against the Deborah number when different porous media are used. In addition, they also, in a qualitative sense, explain the experimentally observed maxima in the plots of the relative pressure drop as a function of the deformation rate.

Caractérisation de la gélification d'une résine thermodurcissable par méthode rhéologique

Abstract: Une nouvelle facon de reperer la gelification d'une resine thermodurcissable est proposee, a partir de mesures rheologiques. Le point de gel est relie a une diminution de la vitesse de croissance du module visqueux observee sur les courbes experimentales en cours de cinetique a temperature constante. Les temps de gel obtenus sont du meme ordre que ceux donnes par les autres methodes rheologiques, mais font cependant apparaitre des differences sensibles. Le temps de gel obeit a une loi d'Arrhenius en fonction de la temperature de cuisson. Le module visqueux au point de gel et, par consequent la viscosite en ce point, varient avec la temperature. Il en est de meme pour le facteur de perte tan δ. Par contre, le module elastique au point de gel se conserve quelle que soit la temperature. Ces resultats ont ete obtenus sur deux formulations de resine: DGEBA (n = 0) − mPDA et DGEBA (n = 0) − DDM a la stoechiometrie.

Effect of sample dimensions, lubrication and deformation rate on uniaxial compression of gelatin gels

Abstract: The response of 10% gelatin gels to uniaxial compression is determined in part by frictional effects at the gel-platen interface. By using teflon-coated plates, lubricated with paraffin or silicone oil, these frictional effects are effectively eliminated. The stress-strain response can then be described by the two-constant Mooney-Rivlin relation, the sum of the two parameters (C1 +C2) being about 25% lower in lubricated compression than the value obtained in simple shear and torsion. Cross-head speed (for total testing times of 0.2–3 min) had no effect on material response, but long-term stress relaxation does occur over periods of about 30 min and longer. Sample radius did not affect the response in lubricated compression but had a major effect under unlubricated conditions. No systematic change in response was seen with sample diameter to height (aspect) ratios between 9.6 and 3.1 in lubricated compression, but data scatter for a given sample diameter was worst at the lowest heights (highest aspect ratio). Agreement of all true stress versus strain data was within about ± 7% regardless of sample height or deformation rate.

Drag reduction effectiveness and shear stability of polymer-polymer and polymer-fibre mixtures in recirculatory turbulent flow of water

Abstract: The turbulent drag reduction caused by polymer-polymer and polymerfibre mixtures has been measured in recirculatory flow of water. Shear stability studies have also been made on a number of drag reducing polymers, asbestos fibres and their mixtures in recirculatory turbulent flow of water. Reynolds numbers ranged from 20,000 to 57,000. Both positive and negative deviations from linear additive behaviour have been observed in drag reduction caused by the polymer-polymer mixtures depending upon their compositions, flow rate and polymer species in the mixture. The drag reduction by the mixtures has been predicted by using simple mixture rule equations including an interaction parameter. This interaction parameter is believed to depend upon the polymer interaction in the polymer mixture. The random coil size and rigidity of the polymer molecules appear to be responsible for the synergism observed in the drag reduction caused by the mixture. In general, mixtures having larger solvation number seem to give positive synergism.

Dynamic and transient rheological properties of glass filled polymer melts

Abstract: The dynamic and transient rheological properties of a low density polyethylene melt and a plasticized polyvinylchloride melt filled with glass beads were measured at 200 °C and 180 °C respectively in a modified Weissenberg Rheogoniometer R-17. Its main modification consisted of the use of a piezoelectric transducer instead of the conventional torsion bar, and of the interfacing of a microcomputer Apple II plus to the Rheogoniometer for data acquisition and analysis. The glass beads were pretreated with silane and titanate coupling agents to observe the effect of the chemical modification of the polymer filler interface on these properties. It was observed that both the dynamic viscosity and the storage modulus increased with the weight fraction, but this last parameter did appreciably affect the stress growth and stress relaxation curves of the polymeric matrices at low shear rates. The effect of coupling agents on these properties was varied.

