Showing papers in "Rheologica Acta in 1986"

Yield stress: A time-dependent property and how to measure it

Abstract: This paper reviews the different aspects of the yield stress phenomenon and attempts a synthesis of knowledge. Yield stress can be probed using constant shear stress or shear rate. The magnitude of the result depends on the time allowed to determine whether the sample has developed continuous flow or has ceased flowing. It is closely associated with creep, stress growth and thixotropic breakdown and recovery, and the characteristic times of these transient responses play a part in yield stress measurement. In thixotropic fluids, yield stress is a function of structure and hence of time. In simple thixotropy, the yield stress derived from the equilibrium flow curve is the same as that for the fully built-up structure. But in many materials, the static yield stress obtained after prolonged rest is much higher than the dynamic yield stress from the equilibrium flow curve. This is associated with the phenomenon in which the equilibrium flow curve bends upwards as the shear rate is reduced to very low values. The paper also reviews the many methods that can be used to measure yield stress. It is pointed out that the choice of observation time or shear rate to use should be related to the characteristic time of the flow process to which the result is to be applied. Examples discussed are solids suspension capability of fluids, levelling and sagging, pipeline flow and start-up power requirement of mixers.

Surfactant systems for drag reduction: physico-chemical properties and rheological behaviour

Abstract: The first part of the work presents an overview of the physical chemistry of surfactants which in aqueous solutions reduce the frictional loss in turbulent pipe flow. It is shown that these surfactants form rodlike micelles above a characteristic concentraionc t. The experimental evidence for rodlike micelles are reviewed and the prerequisites that the surfactant system must fulfill in order to form rodlike micelles are given. It is demonstrated by electrical conductivity measurements that the critical concentration for the formation of spherical micelles shows little temperature dependence, whereasc t increases very rapidly with temperature. The length of the rodlike micelles, as determined by electric birefringence, decreases with rising temperature and increases with rising surfactant concentration. The dynamic processes in these micellar systems at rest and the influence of additives such as electrolytes and short chain alcohols are discussed. In the second part, the rheological behaviour of these surfactant solutions under laminar and turbulent flow conditions are investigated. Viscosity measurements in laminar pipe and Couette flow show the build-up of a shear induced viscoelastic state, SIS, from normal Newtonian fluid flow. A complete alignment of the rodlike micelles in the flow direction in the SIS was verified by flow birefringence. In turbulent pipe flow, drag reduction occurs in these surfactant systems as soon as rodlike micelles are present in the solution. The extent and type of drag reduction, i.e. the shape of the friction factor versus Reynolds number curve, depends directly on the size, number and surface charge of the rodlike micelles. The friction factor curve of each surfactant investigated changes in the same characteristic way as a function of temperature. For each surfactant, independent of concentration, an upper absolute temperature limit,T L, for drag reduction exists which is caused by the micellar dynamics.T L is influenced by the hydrophobic chain length and the counter-ion of the surfactant system. A first attempt is made to explain the drag reduction of surfactants by combining the results of these rheological measurements with the physico-chemical properties of the micellar systems.

Peristaltic transport of a couple-stress fluid

Abstract: The problem of peristaltic transport of a couple-stress fluid has been investigated under a zero Reynolds number and long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of the pressure rise under a given set of conditions is greater in the case of the couple-stress fluid. The pressure rise increases as the couple-stress parameter\(\bar \eta \) decreases. The difference between the pressure rise for a Newtonian and a couple-stress fluid increases with increasing amplitude ratio at zero flow rate. However, increasing the flow rate reduces this difference.

Shear viscosity behavior of highly concentrated suspensions at low and high shear-rates

Abstract: A method is proposed for determining the shear viscosity behavior of highly concentrated suspensions at low and high shear-rates through the use of a formulation that is a function of three parameters signifying the effects of particle size distribution. These parameters are the intrinsic viscosity [η], a parametern that reflects the level of particle association at the initiation of motion and the maximum packing concentrationΦ m. The formulation reduces to the modified Eilers equation withn = 2 for high shear rates. An analytical method was used for the calculation of maximum packing concentration which was subsequently correlated with the experimental values to account for the surface induced interaction of particles with the fluid. The calculated values of viscosities at low and high shear-rates were found to be in good agreement with various experimental data reported in literature. A brief discussion is also offered on the reliability of the methods of measuring the maximum packing concentration.

