Showing papers in "Rheologica Acta in 1973"

On the behaviour of a sphere in the laminar tube flows

Abstract: The behaviour of a spherical particle in the no flow system and the laminar flow system was studied experimentally, using the square- and circular-section tube. And, the following facts became evident: Besides, on the mechanism of the tubular pinch effect, a proposal was done on the basis of the observed results.

Testing of a constitutive equation for entangled networks by elongational and shear data of polymer melts

Abstract: An entangled network such as a polymer melt or a concentrated solution is here described by a set of two simultaneous equations. One of them is a balance of entanglements, the other gives the stress in the classical form of aMaxwell equation.

Isotropic composites with elastic or viscoelastic phases: General bounds for the moduli and solutions for special geometries

Abstract: General bounds on the moduli of isotropic composites of two isotropic and purely elastic phases have been obtained byHill, Hashin andShtriknan, andWalpole. It may be shown that, in most cases of importance, these are best possible bounds for arbitrary phase geometry. Bounds can also be found for the real and imaginary parts of the complex moduli of composites with viscoelastic phases. In all cases, however, the bounds are wide when the moduli of the phases are very different, so phase geometry must be taken into account in order to obtain results of practical value. Calculations of rigidity are therefore made for incompressible composites in which one phase forms spherical inclusions in the other. An exact formula is obtained for a case in which the size distribution of these inclusions is very wide, and approximate formulae for two cases of inclusions of uniform size (nearest-neighbour distance being a maximum in the one and a minimum in the other). These have been applied in a study of the frequency variation of the real part of the rigidity and the loss tangent of a composite of equal volumes of two viscoelastic phases, each having sharp loss-tangent peaks at different frequencies. The effect of variations in the spatial distribution and size distribution of the inclusions can be inferred from the results, as well as the effect of phase inversion.

Comparison of network theory predictions with stress/time data in shear and elongation for a low-density polyethylene melt

Abstract: Experimental data are presented which show the variation with time of the shear stress and primary normal stress difference during shear flow with a stepfunction shear rate; the material (“Melt I” at 150 °C) is a low-density polyethylene melt for which stress-growth and elastic recovery data in elongational flow experiments have been previously reported. A method of comparing the data with the predictions of the rubberlike-liquid constitutive equations is given, based on the use of a specially-chosen rate-of-strain invariantIIV, defined in [4.1]. From this comparison, it is shown that the disagreement between theory and experiment is about the same for shear flow and for elongational flow, and that the extent of disagreement does not exceed 10% for short-duration flows such thatIIVt ⩽ 3.

Numerical solutions of some unsteady flows of elastico-viscous liquids

Abstract: Consideration is given to the rectilinear flow of anOldroyd model fluid in a straight pipe of circular cross-section. A numerical solution of the full non-linear equations is obtained without the necessity for a perturbation analysis in terms of some small parameter. Results are presented for a number of different flow conditions.

Critical regimes of deformation of liquid polymeric systems

Abstract: The principal peculiarity of typical polymers at temperatures above the glass-transition region and the melting point is their ability to exist in two physical states — fluid and high-elastic (rubbery). Accordingly, they manifest two main relaxation mechanisms. In the fluid state, irreversible displacement of the centres of gravity of macromolecules relative to each other is possible, and irreversible deformations may be infinitely large. In the high-elastic (rubbery) state, the determining role is played by rapid changes in the spatial arrangement of groups of atoms forming the macromolecular chain, and this enables it to unwind, thereby accumulating a considerable amount of reversible (high-elastic) deformation. In the fluid state polymers manifest both relaxation mechanisms, and during the flow they may accumulate large amounts of reversible deformations.

A rheometer for oscillatory studies of nonlinear fluids

Abstract: This paper describes the coupling of a minicomputer with two rotational rheometers. In the first instance, the computer acquires output data from aWeissenberg Rheogoniometer in oscillatory shear, andFourier-analyzes stress and strain signals. The second instance utilizes a rotational rheometer specifically designed to be controlled by the computer, employing a servo-driven torque motor. The computer-rheometer system is used to analyze steady-state non-Newtonian viscosity and linear viscoelasticity, as well as non-linear dynamic behavior.

