Showing papers in "Rheologica Acta in 1984"

Flow of a viscoelastic fluid over a stretching sheet

Abstract: This paper presents a study of the flow of an incompressible second-order fluid past a stretching sheet. The problem has a bearing on some polymer processing application such as the continuous extrusion of a polymer sheet from a die.

Thermal contraction and volume relaxation of amorphous polymers

Abstract: Two experimental techniques are described for the determination of the change of specific volume of polymers with temperature and aging time, which allow measurements between − 160 °C and + 200 °C. Four technical amorphous polymers, PS, PVC, PMMA and PC have been investigated. Volume-temperature curves under constant rate of cooling are presented and interpreted with respect to relaxation processes known from other physical investigations. The rate dependence of dilatometric glass transition temperatures is compared with the time dependence of rheometric glass transition temperatures from shear creep data. Volume relaxation data at constant aging temperature are presented. Aging is found to proceed until very low temperatures in the glassy state for e.g. PMMA.

Viscosity of suspensions modeled with a shear-dependent maximum packing fraction

Abstract: A large amount of data from the literature on viscosity of concentrated suspensions of rigid spherical particles are analyzed to support the new concept that the maximum packing fraction (ϕ M ) is shear-dependent. Incorporation of this behavior in a rheological model for viscosity (η) as a function of particle volume fraction (ϕ) succeeds in describing virtually all non-Newtonian effects over the entire concentration range and also accounts for a yield stress. The most successful model is one proposed by Krieger and Dougherty for Newtonian viscosities,η (ϕ, ϕ M ), but withϕ M varying from a low-shear limitϕ M0 to a high-shear limitϕ M∞. Microstructural interpretations of this behavior are advanced, with arguments suggesting that similar rheological models should apply to suspensions of nonspherical and irregular particles.

Electric fields in the rheology of disperse systems

Abstract: In the present survey, the influence of electric fields on the structure and rheological properties of disperse systems as well as the effect of deformations on their electrical characteristics are discussed. The properties of these systems are considered in terms of the dielectric permittivity and electrification potential. The considerable thickness of the double electric layer around the disperse phase particles, which is characteristic of disperse systems with nonpolar hydrocarbon dispersion media, provides the possibility for strong electric fields to produce an electric nonuniformity on the surface of the disperse phase particles. The formation of hydrate layers on the particles creates the possibility of polarization of the disperse phase. In plastic disperse systems such as greases, a strong orientation effect is observed, which contributes to the creation of frozen flow patterns when the flow is suddenly stopped. The survey is concluded with a consideration of the process of formation of chain structures in the direction of the lines of force of the electric field whose orientation is normal to the direction of flow, which can lead to complete stoppage of the flow.

The shear viscosity dependence on concentration, molecular weight, and shear rate of polystyrene solutions

Abstract: The solution viscosity of narrow molecular weight distribution polystyrene samples dissolved in toluene and trans-decalin was investigated. The effect of polymer concentration, molecular weight and shear rate on viscosity was determined. The molecular weights lay between 5 ⋅ 104 and 24 ⋅ 106 and the concentrations covered a range of values below and above the critical valuec*, at which the macromolecular coils begin to overlap. Flow curves were generated for the solutions studied by plotting logη versus log\(\dot \gamma \). Different molecular weights were found to have the same viscosity in the non-Newtonian region of the flow curves and follow a straight line with a slope of − 0.83. A plot of logη0 versus logMw for 3 wt-% polystyrene in toluene showed a slope of approximately 3.4 in the high molecular weight regime. Increasing the shear rate resulted in a viscosity that was independent of molecular weight. The sloped (logη)/d (logMw) was found to be zero for molecular weights at which the corresponding viscosities lay on the straight line in the power-law region.

The rheological behavior of flexible-chain polymers in the region of high shear rates and stresses, the critical process of spurting, and supercritical conditions of their movement at T > Tg

Abstract: Methods of capillary viscometry were used in studying the rheological properties and behavior of a broad range of rubbers, including polymers with narrow and wide molecular-weight-distribution as well as commercial rubber grades, at widely varying shear rates and stresses. As is shown, in full conformity with the previously conducted experiments, during transition from a fluid to highelastic (quasi-cross-linked) state, they are chracterized by spurting followed by sliding over the channel walls. This relaxation transition is characterized by a critical shear stress value invariant with respect to the molecular weight, molecularweight distribution and temperature. The parameters defining spurting of polymer flow as a function of molecular-weight characteristics, temperature, and channel geometry have been investigated in detail. It is shown for the first time that under supercritical conditions the rate of polymer flow through channels does not depend, in the first approximation, on the molecular weight of the polymer, its molecularweight distribution, temperature, and filling, but is determined only by the shear stress.

