A novel geometry for rheological characterization of viscoelastic materials

A novel geometry for generating a viscometric flow presents advantages of both cone and plate and parallel plate geometries, regarding uniform shear field and adjustable range of measurement. Kinematics and dynamics of the generated flow have been described mathematically utilizing an orthogonal curvilinear coordinate system based on the shapes of the shearing surfaces which are similar to the surface that generates the flow. Simple equations that allow the calculation of quantities of experimental interest in the rheological characterization of liquid materials, namely, shear rate, shear stress and two normal stress differences, have also been derived.The geometry, called pseudosphere, was tested with two types of fluids (Newtonian and pseudoplastic). Results show that the geometry can be used with low viscosity liquids (Newtonian liquids) by only adjusting the gapH. The behavior of pseudoplastic fluids for both low and moderately high viscosity could also be studied with this geometry. Very reproducible results were obtained when compared with those obtained with cone and plate geometry. Regions of lower shear rate could be studied using only the pseudosphere geometry.     

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG _c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG _c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG _c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m^–2; - G loss shear modulus,N·m^–2; - G _c calculated storage shear modulus,N·m^–2; - G _c calculated loss shear modulus,N·m^–2; - G _e equilibrium shear modulus,N·m^–2; - G _ec calculated equilibrium shear modulus,N·m^–2; - G(t) relaxation shear modulus,N·m^–2; - G _c (t) calculated relaxation shear modulus,N·m^–2; - G ^*(t) pseudo relaxation shear modulus,N·m^–2; - H relaxation spectrum,N·m^–2; - t time,s; - relaxation time,s; - angular frequency, rad·s^–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].     

Simple linear viscoelastic models of dilute solutions of polymer molecules and emulsion droplets

The complex viscosity of microemulsions shows relaxation processes of which the largest relaxation time is about 10^–5 s or less. This time can be attributed to relaxation of stresses in the surface of emulsion droplets pertaining to interfacial tension. Superimposed on a spherical droplet surface shape fluctuations can occur due to thermal energies. Our aim is to show the influence of thermal shape fluctuations on the complex viscosity of emulsions. The method used in the derivation has also been applied to inflexible rods to demonstrate its feasibility by showing the formal rheological equivalence of in length thermally fluctuating rods and Rouse's simple model of polymers. The emulsion results have been applied to a dilution series of a non-ionic microemulsion.     

Attempts to find a molecular theory for which the high-frequency dynamic viscosity is less than the solvent viscosity

It has been found that for some dilute polymer solutions the dynamic viscosity at very high frequencies is less than the zero-shear-rate solvent viscosity. Such an effect cannot be explained by the usual kinetic theories using bead-spring-rod models. Here we examine several modifications of the kinetic theories that might be expected to explain the experimental facts.This paper is dedicated to Prof. Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

An investigation of the viscoelastic properties of molten polypropylene

Two series of polypropylene samples of different molecular weight, the first obtained directly from polymerization reactions and the second from controlled thermal degradation, were studied by dynamic testing in the melt state. Several viscoelastic parameters were determined, and correlated with weight-average molecular weightM _w . It is found that theM _w -dependence of the two series is rather different.     

Shear-induced structures in macroscopic dispersions

Observations are reported on structures induced in an oscillatorily sheared dispersion of glass spheres in a silicon oil and in a highly viscoelastic fluid (mixture of polyisobutylenes). The shear flow used in these experiments is oscillatory with a frequency 200 Hz) and has displacement amplitudes of the order of magnitude as the sphere diameter (40 µm).The interpretation of the structures observed is based on non-linear effects which, even when small, in comparison to the viscous effects, may lead to the irreversible formation of structures over a long time, i.e. a time much larger than the period of the shear. A comparison between similar experiments performed with two different suspending fluids (silicon oil, in which the spheres line up perpendicular to the velocity direction; polyisobutylene mixture, in which the spheres line up in the velocity direction) confirm our interpretation.     

Representation of the rheological properties of polymer melts in terms of complex fluidity

In dynamic rheological experiments melt behavior is usually expressed in terms of complex viscosity ^* () or complex modulusG ^* (). In contrast, we attempted to use the complex fluidity ^* () = 1/µ ^* () to represent this behavior. The main interest is to simplify the complex-plane diagram and to simplify the determination of fundamental parameters such as the Newtonian viscosity or the parameter of relaxation-time distribution when a Cole-Cole type distribution can be applied. ^* () complex shear viscosity - () real part of the complex viscosity - () imaginary part of the complex viscosity - G ^* () complex shear modulus - G() storage modulus in shear - G() loss modulus in shear - J ^* () complex shear compliance - J() storage compliance in shear - J() loss compliance in shear - shear strain - rate of strain - angular frequency (rad/s) - shear stress - loss angle - ^* () complex shear fluidity - () real part of the complex fluidity - () imaginary part of the complex fluidity - ₀ zero-viscosity - ₀ average relaxation time - h parameter of relaxation-time distribution     

The effect of dissolved polymers on the rheological properties of coating colours

Coating colours used for the coating of paper and board consist mainly of a mineral pigment, which is very often clay, a synthetic binder such as a styrenebutadiene latex, dispersion agents and water retention aids. The latter are often water soluble polymers. These polymers have a very strong influence on the rheological properties of the coating colours, both on the strain rate dependence of the apparent viscosity and on the viscoelasticity. The effects of two different grades of carboxymethylcellulose (CMC) and one grade of hydroxyethylcellulose (HEC), on the rheological properties at room temperature of a clay-based coating colour at pH 8, have been investigated. It is concluded that the high values of the dynamic modulus of the colours are due to interactions between the cellulose derivatives and the solid particles, i.e. mainly the clay particles. For HEC this interaction is associated with adsorption of the polymeric molecules on the clay particles. In the case of CMC, the adsorption is strongly retarded by the presence of the dispersant (a polyacrylate salt). It is suggested that the marked elasticity of the CMC-containing colour in addition to a possible polymer adsorption may be due to charge interactions and/or depletion flocculation. The effect of CMC and HEC on the water-retention properties of the colour is also discussed.     