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

Abstract: The main purpose of this study was to examine the viscous and elastic properties and capillary flow of fiber suspensions in Newtonian fluids as well as in polymer solutions. The fillers used were glass, carbon, nylon and vinylon fibers. Glycerin was used as a Newtonian suspending medium and HEC and Separan solutions as viscoelastic suspending media. The viscosity and the first normal-stress difference were measured using a coaxial cylindrical rotating viscometer and a parallel-plate rheogoniometer respectively. The influence of the concentration, aspect ratio, diameter and flexibility of the fibers on the viscous and elastic properties of the fiber suspensions was investigated. Empirical equations were obtained for the relative viscosity and first normal-stress difference for the fiber suspensions in glycerin. The capillary flow of these suspensions is discussed in part II.

The rheological characterization of HPG gels: Measurement of slip velocities in capillary tubes

Abstract: Measurements are reported for the properties of two hydroxypropyl guar (HPG) gels. The flow curves are composed of three distinct regions: a yield value at low stress levels, a quasi-linear region at intermediate stress or deformation rate levels, and a broad region at high deformation rate levels in which the flow is entirely dominated by slip phenomena.

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions. II: Capillary flow

Abstract: This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

Abstract: In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.

The effect of molecular weight on the rheological properties of poly(dimethylsiloxane) filled with fumed silica

Abstract: The viscometric, stress relaxation, and stress growth rheological properties were measured for various molecular weight PDMS fluids filled with fumed silica. The stress growth function exhibited significant overshoot, when the continuous phase molecular weight was slightly greater than the entanglement molecular weight; however, significant overshoot peaks were not observed, when the continuous phase molecular weight was less than or much greater than the molecular weight between entanglements. The experimentally observed transient rheological properties are rationalized in terms of a molecular model, where interparticle interactions occur via entanglements of the polymer adsorbed on the silica surface. When the molecular weight of the adsorbed polymer is greater than the entanglement molecular weight, the strength of the interparticle interaction will increase substantially and the particle diffusivity will substantially decrease.

The rheology of polymeric liquid crystals

Abstract: The molecular theory of Doi has been used as a framework to characterize the rheological behavior of polymeric liquid crystals at the low deformation rates for which it was derived, and an appropriate extension for high deformation rates is presented. The essential physics behind the Doi formulation has, however, been retained in its entirety. The resulting four-parameter equation enables prediction of the shearing behavior at low and high deformation rates, of the stress in extensional flows, of the isotropic-anisotropic phase transition and of the molecular orientation. Extensional data over nearly three decades of elongation rate (10−2–101) and shearing data over six decades of shear rate (10−2–104) have been correlated using this analysis. Experimental data are presented for both homogeneous and inhomogeneous shearing stress fields. For the latter, a 20-fold range of capillary tube diameters has been employed and no effects of system geometry or the inhomogeneity of the flow-field are observed. Such an independence of the rheological properties from these effects does not occur for low molecular weight liquid crystals and this is, perhaps, the first time this has been reported for polymeric lyotropic liquid crystals; the physical basis for this major difference is discussed briefly.

The conformation of drag reducing micelles from small-angle-neutron-scattering experiments

Abstract: Small-angle-neutron-scattering measurements (SANS) were done with a dilute solution of the surfactant n-tetradecyltrimethylammoniumbromide (TTAB) with sodium salicylate (Na Sal) in pipe and channel flow. The solvent used was heavy water. The anisotropy observed in the SANS-curves can be related to the drag reduction behaviour of the surfactant solution. The breakdown of the drag reducing properties above the critical wall shear stress is accompanied by a strong decrease in the scattering anisotropy. However, in this flow region the scattering curves reveal a very similar micellar structure to that found in the fluid at rest. This shows that the micelles exist above the critical wall shear stress.

An analysis of apparent slip flow of polymer solutions

Abstract: Theapparent slip flow phenomenon of polymer solutions in capillary tubes is analyzed by a thermodynamic diffusion model. An approximate solution of the developing concentration profiles shows a significant decrease in the polymer wall concentration. The approximate concentration profiles are coupled with the concentration-dependent viscosity for aqueous polyacrylamide solutions to provide a priori predictions of the magnitude of the effective slip velocity at the wall. The results are in a reasonable agreement with the available apparent slip data for 1% and 0.5% solutions of partially hydrolyzed polyacrylamide.

Motion of a slender body in quiescent polymer solutions

Abstract: The motion of a slender body falling in quiescent polymer solutions is investigated experimentally. It represents the simplest model of motion of single fibers in the flow of fiber suspensions. The fall behavior in quiescent polymer solutions is compared with that in water. It is demonstrated that a slender body falling in Newtonian liquids rotates to adopt a horizontal orientation, whereas in non-Newtonian liquids it rotates towards a vertical orientation but for less concentrated solutions is not able to reach the vertical orientation and moves sideways with a constant orientation angle. The effects of shear thinning and elasticity on the motion of the body are discussed.