The viscosity of concentrated polymer solutions: Corresponding states principles

Abstract: The concern of this paper is the zero shear viscosity in the concentration region bridging the highly dilute system, where the properties of the isolated solute particle or molecule and its interaction with the solvent medium are the determining factors, and the dense fluid, formed by the polymer melt or closely packed suspension. In the former domain, Einsteins point of view, i.e., the consideration of difference effects, arising from a hydrodynamic perturbation of the solvent flow by suspended particles, has governed subsequent theoretical work for all types of macrosolutes.

The entropy problem in thermodynamics of processes

Abstract: When building up thermodynamics of continuous matter, one of the main points is, of course, that the concepts to be used are clearly developed and generally accepted so that one knows what one is talking about. Such can be done only by using the available experience. The development of the concepts cannot be separated from laying down the basic laws which also can be inferred from experiments only.

The anisotropy of simple shearing flow

Abstract: The optical analogue of the second normal stress difference, namely,n 22 –n 33 has been measured for several polymer systems. The experimental method is direct and makes use of capillary and slit dies. For the polymer melts examined — ranging from a polystyrene with a viscosity of 104 Ns/m2 to a PIB of viscosity 50 Ns/m2 — a non-zero (n 22 –n 33) was found which could not be accounted for by any systematic errors. Except for one case, where (n 11 –n 22) could not be evaluated, the ratio (n 22 –n 33)/(n 11 –n 22) was found to be negative with an absolute value of 0.05 to about 0.1. For solutions the results are not clear-cut: in several casesn 22 –n 33 was immeasurably small but in one case (23% PIB in oil) the above ratio was the same as for the melts. A modification of the (dilute solution) molecular theories is suggested which is qualitatively able to describe most of the experimental results here outlined.

A concentric-cylinder rheometer for polymer melts

Abstract: If one wishes to measure the viscosity of a polymer melt at high shear rates there are substantial fluid dynamical and heat transfer difficulties. Cone-plate instruments are limited because of secondary flows and because the fluid tends to leave the gap. In capillary-flow instruments, there are substantial radial temperature gradients and the possibility of flow irregularities.

A differential form of constitutive relation for thixotropy

Abstract: A differential form of constitutive equation for the thixotropy $$\dot F = \alpha (F,D)\dot D + \beta (F,D)$$ (whereF is the shear stress,D the shear rate,\(\dot F\) and\(\dot D\) the time derivatives, andα andβ are material functions), is derived from the structural constitutive equations ofCheng andEvans (1965). The restrictions on the forms ofα andβ are discussed and the ways in which they may be determined using the cone-and-plate and coaxial cylinder viscometers are described. The use of the equation in the prediction of industrial problems such as pipeline flow and sagging and levelling of films and coatings are indicated.

Pressure development in a non-Newtonian flow through a tapered tube

Abstract: The flow of viscous fluids through a tapered tube is very interesting from the standpoint of blood flow in blood vessels. The taper of the tube is an important factor in the pressure development. In the first place, we have given a brief summary of our theory of the steady convergent flow of non-Newtonian fluids characterized by an arbitrary time-independent flow curve through a slightly tapered tube. Based on our general formula for the flow per unit time, explicit formulae of the pressure gradient are obtained in several cases of non-Newtonian fluids specified by particular flow curves: power law fluid,Bingham body, and the fluid obeyingCassons equation. In all these cases it is shown that the pressure gradient is not constant along the axis but increases with decrease in the radius of the tapered tube. If we neglect quantities of orderα 2 (α: angle of taper), then the pressure gradient increases linearly with the distance along the axis of the tube.