Shear flow rheological properties of Vinylon- and glass-fiber reinforced polyethylene melts

Abstract: Shear viscosity, shear stress and first normal-stress difference have been investigated for glass- and vinylon-fiber filled polyethylene melts over a wide range of shear rate by means of three kinds of instruments. The influence of fiber content and fiber properties on the rheological properties is discussed. The viscosity increases with increasing aspect ratio and fiber content, and the influence of these parameters on the flow properties is evident at low shear rates. The first normalstress difference increases more rapidly with increasing glass fiber content, especially at low shear stresses. The influence of vinylon fibers on the first normal stress-difference vs. shear-stress relationship is different from that of glass fibers.

On physical criteria for the selection of wood for soundboards of musical instruments

Abstract: In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE′, static Young's modulusE, internal frictionQ −1 in longitudinal direction, and specific gravityγ for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ −1/(E′/γ), and that there were very high correlations betweenQ −1/(E′/γ) andE′/γ, and betweenE′ andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/γ, which can be measured easily, and it was derived that the relation betweenE′/γ andQ −1 of wood could be expressed by an exponential equation regardless of wood species.

Impulsive motion of a flat plate in a Rivlin-Ericksen fluid

Abstract: The problem of the impulsive motion of a flat plate in a Rivlin-Ericksen fluid is reconsidered. An exact solution for the velocity distribution is found in terms of a definite integral. It is shown that a solution obtained earlier does not satisfy the boundary condition at the plate in the sense of generalized functions.

Heterogene Widerstandsverminderung bei turbulenten Rohrströmungen

Abstract: Es wird uber Experimente berichtet, bei denen eine viskoelastische Flussigkeit in die Achse einer ausgebildeten turbulenten Rohrstromung eines newtonschen Fluids injiziert wurde. Bei der Injektion von hoher konzentrierter Polymerlosung tritt eine deutliche Widerstandsverminderung auch dann auf, wenn die Losung als elastischer Faden im Kernbereich mitgefuhrt wird, d. h. das Polymer noch nicht merklich in die wandnahe Schicht hineindiffundiert ist. Es werden Ergebnisse uber die Veranderung des Druckabfalls langs des Rohres in Abhangigkeit von der Gesamtkonzentration des Polymers im Rohr, der Konzentration im injizierten Faden und der Reynoldszahl mitgeteilt und diskutiert. Weiterhin werden die Profile der Hauptstromung, der Turbulenzintensitaten in radialer und axialer Richtung sowie der Reynoldsschen Schubspannungen bei solchen Injektionsexperimenten bestimmt und mit denjenigen des reinen Losungsmittels sowie einer homogenen Polymerlosung von gleicher, uber den Rohrquerschnitt gemittelter Polymerkonzentration verglichen. Der Verlauf des dimensionslosen Geschwindigkeitsprofils und der Reynoldschen Schubspannungen zeigt, das der Ubergangsbereich zwischen viskoser Unterschicht und turbulentem Kern bei der Injektion wesentlich anders strukturiert ist als beim Vorliegen von homogener Widerstandsverminderung. Er ist sowohl im Vergleich zu einer newtonschen Flussigkeit als auch zu einer homogenen Polymerlosung deutlich vergrosert, und es findet in ihm eine drastische Reduzierung der Reynoldsschen Schubspannungen statt. Die beobachtete Struktur der turbulenten Stromung deutet in Verbindung mit den gemessenen viskoelastischen Eigenschaften der injizierten Polymerlosung darauf hin, das die grosen Turbulenzelemente durch den Polymerfaden in ihrer Bewegung behindert werden. Infolgedessen ubertragen sie weniger Energie auf die die Dissipation bewirkenden kleinen Wirbel, wodurch sich eine Widerstandsverminderung ergibt.

Dynamic flow properties of vinylon fibre and glass fiber reinforced polyethylene melts

Abstract: An experimental study of the dynamic shear flow properties of polyethylene melts filled with glass fibers and vinylon fibers was carried out and comparison with the steady shear flow properties was made. The effects of loading level and the characteristics of the fibers on the rheological properties of the fiber-filled systems is discussed. The rigidity and complex viscosity of the fiber-filled systems is sensitive not only to the quantity of fibers but also to their length, distribution and properties. The Cox-Merz empirical law for complex viscosity and steady shear viscosity, and Roscoe's empirical relation for estimating the normal-stress coefficients are both able to be applied to pure polymer melts but not to fiber-filled systems.

Precise viscosity measurements of Newtonian liquids withv < 1 mm2/s for the selection of suitable standards

Abstract: The application of long capillary Ubbelohde viscometers in the determination of low viscosities is described. Corrections and measurement uncertainties are discussed. Viscosity and density data are given for 18 Newtonian liquids of commercially available purity, with viscosities below about 1 mm2/s. For several liquids the commonly used purity specifications were found to be sufficient to qualify these liquids as viscosity standards, which can be used for viscometer calibration.