A simple method of evaluating the complex moduli of polystyrene blends

Abstract: In the search for a workable mixing rule, use was made of experimental data for complex moduli of melts of narrow molar mass distribution polystyrenes and their homogeneous blends. In the course of this work two basic observations were made as to the nature of the relaxation time spectra of these blends: For both processes approximate empirical equations could be found. It turned out that, after the application of the required modifications, the complex moduli of the components could successfully be added in order to obtain the complex moduli of the blend at circular frequencies characteristic for the flow and rubber transition regions. On the basis of these results one may expect that for the melt of any linear polymer the linear viscoelastic properties can be evaluated with reasonable accuracy from the knowledge of the molar mass distribution.

Primary normal-stress difference for two liquid crystalline copolyesters

Abstract: The primary normal-stress difference,N 1, was determined in both steady and transient shear flow experiments for thermotropic copolyesters of 60 and 80 mole% p-hydroxybenzoic acid (PHB) and polyethylene terephthalate (PET).N 1 was observed to be negative for the 80 mole% system at low shear rates and temperatures below 332 °C (a tensile stress, e.g. σ11 is taken here to be positive). At higher shear rates and for temperatures above 332 °C,N 1 was found to be positive. Values ofN 1 for the 60 mole% pHBA/PET system were always positive over the same range of shear rates. Although it is not certain as to the origin of the negative values, a probable cause is small density changes upon the inception of flow as well as the existence of a solid phase or some texture development in the melt. However, it is shown that it is thermodynamically admissible for liquid crystalline fluids to exhibit negative values ofN 1.

Influence of disperse phase concentration upon the viscoelastic behaviour of emulsions

Abstract: Rheology of soya oil-water emulsions in the linear region has been studied. The viscoelastic response consisted of three contributions. There was a purely elastic component, a purely viscous component and a contribution due to the retarded compliance. Emulsions became more viscous and elastic with increasing soya oil concentration. Sharp changes in rheology were observed as the concentration approached the random close packed limit. There was also a marked increase in zero-shear viscosity. Breakdown of coagulation structure was observed as the shear stress was increased into the non-linear region. The rheological behaviour of the emulsions in the linear region could be adequately described by the generalized Kelvin-Voigt model.

Threshold-type shear-thickening in polymeric solutions

Abstract: Threshold-type shear-thickening has been reported in the literature for relatively complex mixtures and one of the most famous is a solution of poly(vinylalcohol) in water in which a substantial amount of sodium borate is added. As far as we know, relatively few polymer solutions have been shown to be shear-thickening, even less of the threshold type. Two cases of threshold-type shear-thickening are examined. One of them is reversible [HPAM Pusher 700 or partially hydrolyzed poly(acrylamide) aqueous solution], the other one (in vitro-synthesized native dextran aqueous solution) leads to the formation of an irreversible structure provided sufficient strain is applied. In both cases, the occurrence of shear-thickening above a critical value of shear rate is related with a change in macromolecular conformation. This conformational change (reversible) can be followed by the formation of intermolecular bonds (irreversible).

Simulation of two-dimensional planar flow of viscoelastic fluid

Abstract: A numerical scheme based on the Finite Element Method has been developed which uses a relaxation factor in the momentum equation with the stresses being evaluated via a streamwise integration procedure. A constitutive equation introduced by Leonov has been used to represent the rheological behavior of the fluid. The convergence of the scheme has been tested on a 2 : 1 abrupt contraction problem by successive mesh refinement for non-dimensional characteristic shear rates, of 5 and 50 for polyisobutylene Vistanex at 27 °C. The recirculation region is shown to increase in size with non-dimensional characteristic shear rate.

Die räumliche Staupunktströmung für ein viskoelastisches Fluid

Abstract: In dieser Arbeit wird die raumliche Staupunktstromung fur ein Rivlin-Ericksen-Fluid berechnet Mit Hilfe einer Ahnlichkeitstransformation erhalt man fur die dimensionslose Stromfunktion eine Differentialgleichung vierter Ordnung Es wird gezeigt, das man dennoch mit den bekannten drei Randbedingungen auskommt In Beispielen werden fur bestimmte Parameterkombinationen Geschwindigkeitsprofile dargestellt und diskutiert Ebenso werden Aussagen uber die Wandschubspannung gemacht

The elastic modulus of particulate composites using the concept of a mesophase

Abstract: A theoretical model for the evaluation of the elastic modulus in particulate composites has been developed. The method takes into account the existence of a mesophase between main phases, which constitutes an important parameter influencing the behaviour of a composite material. This layer between the matrix and filler develops different physico-chemical properties from those of the constituent phases and variable ones along its thickness. The effect of the progressive variation of the elastic modulus of the mesophase on the modulus of the composite was estimated by applying various simple laws of variation. Convenient laws of variation were introduced, varying from a simple one, assuming a linear law, to a more refined one using a parabolic law. Experimental results with particulates, based on iron-filled epoxy composites, compared satisfactorily with other models. However, the model based on a parabolic law was superior to all others on physical grounds.