The mirror relations and nonlinear viscoelasticity of polymer melts

Abstract: An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS12 (γ) =γ − a (γ − 1) (a = 0 forγ ≦ 1,a = 1 forγ ≧ 1) for the mirroring of the viscosities,S12 (γ) =γ − a (γ−k2/γ) (a = 0 forγ ≦k, a = 1 forγ ≧k) for the mirroring of the first normal-stress coefficients, and\(S_{12} (\gamma ) = \frac{1}{2}\gamma \{ 1 - erf [ln (\gamma /2 \sqrt k )/\sqrt {2 ln k} ]\}\) for the third relation. Hereγ denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.

Experimental and theoretical study of short fiber orientation in diverging flows

Abstract: Two types of experiments have been carried out to study the fiber orientation in flow through a divergent channel. First, a reinforced polyamid mold sprue containing two types of orientation was investigated: near the center, the fibers are mostly oriented perpendicular to the flow lines, whereas on the periphery, they are oriented parallel to them. Second, direct observation of copper fibers moving in a corn syrup was performed in a transparent diverging device: the fibers rapidly become oriented transverse to the flow lines. The solution of Stokes equations for the undisturbed fluid motion gives the shear rate and elongation rate, which are then substituted in Jeffery's orientation equations. The resolution shows two types of behavior: in a large area in the center, the fiber tends to a stable equilibrium position which depends strongly on the flow line on which it moves. On the periphery, the fiber follows a shear-like behavior. The strong influence of the elongational component relative to the shear component is demonstrated and the time necessary for orientation is calculated. The theoretical results are found to be in agreement with the observations.

Flows of constant stretch history for polymeric materials with power-law distributions of relaxation times

Abstract: It is herein shown that for separable integral constitutive equations with power-law distributions of relaxation times, the streamlines in creeping flow are independent of flow rate.

Generalized stress relaxation behaviour and physical aging in heterogeneous amorphous polyblends

Abstract: The influence of physical aging on viscoelastic behaviour of heterogeneous amorphous polyblends of ABS and polycarbonate was studied by means of stress relaxation experiments at different temperatures. The stress relaxation data of the constituent phases ABS and PC are found to be in agreement with the universal description of relaxation behaviour of amorphous polymers at the onset of the glass-rubber transition. The regimes where master curve construction by time-temperature and time-aging time superposition is permitted could be deduced for the thermorheologically complex polyblends. It is shown that the relaxation curves of the ABS/PC blends can be calculated by means of a quasi-elastic extension of the van der Poel-model using the stress relaxation data of the constituent phases and their volume fractions.

Multiaxial elongation of polyisobutylene with various and changing strain rate ratios

Abstract: The multiaxial elongational rheometer equipped with rotary clamps is modified such that in addition to simple, equibiaxial and multiaxial elongations also tests with new modes of elongation can be performed. As an example, polyisobutylene is elongated with a ratio of the principal strain rates of\(m = \dot \varepsilon _{22} /\dot \varepsilon _{11} = 0.5\) and magnitudes of the maximum strain rate\(\dot \varepsilon _{11} = 0.008\), 0.04 and 0.08 s−1. As a test result, the first elongational viscosityµ1(t) is obtained which follows closely the linear viscoelastic shear viscosity\(\mathop \eta \limits^ \circ (t)\). In contrast, the second elongational viscosityµ2(t) remains below\(\mathop \eta \limits^ \circ (t)\). By means of a further modification of the rheometer, the test modes can be varied during the deformation period. This allows one to investigate the influence of a well-defined rheological pre-history on the following rheological behaviour. As an example a variation ofm = 0.5 → 2 was performed. The measured normal-stress differences superpose from the single steps of deformation similar to the linear viscoelastic prediction.

Measuring device for precise evaluation of torsional creep and recovery data

Abstract: An apparatus has been designed and built up to determine the shear creep compliance and viscosity with high accuracy in a wide range of temperature and time. The characteristic feature of this apparatus is the possibility to measure directly the recoverable compliance and to determine the steady state recoverable complianceJ e . Disturbing instrumental forces are minimized by use of a magnetic bearing. The torque is applied inductively by a modified three phase asynchronous motor. The torsional angle is measured with a laser beam reflected from a mirror to an electro-optical measuring device. Sample thermostating is performed by radiation in a heating chamber, which allows observation of the specimen during measurement. First results of creep and creep recovery measurements are reported, which were carried out on a technical polystyrene above the glass rubbery transition.