Torsion pendula with electromagnetic drive and detection system for measuring the complex shear modulus of liquids in the frequency range 80–2500 Hz

Abstract: An apparatus for the measurement of liquid complex shear viscosity in the frequency range 80–2500 Hz, with the use of a torsion pendulum operating in forced oscillation, is described. The drive and detection system consists of a magnet inside the pendulum, two excitation and two measuring coils. The determination of the complex shear viscosity is based on the measurement of the resonance frequency and the damping of the torsion pendulum. The feasibility of this method is demonstrated with a number of Newtonian liquids in the viscosity range 0.3 to 60 m Pa s. Results for a viscoelastic polymer solution are presented. A comparison is made with other apparatus working in the same frequency range.

Rheological behaviour of a commercial TGDDM-DDS based epoxy matrix during the isothermal cure

Abstract: The change of the viscosity profile during the isothermal cure of a commercially available epoxy system commonly used as a matrix for high performance composites, TGDDM-DDS from CIBA, has been obtained by means of both a constant shear rate viscometer and a dynamic one. The range of temperature investigated varied from 120 up to 180°C. The increase of the molecular weight during the cure reaction is reflected on a macroscopic level in a progressive linear increase of the logarithm of the shear viscosity up to a critical point, near gelation, where an upturn is observed. The values of the time and viscosity at the critical point have been used to normalize the experimental data in a single generalized curve of the cure-viscosity profile. The William, Landel and Ferry equation has been found to adequately describe the temperature dependence of the viscosity for systems in the range of temperatures where the cure reaction did not occur. The apparent activation energy of the cure reaction, 19.7 Kcal/mole, obtained from the critical times, is consistent with calorimetric determinations.

On hydrodynamic boundary conditions for microstructural fluids

Abstract: Various types of boundary conditions used when investigating microrotation are analysed. A boundary condition for studying microstructural fluid flows, which depends on experimental parameters, is suggested. To illustrate the result, expressions are derived for the velocity and microrotation of a micropolar fluid between two coaxial cylinders with a constant relative speed of rotation.

Dynamic shear properties of a technical polystyrene melt

Abstract: A dynamic viscometer of the Couette type is described which permits the determination of storage and loss shear modulus of polymer melts with high accuracy. For a technical polystyrene, results of measurements of storage and loss moduli are reported in the temperature interval between the rubbery plateau and degradation. From these data, the courses of storage and loss compliances and the course of the time-dependent shear compliance are derived and compared with the results of creep measurements.

Macromolecules in nonhomogeneous flow fields: a general study for dumbbell model macromolecules

Abstract: The hydrodynamics of bead-spring model macromolecules in nonhomogeneous flows has recently been worked out. By taking a non-infinite distance between the beads (relative to the bead size) into account a hydrodynamic driving force was found. In this paper we explore the kinetic theory consequence of that force and show that non-uniform (polymer) concentration profiles are to be expected in nonhomogeneous flows. The diffusion equation for a dilute polymer solution is derived from the continuity equation for the distribution function. Arguments, leading to a well-ordered pertubation expansion of the continuity equation are advanced and the zeroth order function of this hierarchy is studied for models with linear springs. Details for the channel flow system are worked out with special emphasis on the relation between the polymer concentration and the parameters of the system. Explicit results are presented for models with linear springs. It is shown that if the Oseen tensor is not preaveraged, inadmissible results emerge.

The dynamic and steady shear properties of synovial fluid and of the components making up synovial fluid

Abstract: Steady-shear and dynamic properties of a pooled sample of cattle synovial fluid have been measured using techniques developed for low viscosity fluids. The rheological properties of synovial fluid were found to exhibit typical viscoelastic behaviour and can be described by the Carreau type A rheological model. Typical model parameters for the fluid are given; these may be useful for the analysis of the complex flow problems of joint lubrication.

The BKZ as an alternative to the Wagner model for fitting shear and elongational flow data of an LDPE melt

Abstract: For the low density polyethylene Melt I, which is the melt for which the most complete set of shear and elongational data exists, the semi-empirical single integral Wagner model gives an excellent data-fit, but suffers the drawback of having no entropic constitutive equation, that is a relationship between strain history and elastic free energy from which viscous heating and cohesive failure can be predicted. We show here that the BKZ model, which does possess an entropic constitutive equation, gives as good a fit as does the Wagner model to both the shear and elongational data.

