Showing papers on "Rheometer published in 1970"

Simple shear flow round a rigid sphere: inertial effects and suspension rheology

Abstract: An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

Non‐Linear Behavior of Viscoelastic Materials. I. Disperse Systems of Polystyrene Solution and Carbon Black

Abstract: To determine non‐linear viscoelasticity parameters for disperse and high‐polymeric systems, some fundamental relations have been derived between these parameters and the experimental quantities by viscoelastometry, particularly with a torsionally oscillating rheometer, on the basis of the general theory presented by Green and Rivlin. The non‐linear viscoelasticity of several disperse systems consisting of polystyrene solutions and carbon black has been measured by means of the torsionally oscillating rheometer at various temperatures ranging from 100 to 170°C, and in a frequency range from 2×10−3 to 0.5 cycle per sec. As a result of harmonic analysis of the experimental results, it has been revealed that the resultant torque consists of the fundamental component and odd harmonics, and that the energy dissipated during one cycle is the same as that calculated from the fundamental component alone. Frequency dependence curves at various temperatures for G1′ and G1″, which correspond to G′ and G″ for linear v...

Rheometrical flow systems Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations

Abstract: Consideration is given to the flow of viscous and elastico-viscous liquids contained between two infinite parallel plates which rotate with the same angular velocity Ω about axes normal to the plates but not coincident. In the viscous case, it is shown that a simple exact solution of the relevant equations can be obtained. In the elastico-viscous case, certain formulae are derived which should facilitate the interpretation of experimental results obtained from the Maxwell orthogonal rheometer.

Rheological properties of suspensions of spheres in non-Newtonian media

Abstract: The results of an experimental investigation of the rheologioal properties of dilute suspensions of rigid spheres 100μm in diameter in non-Newtonian pseudoplastic liquids are reported. The shear flow properties of suspensions in a solution of polyisobutylene in tetralin, in aqueous solutions of polyacrylamide and sodium carboxymethylcellulose and in a Newtonian fluid have been investigated at solid concentrations up to 10% by volume. A concentric cylinder viscometer was used, results being corrected for end effects and variations in shear rate across the gap. Results for the Newtonian fluid were not inconsistent with published data. It was found that, within the range of variables investigated, for each of the non-Newtonian fluids the relative fluidity, comparing the suspension and the suspending fluid at the same shear stress, was a function of concentration only whereas the relative fluidity comparing the suspension and the fluid at the same shear rate depended on both concentration and shear rate. The fractional decrease in fluidity produced by a given concentration of spheres in polyisobutylene solution was about double that produced by the same concentration in any of the other fluids. In what are believed to be the first reported measurements of normal stress in suspensions, the first normal stress difference (p 11-p 22 for the fluids was derived from the normal force exerted on the cone of a Rheogoniometer during steady rotation. Over ranges of concentration and shear rate limited by experimental difficulties the ratio of shear rate to normal stress for the suspension divided by the corresponding quantity for the base solution appeared to be a function of concentration only when the liquids were compared at the same normal stress but not when compared at the same shear rate. However, this conclusion was less certain than the corresponding result for relative fluidity.

Orientation and Structure of Polyethylene Crystallized under the Orientation and Pressure Effects of a Pressure Capillary Viscometer

Abstract: A commercial high‐density polyethylene has been crystallized in the Instron Capillary Rheometer under the combined influence of pressure and orientation. A transparent high‐modulus, and highly oriented filament structure was produced. In order to determine quantitatively the degree of orientation, azimuthal x‐ray scans of the 002 reflection plane were used to obtain the orientation function of the orthorhombic unit cell relative to the flow axis in the rheometer (identified with the filament axis). A value of +0.996±0.002 was measured for this orientation function indicating that the backbones of the crystalline polyethylene chains were virtually aligned perfectly parallel to the flow axis of the rheometer. This report is concerned with the high‐resolution techniques required to measure such highly oriented samples. In conjunction with the x‐ray study, birefringence measurements are included which permit the determination of the orientation of the amorphous component as well as the crystalline component.

Effect of Internal Viscosity on the Deformation of a Linear Macromolecule in a Sheared Solution

Abstract: The deformation of macromolecules in a solution subjected to time‐dependent shear flow is described by means of a modified Rouse model. Into every segment of this model an internal viscosity force is introduced which is proportional to the rate at which the end‐to‐end distance of the segment is changed, and acts in the direction of the tie line between the end points. No a priori assumptions have been made on the motion of the segments themselves. An analytical solution for the distribution function of the segment lengths can now no longer be derived. At low values of the internal viscosity, an approximate solution can be obtained by means of a perturbation calculus. The effect of internal viscosity on the moments of the distribution function and, hence, on the average dimensions of the macromolecules, can be calculated. It appears that with constant shear flow at high rates of shear, as well as with oscillatory shear at high frequencies, an increase of the internal viscosity results in a decrease of the ...