A note on the calculation of strain histories in orthogonal streamline coordinate systems

Abstract: An extension of a previous work concerning the calculation of strain histories along streamlines is made to get more complete and useful expressions of Finger's strain tensor in a cylindrical (or Cartesian) coordinate system as well as in an orthogonal streamline coordinate system. One of the results shows that Winter's tracking model is correct. Relations among the recent three results of Winter, Adachi and Crochet et al. are presented clearly. Moreover useful applications of Frenet-Serret's formula to the study of the deformation and flow kinematics along streamlines are shown in comparison with the ordinary tensor approach.

Shear dependence of viscosity for perfluoropolyether fluids

Abstract: The shear dependence of the bulk viscosities of two structurally different types of perfluoropolyether fluids was determined by two different techniques. The first involved direct measurement in a high shear Couette viscometer, the second utilized the time-temperature superposition principle to establish master curves from viscosity determinations at low shear rates and temperature; the results are comparable. Both fluids begin to show non-Newtonian behavior at shear rates above 10,000 s−1.

Slip flow of non-plasticized PVC compounds

Abstract: Measurements on seven rigid PVC compounds were carried out with a slit rheometer working in combination with an injection moulding machine. Plastication of the compounds occurred in the screw of the plastication unit, which also forced the melt through the die with a controlled forward velocity. The rectangular slit had a length of 90 mm and a widthB of 20 mm. The heightH could be varied between 0.8 and 3.3 mm. Pressures and temperatures were recorded at several positions in and before the die. Measurements were carried out at shear rates from 10 to 2000 s−1.

Extended thermodynamics of a non-Newtonian fluid

Abstract: Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.

The rational mechanics and thermodynamics of polymeric fluids based upon the concept of a variable relaxed state

Abstract: The conceptual framework of polymer continuum mechanics based upon Eckart's idea of a variable relaxed state is developed. No constitutive models are explicitly used. The theory admits four constitutive functions only, the scalar specific internal energy, the vectorial heat flux, and two tensorial fluxes representing non-elastic stress and flow (slippage). The non-linearity of the constitutive relations includes self-induced anisotropy (Leonov) with Reiner-Rivlin's equation representing a special example for this. — The effectiveness of this non-linear theory is demonstrated by treating elongational flows of polymer melts.

Flow of viscoelastic fluids between plates rotating about distinct axes

Abstract: We discuss the flow of BKZ fluids in an orthogonal rheometer. Some analytical results are proved, and numerical solutions are obtained for the Currie model. These solutions show a boundary layer behavior at high Reynolds numbers and the possibility of discontinuous solutions or nonexistence at high Weissenberg numbers.

Prediction of the creep behaviour of polyethylene and molybdenum from stress relaxation experiments

Abstract: In many applications it is useful to be able to convert observed creep data of a material to corresponding stress relaxation data or vice versa. If the material exhibits non-linear viscoelasticity such a conversion can be rather difficult. In this paper two semi-empirical flow equations, the power law and the exponential law, are used to convert stress relaxation data into corresponding creep behaviour data. These two flow equations are often used to describe non-linear viscoelastic behaviour. The procedure adopted here is based on the assumption that the creep data during the experiment decrease due to an increase in the internal stress level, thus decreasing the effective stress for flow. The conversion method is applied to high density polyethylene and polycrystalline molybdenum at room temperature. In general predictions using the power law are in better agreement with the experimental results than predictions using the exponential formula. The concepts of secondary and ceasing creep are discussed in terms of build-up of internal stress during the creep process.

Linear viscoelasticity and irreversible thermodynamics

Abstract: The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.

Thermodynamic activation functions of viscous flow of non-polar liquids

Abstract: The thermodynamic activation function of viscous flow may be determined from the expression for the pre-exponential factor in the Eyring relationship (the viscosity coefficient), which is a function of density and relative permittivity, together with the thermal dependence of the viscosity coefficient. This method of determination is demonstrated for a series of n-alkanes C6–C20.

Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

Abstract: The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz and Nahme numbers are large and the Pearson number is small. Thus the flows are developing and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity (but the difference between the entry temperature of the polymer to a specific part of the mould network and the melting temperature of the polymer is not).