Prediction of the non-linear rheological properties of polymer solutions by means of the Rouse-Zimm model with slippage

The non-affine deformation of macromolecules and the slippage function are discussed. In case of polymer solutions with moderate concentration the slippage function is determined by means of the Cox-Merz rule. The non-linear viscoelasticity of these solutions is described with the aid of the Rouse-Zimm model with slippage function. The theoretical predictions show good agreement with published experimental data.     

Evolution of the rheological properties during the reactive processing of thermoplastic/thermoset epoxy

The melt state reaction, or fusion process of bisphenol-A and the diglycidyl ether of bisphenol-A can produce both linear phenoxy backbone chains and crosslinked network structures. The linear chains can be thought of as thermoplastic polymer, while the crosslinked molecular matrix is a thermoset; therefore, this resin system can be termed a thermoplastic/thermoset epoxy.Rheological analysis has been performed on this system to determine the occurrence of the crossover of the storage and loss moduli during the reaction using three techniques: isothermal cure, interval frequency sweep, and interval stress relaxation.Determination of the activation energy of the reaction by consideration of the conventional gel-point determination prove unsatisfactory as compared to that which is determined by FTIR. An alternative technique is presented which yields a value in good agreement with that obtained by following epoxide consumption. The thermoplastic/thermoset nature of this material leads to the deviation from traditional thermoset cure behavior.     

Rheological properties of dilute polymer solutions: An extended thermodynamic approach

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.     

Viscoelastic properties of polymerlike reverse micelles

A dramatic increase in the viscosity of reverse micellar solutions of lecithin in a variety of organic solvents of up to a factor of 10⁶ upon the addition of a small amount of water can be observed. The formation of viscoelastic solutions can be explained by a water-induced aggregation of lecithin molecules into flexible cylindrical reverse micelles and the subsequent formation of a transient network of entangled micelles. The viscoelastic properties of these solutions are characterized as a function of water content and temperature for different organic solvents by means of dynamic shear viscosity measurements. The results are interpreted by making analogies to the behavior of semidilute polymer solutions and living polymers.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

Stability of Couette flow of liquids with power law viscosity

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.     

Linear rheology of viscoelastic emulsions with interfacial tension

Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.     

Analysis of Taylor vortex flow by means of laser light scattering

Rheological measurements and light-scattering experiments were performed on dilute solutions of high molecular polystyrene. We are able to describe the orientation behavior of chain molecules under shear flow by means of light-scattering. Beyond that these investigations of light-scattering of flowing polymer solutions are an useful and suitable tool for detection and characterization of Taylor vortex formation. We can estimate the appearance of these hydrodynamic instabilities, which overlay the laminar main flow and we can observe a typical influence of the solvent power on it.Presented in part at the meeting of the Deutsche Rheologische Gesellschaft, Berlin, 13–15 May, 1991.     

On the cone and plate deformation of a rubber-like material: Instability

In this report it is shown that the place boundary-value problem, for a small deformation superimposed on the large cone-and-plate deformation of a Mooney-Rivlin material, has no unique solution at some displacement angles of the cone. The kinematics of the small deformation are chosen such that the problem is reduced to a set of ordinary differential equations. With respect to this restricted class of kinematics the cone-and-plate deformation is unstable.     

Extensional flow resistance of dilute polyacrylamide and surfactant solutions

The extensional flow behaviour of dilute aqueous solutions of a partiallyhy-drolyzed polyacrylamide and a surfactant were investigated in an extensional flow cell. The cell was designed such that fluids were subjected to steady shear before undergoing extensional motion in a converging channel. Extensional resistance was monitored by measuring the pressure drop through the channel. Such measurements were made over a range of extensional rates at fixed values of the upstream shear rate. Solutions of different concentrations were tested — up to 40 ppm of polyacrylamide and 450 ppm of surfactant — at various temperatures in the case of surfactant and for different types and amounts of salt in the case of polyacrylamide. Of the results, the more notable are that the extensional resistance of polyacrylamide solutions is affected much more by CaCl₂ than by NaCl and that surfactant solutions do not exhibit extensional resistance unless they are pre-sheared.     

Comparison of the rheology of polymer melts in shear,and biaxial and uniaxial extensions

The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.     

Melt viscosity of linear and branched poly(butyleneisophthalate)

Linear and branched poly(butyleneisophthalate) samples were synthesized and characterized in terms of the intrinsic viscosity, the molecular weight and the melt viscosity over a wide range of shear rates at 200 °C. An exponent of about 4.6 in the equation relating ₀ to was found for linear samples; this high value is probably due to the high content of cyclic oligomers in low molecular weight samples. Both linear and branched samples exhibited Newtonian behaviour over a rather wide range of shear rates, but for any given melt-viscosity, the branched samples became shear thinning at lower shear rates than the linear ones. Our experimental data were found to fit a previously proposed correlation between the melt viscosity ratio ( _{0, b} / _{0, 1} ) and a branching index quite well.