Macromolecular deformation in periodic extensional flows

Abstract: The response of a dumbbell model for dilute polymer solutions is examined for periodic sequences of homogeneous flows chosen to approximate the unsteady kinematics appropriate for flow through porous media. The evolution of particle shape depends on the kinematic history of the flow and on microrheological properties of the dumbbell such as a variable friction factor and a nonlinear spring. The effect of vorticity on macromolecular stretching is found to differ qualitatively from results for steady flows, and “entrance” effects that persist over timescales much larger than the intrinsic macromolecular relaxation time are observed.

Measurement of the first and second normal stress differences: Correlation of four experiments on a polyisobutylene/decalin solution “D1”

Abstract: Pressure distribution measurements for a polyisobutylene/decalin solution “D1” in the Truncated Cone-and-Plate (TCP) apparatus are combined with elastic hole pressures obtained for the same solution on the Lodge Stressmeter® in order to provide two independent estimates of the second normal-stress difference (N 2). The values ofN 2 from the TCP apparatus, obtained by numerical differentiation of a function of the center-hole pressure and the pressure gradient, are in good agreement with measurements made on the same sample by Tanner et al. with a direct method, namely the Tilted Trough Experiment, and by Christiansen et al. with a method that requires an extrapolation to the pressure at the free surface of coneand-plate rheogoniometer data obtained with flush-mounted pressure transducers. The viscosities from the modified Stressmeter for low shear rates extend over five decades of shear rate, including a zero-shear-rate region, and agree with the data of Christiansen on a torque-driven flow. The Higashitani-Pritchard-Baird-Lodge (HPBL) equation relatingN 1–N 2 to the hole pressure gives good agreement with the data over a certain range of shear stress. The Newtonian hole pressures for several liquids at 20 and 46 °C compare well with a finite-element calculation for a two-dimensional Poiseuille flow. When the elastic hole pressures from the Stressmeter are combined with the extrapolated rim pressures from the TCP Apparatus in order to extract the value ofN 2, an agreement betweenN 2 from the center-hole pressure andN 2 from the rim pressure can only be obtained up to a shear rate of about 40 s−1, beyond which the value of −N 2 from the rim pressure diverges abruptly to negative values. It is possible that this constitutes the first quantitative estimate of an edge effect in cone-and-plate rheometry. Alternatively, the elastic hole pressure in cone-and-plate flow is not equivalent to the elastic hole pressure in Poiseuille flow, at least at high shear rates. The data of Christiansen et al. with flush-mounted pressure transducers appear to confirm this second possibility. Finally, a single set of shift factors obeying the Williams, Landel and Ferry equation superposes the viscosity, the first and the second normal-stress difference within experimental scatter, which can be less than 1% for a certain combination of normal-stress differences. The data were recorded at 3, 20, 30, and 46 °C in the shear rate range 1–260 s−1.

Rheological properties of pressure-sensitive adhesives: polyisobutylene/sodium carboxymethylcellulose

Abstract: The viscoelastic properties of polyisobutylene filled with sodium carboxymethylcellulose were studied. Using shear viscosity data, the relaxation time,λ, defined as the ratioη0/G0 of the initial viscous and elastic constants was evaluated. The flow activation energy, melt flow index and superposition shift factor were also determined and master curves were generated. A relatively small effect of filler concentration on viscosity was observed, whereas its effect onλ and the initial first normal-stress coefficient,ψ0, was found to be significant.

Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

Abstract: The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data

Continuum modelling of polyelectrolytes in solution

Abstract: A phenomenological model for solutions of polyelectrolytes accounting for electromechanical interactions is proposed within the framework of continuum thermodynamics. The modelling involves the conformation of macromolecules in the form of a tensorial “internal variable” and the electric polarization of the solution. The paper aims to demonstrate the possible competition between flow and electricity effects on rigorous phenomenological grounds. Three kinds of dissipative mechanisms are accounted for: viscosity of the solution, electric relaxation and the relaxation of the conformation of macromolecules. Anisotropic effects induced by the applied electric field and flow-induced polarization through changes in conformation are exhibited. These effects are small. By way of application, the problem of the orientation and conformation taken by macromolecules of polyelectrolytes under the combined influence of a simple shear flow and a longitudinal or orthogonal electric bias field is treated in detail and illustrated graphically. Some optical properties are mentioned.