Memory effects in a non-uniform flow: A study of the behaviour of a tubular film of viscoelastic fluid

Abstract: The process is used for the manufacture of a thin sheet or film of a thermoplastic material (e. g. polyethylene) from molten material supplied under pressure by a screw extruder. The polymer melt is forced through an annular die and the tubular film so formed is thinned both by blowing and by axial drawing. The tube is formed into a closed bubble by flattening it when it is cool enough to avoid blocking (the tendency of the film to stick to itself) and then the flattened film is wound onto take-up rolls. The axial tension is provided by the driven nip rolls which close the bubble at the top (the process is usually run vertically with the die at the bottom). The blowing is caused by maintaining an air pressure slightly above atmospheric inside the bubble, and this causes an increase in the radius of the tube and stretching of the film in a circumferential direction. Fig. 1 illustrates the process schematically.

The orientation of liquid crystals by temperature gradients

Abstract: It was reported by Stewart (1) that when the liquid crystal p-azoxyanisole was placed in a vertical temperature gradient the molecular orientation adopted was vertical when the higher temperature was at the bottom and horizontal when the higher temperature was at the top These observations were confirmed by Holland and Stewart (2), Stewart, Holland, and Reynolds (3), and Stewart (4), the latter stressing that the horizontal orientation was not produced by convection currents; in fact the horizontal orientation was observed only when the vertical convection currents were reduced as much as possible More recently, Picot and Fredrickson (5) und Fisher and Fredrickson (6) have doubted that a temperature gradient can exert an orienting influence, while Patharkor, Rajan, and Picot (7) give experimental evidence suggesting that such an influence may exist

Theoretical studies of a suspension of rigid particles affected by Brownian couples

Abstract: In this paper we briefly review the present theoretical understanding of a suspension of particles whose orientation is affected by rotational Brownian motion. The particles are rigid, axially symmetric, sufficiently small so that they and their disturbance flow are inertialess and not acted upon by external body forces or couples. The suspension is dilute so that there are no important hydrodynamic interactions between the particles and is examined for a flow with a sufficiently large length scale that the concept of an equivalent homogeneous material — the bulk suspension — is meaningful. The orientation state of the particles in the suspension is determined by a competition between the random Brownian rotations and the tendency to preferred alignment induced by the gradient in the bulk deformation rate for the suspension. We are interested in the resulting rheological behaviour.

On the use of the rolling-ball viscometer for the measurement of rheological parameters of power law fluids

Abstract: An attempt has been made to determine the flow curve of fluids obeying the power law rheological model on a rolling ball viscometer. The theoretical analysis is based on the hydrodynamical model developed byLewis in 1956 for the purpose of rolling ball viscometer calibration and extended in 1964 byTurian andBird for the two-parametric power law model. The shear rate variation has been accomplished on varying the tube angle of inclination. Experiments performed on an adapted, commercialHoeppler viscometer with aqueous solutions of carboxymethylcellulose and polyacrylamide reproduced the flow curves obtained simultaneously on rotational and capillary instruments with reasonable accuracy.

Helical flow of molten polymers in a cylindrical annulus

Abstract: The paper is concerned with an analytical investigation of helical flow of a non-Newtonian fluid through an annulus with a rotating inner cylinder. The shear dependence of viscosity is described by a power law and the temperature dependence by an exponential function. Velocity and temperature profiles, energy input and shear along the stream lines, pressure drop, and torque are presented for the range of input parameters encountered in polymer extrusion. The results of the study can be applied to a mixing element in a screw extruder and for a device to control extrudate temperature and output.

Steady shear measurement of thixotropic fluid properties

Abstract: Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity

General characteristics of the visco-elastic properties of flexible-chain polymer solutions over a wide range of concentrations

Abstract: The paper summarizes the ideas and results of investigations of viscous and high-elastic properties of polymer solutions in the whole interval of concentrations, chemical structure of the polymers used and the “goodness” of the solvents tried being varied in wide ranges.

Rheological properties of alkali borate glasses

Abstract: A survey is given of the recent work in the Department of Inorganic Chemistry of the Eindhoven University of Technology on the rheological properties of alkali borate glasses.