The degradation of polystyrene during extrusion

Abstract: An investigation was made of the magnitude and mechanism of shear degradation of a narrow distribution, high molecular weight (Mw = 670,000) polystyrene. An Instron rheometer was used to perform the extrusion at temperatures from 164° to 250°C. The change in molecular weight distribution was studied by gel permeation chromatography. The maximum shear stress employed was 5.83 kg/cm2. It was found that degradation could be induced at high stress at temperatures of 50°C lower than degradation of polystyrene would occur exclusively due to thermal forces. An activation energy for the degradation, calculated at constant shear rate, was +20.2 kcal/mole. The direction and magnitude of this value are consistent with degradation induced through a mechanical reduced activation for thermal degradation.

Relations between steady flow and oscillatory shear measurements

Abstract: Results are given of a comparison between dynamic oscillatory and steady shear flow measurements with some polymer melts. Comparison of the steady shear flow viscosity,η, with the absolute value of the dynamic viscosity, ¦η¦, at equal values of the shear rate,q, and the circular frequency,ω, has shown the relation thatCox andHerz had found empirically to be substantially correct. Further, the coefficients of the normal stress differences obtained by streaming birefringence techniques have been compared with 2G′ (ω) ·ω − 2 in the same range of shear rates as covered by the viscosity measurements (G′ is the real part of the dynamic shear modulus). Two polystyrenes with narrow molecular weight distribution showed the same shift factor along theω orq axis for the normal stress coefficients with respect to 2G′ (ω) · ω − 2 and the steady shear flow viscosities with respect to the real part of the dynamic viscosity,η′. For two polyethylenes the results are not so conclusive owing to the smallness of the shift factor found. An empirical equation is proposed predicting the main normal stress difference from dynamic measurements only.

Oscillating disk rheometer

Abstract: Method and apparatus for determining the rheological properties of an elastomer which method comprises subjecting a sample of the elastomer enclosed under pressure in a non-circular chamber, the base of which is star-shaped or rectangular, to oscillating shearing stress and measuring the stress. Dynamic properties are determined by enclosing a sample of the elastomer under pressure in a chamber, subjecting it to oscillating shearing stress at high frequency to provide measurable difference in phase between stress and displacement, measuring the torque required to impose the shearing stress and simultaneously measuring displacement.

Rheometrical flow systems Part 1. Flow between concentric spheres rotating about different axes

Abstract: The flow of an elastico-viscous liquid contained between two concentric spheres which are rotating with the same angular velocity about axes passing through the centre of the spheres is considered. The angle between these axes is small. The solution is obtained by expanding the velocity components in terms of a small parameter α2, which is usually associated with problems involving oscillatory flows. The analysis is shown to have a direct application to the Balance Rheometer. In particular, it is shown that inertial effects in this rheometer are likely to be very small.

Rheometrical flow systems Part 3. Flow between rotating eccentric cylinders

Abstract: We give further consideration to flow situations which are steady in the sense that ∂/∂ t ≡ 0 but for which individual fluid elements are subjected to a small sinusoidal deformation. The particular situation studied involves the flow between eccentric circular cylinders which rotate about their axes with the same angular velocity Ω. The eccentricity is assumed to be small. It is shown that measurements of the force on the inner cylinder can be used to determine the complex dynamic viscosity of an elastico-viscous liquid. The theory provides the necessary mathematical background for the operation of a new commercial rheometer. Consideration is given to the possibility of ‘on-line’ use of such an instrument for control purposes.

Temperature dependence of the properties of low-density polyethylene

Abstract: The dynamic mechanical properties of low-density polyethylene melts were measured as a function of frequency and temperature using the Orthogonal Rheometer. These results were expressed in terms of the components G′ and G″ of the dynamic modulus and the components η′ and η″ of the dynamic viscosity. The functions J′, J″, η*, and G* were also calculated from the results. The method of reduced variables or time-temperature superpositions was attempted on the results. The classical method was found to require modification to be applied to these low-density polyethylenes. From this modified form of the reduced variables technique, the temperature dependence of the elastic and viscous parts of the response could be separated. The experimentally determined temperature dependence of the elastic part of the response was found not to be in accord with the accepted theory of rubber elasticity. The temperature dependence of the viscous part of the response is discussed in terms of the concept of flow activation energy, and clarification of this term is explored. It is concluded that the temperature dependent properties of polymer melts are best compared at equivalent time scales of response in the non-Newtonian region. In order to do this the temperature dependence of the elastic part of the response must be included explicitly in the reduction scheme.