Injection moulding of thermoplastics. II: Freezing-off in cavities

Abstract: The injection moulding of thermoplastics involves, during mould filling, flow of a hot molten polymer into a mould network, the walls of which are so cold that the polymer freezes on them. During the constant pressure drop part of the filling stage, but not during the preceding constant flow-rate part, freezing-off, that is premature blockage of the mould network by frozen polymer, is possible. A semi-quantitative analysis of such freezing-off in a mould cavity is presented here. The length-scales and time-scales of all the relevant physical processes occurring during freezing-off are identified and a criterion is obtained which enables the occurrence of freezing-off to be predicted, at least crudely. This criterion is shown to be corroborated by experimental data for the filling of a spiral mould cavity by three different polymers under a range of different operating conditions.

A simple extensional viscometer

Abstract: An extensional viscometer is described in which the liquid filament leaving a capillary is subjected to a stretching deformation. In order to keep the flow rate through the capillary unaltered upon inception of stretching, the pressure head at the capillary entrance has to be reduced by an amount equal to the extensional viscoelastic stress at the capillary exit. This affords a simple means of measuring small fluid forces such as those that occur in the stretching of dilute polymer solutions. Since stretch rates can be obtained from a knowledge of the mass flow rate and the filament diameter profile, extensional viscosities can be computed. The efficacy of the technique is demonstrated by obtaining the anticipated results for Newtonian liquids.

The flow of Newtonian and non-Newtonian liquids through annular converging regions

Abstract: A coordinate system is introduced in which one of the three sets of coordinate surfaces is constituted by cones. The axes of the cones coincide, but in general the apices of the cones do not. For this so-called special toroidal coordinate system a set of operations is given involving the nabla operator. A few examples of the use of this special toroidal coordinate system will elucidate its advantages for the analysis of the flow of Newtonian and generalized Newtonian liquids in annular convergent regions.

Mathematical model of a single-screw plasticating extruder

Abstract: A five zone mathematical model of a plasticating extruder is presented. Its application in the design of new and improvement of existing extruders is briefly described. The model is based on theories proposed by Darnell and Mol, Tadmor, Broyer, McKelvey, Klein, Schneider, Fenner, Poon and Jankov. A comparison between experiments and theoretical calculations is included.

Extensional flow of polymer solutions through porous media

Abstract: The flow behaviour of various polymer solutions of non-hydrolyzed polyacrylamide, hydrolyzed polyacrylamide, polyox and Xanthan was investigated in a plexiglass column having a succession of enlargements and constrictions, and compared with the flow behaviour and mechanical degradation of a solution of non-hydrolyzed polyacrylamide in a packed column of non-consolidated sand. The flow behaviour of this solution was found to be very similar in both the sand pack and plexiglass pore.

Linear elastico-viscous properties of molten standard polystyrenes. II: Improvement of conventional characterization on molar mass distribution

Abstract: For the investigated standard polystyrenes possessing narrow molecular mass distributions the choice of an analytical distribution function does not pose serious problems, so that the two-parameter Wesslau function can be chosen for ease in handling. The best values for these parameters as well as for two short range molecular parameters are obtained with the aid of a regression method in which traditional data for the molar mass distribution are improved with the aid of elastico viscous data of high accuracy.

Linear and branched poly(butyleneterephthalate): Activation energy for melt flow

Abstract: Poly(butyleneterephthalate) (PBTP) samples of different molecular weights, both linear and branched, were synthetized by mass polymerization and studied in the molten state with a melt-flow-index apparatus at different temperatures in the range 245–270 °C. In our experimental conditions (\(\dot \gamma \) ≦ 20 s−1) the behaviour of PBTP samples was Newtonian, as reported previously. The flow activation energyEa,0 was found to increase with degree of branching: typicallyEa,0 was about 47 and 63–79 kJ/mol for linear and branched polymers respectively.

Injection moulding of thermoplastics. I. Freezing-off at gates

Abstract: The injection moulding of thermoplastics involves, during mould filling, flow of a hot molten polymer into a mould network, the walls of which are so cold that the polymer freezes on them. During the constant pressure drop part of the filling stage, but not during the preceding constant flow-rate part, freezing-off, that is premature blockage of the mould network by frozen polymer, is possible. A semi-quantitative analysis of such freezing-off at a gate is presented here. The length-scales and time-scales of all the relevant physical processes occurring during freezing-off are identified and a criterion is obtained which enables the occurrence of freezing-off to be predicted, at least crudely.