Plane mechanics and kinematics of compressible ideal granular materials

Abstract: The question of the correct formulation of constitutive equations to describe the mechanical and kinematic behaviour of granular materials such as soils and powders remains one of discussion and controversy. The purpose of this paper is to make some contributions to this discussion with particular reference to compressible materials. To this end we put forward some suggestions for consideration, while recognising the existence of alternative approaches to the problems discussed, and of differences of opinion which remain to be resolved.

Rheology of network forming systems

Abstract: The curing reactions of an epoxy-anhydride and a rubber vulcanization system were followed by rheological means. Dynamic shear measurements were used to follow the reaction. The rheological quantities were related to the reaction kinetics of the systems. From these relations, overall activation energies, reaction orders and rate constants were interpreted from the data. These compare favorably with results reported in the literature. The cures of several diallyl phthalate compounds were also examined with dynamic shear measurements. The results correlated well with thermoset molding experience.

Rates of shear in coaxial cylinder viscometers

Abstract: A common geometry used in rotational viscometry consists of two concentric cylinders in which the test fluid is sheared in the annulus between the cylinders. In this type of instrument the calculation of the shear stress from the measured torque is straightforward but the determination of the corresponding rate of shear is a difficult problem unless the type of fluid behavior, e.g. power law, is known a priori. The equation of motion may be solved (1) analytically for the special case of power-law behavior but a completely general analysis results in an expression for the difference in the rates of shear at the two surfaces (2).

Fluides viscoélastiques non linéaires satisfaisant à un principe de superposition étude théorique et experimentale

Abstract: This study is devoted to incompressible viscoelastic fluids in which a superposition principle for stress is assumed. In order to respect the material objectivity, this summation of incremental stress, with corresponding memory factor, is operated in a rheological (corotational) frame. Theoretical study for these fluids in viscometric flows was conducted up to explicit solutions. This study shows some impossibility ranges for such flows. The determination of the memory functions from this type of flow involvesFourier transform and so, would need the knowledge of all the kinematic range, and this is impossible.

The measurements of normal stress differences in a cone-and-plate rheogoniometer using flush-mounted pressure transducers

Abstract: The paper out lines an attempt to measure the second normal-stress difference in a simple shear flow using flush-mounted pressure transducers. The main conclusions reached are

Thermal stresses during annealing of a glass ribbon

Abstract: In order to avoid fracture and to keep transient and residual stresses within acceptable bounds, it is necessary to include in the continuous process of glass forming an annealing phase, during which the temperature of the sheet is slowly brought from approximately 600 °C down to 25 °C. An adequate control of the annealing gallery requests a good understanding of the stress generation during cooling. The problem is quite complex, since the prediction of stresses is intimately related to the thermo-viscoelastic character of glass. Moreover, stress relaxation is accompanied by structural relaxation, which is strongly dependent upon temperature history.

A calorimetric measurement of frictional heat in capillary rheometry of polymer melts

Abstract: A viscometer is described in which the capillary wall temperature is controlled by an adjustable low voltage current directly flowing through the thin tube wall

The effect of pressure on the shear viscosity of polymer melts

Abstract: The shear viscosity of fluids in general, and polymer melts in particular, depends on temperature, pressure, and shear rate. Although the effects of temperature and shear rate have been studied extensively for a large number of polymer types, only recently methods have been devised to study the effect of pressure. As a result of these studies, it has been found that the effect of pressure on the shear viscosity of polymer melts is quite significant. Furthermore, the effect of viscous heating on the determination of viscosity from capillary measurements has been recognized, and some attempts have been made to make corrections for this effect (1, 2).

The shape of a liquid surface between rotating concentric cylinders

Abstract: The purpose of this paper is to calculate the shape of the top free surface of a non-Newtonian, liquid which is contained between axially rotating cylinders which have a common vertical axis. We shall consider the case in which the outer cylinder is stationary and the inner cylinder rotates with an angular velocity Ω. This is the flow situation described by Weissenberg (Nature 159, 310, 1947) and for most non-Newtonian liquids, on rotation, the liquid rises near the inner cylinder and falls near the outer. This effect is now generally known as the Weissenberg effect. Inertial forces alone would, of course, produce a fall at the inner and a rise at the outer cylinder.