Effect of long-chain branching on the relation between steady-flow and dynamic viscosity of polyethylene melts

Abstract: The steady-state viscosity η, the dynamic viscosity η′, and the storage modulus G′ of several high-density and low-density polyethylene melts were investigated by using the Instron rheometer and the Weissenberg rheogoniometer. The theoretical relation between the two viscosities as proposed earlier is:, where ; is the shear rate, H is the relaxation spectrum, τ is the relaxation time, , and . Good agreement between the experimental and calculated values was obtained, without any coordinate shift, for high-density polyethylenes as well as for a low density sample with low nw, the weight-average number of branch points per molecule. The correlation, however, was poor with low-density samples with large values of the long-chain branching index nw. This lack of coordination can be related to nw. The empirical relation of Cox and Merz failed in a similar way.

Shear Rate Dependent Relaxation Spectrum: Conversion from Dynamic Viscosity to Steady Flow Viscosity for Polyethylene Melts

Abstract: The steady flow viscosity η and the dynamic viscosity η′ of several linear polyethylene melts (190°C) were measured using the Weissenberg rheogoniometer and the Instron rheometer. In correlating the two viscosities, the use of Graessley's theory of viscosity in steady shearing flow in combination with the box distribution of relaxation times as suggested by Maruyama et al. has been critically examined. The new approach discussed in this paper uses Graessley's functions h(θ) and g(θ) in conjunction with the relaxation spectrum H(τ) derived from linear viscoelastic data using an iterative method. The required relation is η(γ)=∫H(τ)h(θ)g(θ)3/2τd ln τ, θ=γτ/2; where γ is the shear rate and τ is the relaxation time. Here g(θ)=(2/π) [cot−1 θ+θ/(1+θ2)] and k(θ)=(2/π) [cot−1 θ+θ (1−θ2)/(1+θ2)2]. A good agreement was obtained in all cases without involving any coordinate shift. The approach illustrated in this article enabled us to estimate quantitatively the effect of shear rate on the relaxation spectrum and ...

Transient and Steady State Rheological Properties of Very Dilute Drag Reducing Polymer Solutions

Abstract: Viscous and elastic rheological properties of three very dilute solutions (100 to 500 parts per million) of a commercial drag reducing high molecular weight Polyacrylamid in distilled water are presented. Shear stress (apparent viscosity) was determined over a shear rate range of about 107 (sec−1) by a combination of cone and plate, couette, and capillary tube viscometers, and the first normal stress difference was determined versus shear rate in the cone and plate geometry. Transient response (rebound) characteristics were determined in a unique, specially designed, transient rheometer. A “pseudo‐linear” interpretation of the results of these tests is made in which three fluid parameters, defined in terms of a linear viscoelastic model, are determined as a function of strain.

Modifications of an R‐16 Weissenberg Rheogoniometer

Abstract: In the course of our work on the characterization of materials by our kinetic interpretation of non‐Newtonian flow, it had become desirable to make measurements other than at steady state constant shear rate and the sudden application of a steady shear. The present paper describes four modifications we have made and used: (1) a torque detection system to eliminate upper cone motion during transient and oscillatory measurements; (2) measurements under both unsteady and steady state condition in a constant stress field; (3) a versatile and inexpensive oscillatory capability to allow both amplitude and frequency variation of nearly any wave form desired; and, finally, (4) the measurement of the primary normal force difference under any conditions, with essentially no change in gap setting. Examples of typical results on a concentrated polymer solution are presented.

Torque rheometer evaluation of polypropylene process stability

Abstract: A new method of treating torque rheometer test data has been developed. First, it involves converting the torque values measured over a range of temperatures to torques corresponding to a constant reference temperature. Then the log of the calculated torques is plotted against time. The method has been applied to several polypropylene grades, and the effects of numerous test variables have been explored. Correlations have been developed between torque rheometer data and fundamental polymer properties of viscosity and molecular weight. The method should also be applicable to polymers other than polypropylene.

Recoverable shear measurements in a parallel plate rheometerz

Abstract: A parallel plate rheometer has been devised which permits measurements of shear stresses of 102 to 105 dynes/sq.cm. and shear rates of 10−5 to 1 sec.−1. A linear, air lubricated bearing is used to align the apparatus, and a linear variable differential transformer is used to sense changes in position. With a sample of polyisobutylene and with several samples of poly(dimethyl siloxane), it has been established that a Hookean range exists for each sample at low stresses. Hooke's law in shear states that the modulus is independent of stress, where the modulus is defined as the ratio of the shear stress in steady, creeping flow to the strain which can be recovered after the stress is removed. Other conclusions supported by the present work are that the Hookean range does not extend to stresses which are high enough to cause non-Newtonian flow, that the modulus decreases with increasing molecular weight although not in direct proportion, and that a sample with a broad molecular weight distribution has a lower modulus than one with a narrow distribution.

