Generalized Cole-Cole behavior and its rheological relevance

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.     

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.     

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.     

A “zero-parameter” constitutive relation for simple shear viscoelasticity

Based on the Cox-Merz rule and Eyring's expression for the nonlinear shear viscosity, a Wagner-type constitutive relation with no nontrivial adjustable parameters is proposed for simple shear viscoelasticity. The predictions for a number of non-steady shear flows are worked out analytically. It is shown that most features of shear viscoelasticity are reproduced by the model.     

On-line measurements of the rheological properties of fermentation broth

The paper is concerned with measurements of rheological properties of fermentation broth. An on-line rheometer, Rheohelix-1, based on the application of a helical screw impeller rotating in a draught tube has been constructed. The instrument was used for measurements of the rheological parameters of fermentation broth of Aspergillus niger in a submerged fermentation process. The results of rheological and some standard measurements have been compared and proved the applicability of the instrument.Presented at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Flow mechanisms in dense silica-metal oxide-water suspensions

The rheological properties of dense silica in water suspensions (approx. 50% solids by volume) containing additions of metal oxides were examined. Metal oxides used were ferric, zinc and stannic. To prevent settling, testing was performed in a rheometer which was modified to provide for continual stirring of the materials. Relatively small oxide additions had the effect of thickening the mixtures and making them non-Newtonian. Different rate-limiting steps for flow were identified depending on the particular mixture, testing temperature and shear strain rate. Flow could be described using empirical equations which are identical to those often used to describe plastic flow in solid crystalline materials.     

Driven torsion pendulum for measuring the complex shear modulus in a steady shear flow

To investigate the viscoelastic behavior of fluid dispersions under steady shear flow conditions, an apparatus for parallel superimposed oscillations has been constructed which consists of a rotating cup containing the liquid under investigation in which a torsional pendulum is immersed. By measuring the resonance frequency and bandwidth of the resonator in both liquid and in air, the frequency and steady-shear-rate-dependent complex shear modulus can be obtained. By exchange of the resonator lumps it is possible to use the instrument at four different frequencies: 85, 284, 740, and 2440 Hz while the steady shear rate can be varied from 1 to 55 s^–1. After treatment of the theoretical background, design, and measuring procedure, the calibration with a number of Newtonian liquids is described and the accuracy of the instrument is discussed.Notation a radius of the lump - A geometrical constant - b inner radius of the sample holder - c constant - C ₁, C ₂ apparatus constants - D damping of the pendulum - e _x , e _y , e _z Cartesian basis - e _r , e , e _z orthonormal cylindrical basis - E geometrical constant - E _t , ⁰ E _t , _t relative strain tensor - f function of shear rate - F _t relative deformation tensor - G (t) memory function - G ^* complex shear modulus - G Re(G ^* ) - G Im(G ^* ) - h distance between plates - H ^* transfer function - , functional - i imaginary unit: i ²= – 1 - I moment of inertia - J _exc excitation current - J ₀ amplitude of J _exc - k ^* = k – ik complex wave number - K torsional constant - K fourth order tensor - l length of the lump - L mutual inductance - M _dr driving torque - M _liq torque exerted by the liquid - ⁰ M _liq, _liq steady state and dynamic part of Mliq - n power of the shear rate - p isotropic pressure - Q quality factor - r radial position - R,R ₀, R _c Re(Z ^*, Z ₀ ^* , Z _c ^* ) - s time - t, t time - T temperature - T, ⁰ T, stress tensor - u velocity - U lock-in output - ₀ velocity - V _det detector output voltage - V _sig, V _cr signal and cross-talk part of V _det - x Cartesian coordinate - X , X ₀, X _c Im(Z ^*, Z ₀ ^* , Z _c ^* ) - y Cartesian coordinate - z Cartesian coordinate, axial position     

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.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

The shear modulus in the fiber direction of unidirectional fiber composites based on the concept of mesophase

A new and accurate relationship for the shear modulus in the fiber direction of unidirectional fiber composites is derived, based on the Kerner model concepts but not using its approximate relationships. Furthermore, this model is extended by taking into account the mesophase between the fiber and the matrix accomodating smoothly the mechanical properties between neighbouring phases. The introduction of the mesophase results in an improvement of the theoretical predictions, which now approach close to experimental values for the moduli of different fibrous composites.     

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.     

Measurement of rheological and ultrasonic properties of food and synthetic polymer melts

A slit die viscometer has been used in conjunction with a co-rotating twin screw extruder to study the rheological behaviour of maize grits, potato powder and low density polyethylene, as a function of feed rate, screw speed and temperature. The shear viscosity of both maize and potato decreased with increasing feed rate. Increasing the temperature or screw speed at any given feed rate also reduced the viscosity. The ultrasonic velocity through the material has also been shown to be sensitive to the extruder operating conditions. Overall, the ultrasonic velocity decreased as screw speed and temperature increased and feed rate decreased.     

Accurate evaluation of the transverse shear modulus in unidirectional fibrous composites

A new relation for the prediction of the transverse shear modulus in unidirectional fiber composites has been derived. The theoretical results of this relationship are in better agreement with the experiments than those of other relations, existing in the literature. The discrepancies, which are observed among the theoretical predictions and the experimental values, are explained by the consideration of the boundary layers existing between the matrix and the fibers of the composite. A new model, which includes the intermediate phase between the matrix and the fiber, called the mesophase, is considered in order to take into account the above-mentioned layers.     

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.     

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.     

On the relaxation of shear and normal stresses of viscoelastic fluids following constant shear rate experiments

By means of a cone and plate rheometer the relaxation of the shear stress and the first normal stress difference in polymer liquids upon cessation of a constant shear rate were examined. The experiments were conducted mostly in a high shear rate region of relevance for the processing of these materials. The relaxation behavior at these shear rates can only be measured accurately under extremely precise specifications of the rheometer. To determine under which conditions the integral normal thrust is a convenient measure for the relaxing local first normal stress difference the radial distribution of the pressure in the shear gap was measured. The shape of relaxation of both the shear stress and the first normal stress difference could be closely approximated for the entire measured shear rate and time range by a two parameter statistical function. In the range of measured shear rates, one of the parameters, the standard deviationS, is equal for the shear and the normal stress, and is independent of the shear rate within the limit of experimental error. The second parameter, the mean relaxation timet _50, of the shear stress andt _50, of the first normal stress difference, can be calculated approximately from the viscosity function and only a single relaxation experiment.     

Different behaviors of concentrated polysaccharide systems in large-amplitude oscillating shear fields

Two series of oscillatory flow tests were carried out on two concentrated polysaccharide systems (hydroxyethyl guar gum and scleroglucan) in order to evaluate the possibilities offered by large-deformation techniques for the discrimination between different classes of macromolecular systems (i.e., entanglement networks and weak gels). Frequently and strain sweeps, as well as combined steady and oscillatory shear tests were performed to analyze the influence of strain amplitude and of the superposed parallel shear rate on the dynamic properties of these materials.