A versatile recording couette‐type viscometer

Abstract: A coaxial-cylinder viscometer with novel drive, control, and recording features was developed. It is capable of measuring many of the rheological properties of fluid systems over a wide range of viscosities and shear rates. The instrument is load-independent and thermostatically controlled, and has good frequency response. The viscometer can be driven according to a variety of input wave forms either unidirectionally or in an oscillatory mode about zero with the output fed into an X-Y recorder. A continuous shear rate/shear stress flow curve can be obtained in less than 30 sec.

On the flow induced by a Maxwell-Chartoff rheometer

Abstract: Most steady-slale rheometcl's in use today utilize some form of viscometric flow, i.c., a flow which is dynamically equivalent to a plane steady simple shearing motion [1].1 Recently, there has been a grcat deal of interest in extending rheological studies to nonvi scometri c flows, such as the flow in a Maxwell-ChartofI rheometer [2-5:1. This apparatus is basically a pair of parallel plates rotat· ing steadily and in the same sense about noneoineident r axes perpendicular to the plates. The test sample is placed between the plates and rotates with them and must consequently undergo some shearing. A flow has been proposed [41 which is supposed to take place in the MaxwelI·Cha rtofl rheometer, and which '\" has been studied in considerab le detail along with its rheological consequences [5, 61. In this proposed flow the \\material particles travel within planes parallel to the confining planes and describe circles about a center on the straight line connecting the cen ters of rotation of the confini ng planes. Thus, the material forms a cylinder whose cross section perpendicular to its generators is an \" ellipse. This flow can be described by the following deformation

The flow characteristics of highly viscous elastic fluids.

Abstract: The flow properties of several polymer melts have been investigated in steady shear flow and when shear flow was applied or removed. The results have been compared with the predictions of three rheological equations of state which have been proposed to describe the behaviour of elastic fluids. In steady shear flow the viscosity eta and the normal stress differences alpha1 and alpha2 have been determined for two polyisobutylenes (Vistanex LM-MH and Vistanex LM-MS) and a depolymerised natural rubber (Lorival R25). There is some disagreement about the magnitude of alpha2 and the main objective was to determine if it was zero or not. The data were obtained from total thrust and torque measurements in a Weissenberg Rheogoniometer using cone-plate and parallel plate geometries. For the polyisobutylenes alpha2 was negative but small compared with alpha1; the ratio |alpha[2]/alpha[1]| was less than 0.3. The Lorival R25 data were not inconsistent with these conclusions. Attempts have been made to measure stress relaxation on the cessation of shear flow and stress growth at the onset of shear flow. The measurements were carried out on the Weissenberg Rheogoniometer. For Vistanex LM-MH the form of the relaxation depended on the stiffness of the torque measuring system. This is shown to be due to illdefined boundary conditions for transient measurements with high viscosity fluids. However reliable data could be obtained on the lower viscosity polyisobutylene (Vistanex LM-MS) provided a stiff torsion bar was used. For this material the shear stress relaxation and growth were more rapid as the shear rate increased. The normal stress transient measurements were unreliable but it appeared that relaxation and growth times for p[21] were less than for alpha1. A cone-plate rheometer, which can measure the steady shear viscosity and elastic recovery of polymer melts, is described. The form of the recovery curve can also be obtained. A constant shear stress is applied to the sample and the resultant rotation and recovery when the stress is removed are measured by a capacitance technique. Data obtained on the two polyisobutylenes are reported. It is shown that the Weissenberg and Lodge theories of elastic recovery are not valid. Die swell measurements have been carried out on an elastic fluid (Lorival R25) and a high viscosity Newtonian fluid (Paralac 385, a modified alkyd resin). The measurements were made on a capillary rheometer at shear rates below 1 sec[-1]. Both fluids showed a significant amount of die swell. For the Newtonian fluid the average die swell was 13.5% and independent of the capillary radius, viscosity and volume rate of flow. Die swell increased with shear rate for the elastic fluid but did not depend on the capillary radius, and at low shear rates was asymptotic to the Newtonian value. It is shown that the momentum balance theory of die swell is not appropriate to high viscosity fluids of any type. The data obtained on the two polyisobutylenes have been compared with the predictions of the WJFLMB, OWFS and Kaye integral rheological equations of state. The OWFS theory is not an appropriate model for high viscosity elastic fluids such as polymer melts. It predicts elastic recovery values which are much too high and in stress growth experiments it is incapable of predicting stress overshoot which has been reported in the literature. The agreement between theory and experiment for the WJFLMB and Kaye models is reasonable for steady shear flow, stress relaxation, stress growth and total elastic recovery. However these theories do not describe the form of the recovery curve well. Both the WJFLMB and Kaye models predict stress overshoot in stress growth experiments at high shear rates. There is some evidence that the Kaye theory might be a more useful model than the WJFLMB theory in some applications.