The charged dumbbell model for dilute polyelectrolyte solutions in strong flows

Abstract: A charged dumbbell model is used to investigate the behavior of dilute polyelectrolyte solutions in a general linear two-dimensional flow. The model studied has a nonlinear spring, conformation dependent friction and a Coulombic repulsive force due to an effective electrostatic charge on the two beads. The relative importance of the electrostatic charge is reflected by an effective charge density parameter,E. Equilibrium properties such as end-to-end distance and intrinsic viscosity are strongly dependent onE. In strong flows, which produce a dramatic increase in the dumbbell dimensions (a coil-stretch transition), the onset behavior is influenced byE. IncreasingE causes the onset velocity gradient to shift to much lower values. Large values ofE change the qualitative behavior to that of rigid (or slightly extensible) macromolecules or fibers. Results are presented for a charged dumbbell at equilibrium, in steady flows, and in transient flows.

A study of conformation-dependent friction in a dumbbell model for dilute solutions

Abstract: We consider predictions of rheological behavior in a variety of shear and extensional flows for an elastic dumbbell model with a nonlinear spring, and conformation-dependent hydrodynamic properties. The latter include a conformation-dependent anisotropic bead friction coefficient, and a related conformation-dependent degree of inefficiency for rotation in straining flows. With these features, the dumbbell exhibits hydrodynamic behavior consistent with a particle of finite axis ratio over the complete set of possible polymer conformations, from random-coil to a fully extended thread-like configuration. The predicted rheological behavior in shear flow is improved, relative to data, by the inclusion of anisotropy and strain-inefficiency in the frictional properties of the model, while other desirable features such as the sudden onset of fully extended states at a critical value of the velocity gradient, the presence of a hysteresis-loop in end-to-end dimension as a function of the velocity gradient, and the correlation of end-to-end distance (or birefringence) with the eigenvalue of the velocity gradient tensor for a wide variety of two-dimensional flows, are maintained.

A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

Abstract: In this paper, Poiseuille flow of a polar fluid (model of a red blood cell suspension) under various boundary conditions at the wall, viz., slip or no-slip in the axial velocity and couple stresses zero or non-zero at the boundary, is considered from the point of view of its applications to blood flow. Analytic expressions for axial and rotational velocities, flow rate, effective viscosity and stresses are obtained. The magnitudes of the length ratioL and the coupling number N are determined in accordance with concentration and tube radius (in the existing literature, values ofL andN are chosen arbitrarily). Velocity profiles (both axial and rotational) and the variation of the effective viscosity with concentration, tube radius and for various values of the boundary condition parameters are shown graphically. The analytic results obtained are compared with experimental results (for blood flow). It is found that they are in a reasonably good agreement. The effective viscosity exhibits the Inverse Fahraeus-Lindquist Effect in all the cases (including the slip or no-slip in the velocity fields). A method is given for determining the non-zero couple stress boundary condition for a given concentration. Applications of this theory to blood flow are briefly discussed.

Molecular theories of nonlinear viscoelasticity of polymers

Abstract: It is emphasized that considerable advances have been made recently in the development of the molecular theories of nonlinear viscoelasticity of concentrated solutions and melts of linear polymers. The new ideas in this exceptionally important field of the rheology of polymers are analysed. The methods by which the constraints (entanglements) imposed on the motion of macromolecules by the polymer environment are taken into account are also considered in the paper. The most detailed discussion is devoted to the model of topological constraints in the form of a tube and to the self-consistent theory of anisotropic micro-viscoelasticity which takes into account the relaxation nature of the interaction of macromolecules with their surrounding medium as well as the anisotropy of their mobility.

The dynamic performance of the Weissenberg rheogoniometer III. Large amplitude oscillatory shearing — harmonic analysis

Abstract: The harmonic content of the nonlinear dynamic behaviour of 1% polyacrylamide in 50% glycerol/water was studied using a standard Model R 18 Weissenberg Rheogoniometer. The Fourier analysis of the Oscillation Input and Torsion Head motions was performed using a Digital Transfer Function Analyser.

The influence of blending polystyrenes of narrow molecular weight distribution on melt creep flow and creep recovery in elongation

Abstract: Creep and creep recovery experiments in elongation were performed with melts of anionically polymerized polystyrenes (PS) and with their blends at a temperature of 150 °C. For stressesσ 0 < 10 000 N/m2 the samples with narrow molecular weight distribution show linear viscoelastic behavior up to the maximum Hencky straine = 3.5, achievable in a newly developed elongational rheometer for polymer melts. The compliances,D (t), of the blends are linear-viscoelastic only up to a strain limite L . For strains beyonde L the compliance of each blend depends on the stressσ 0. For a series of binary blends, prepared from the same components of narrow MWD, the linear-viscoelastic limite L seems to be independent of the mixing ratio and stress.e L seems to be a function only of the molecular weights of the original components, the blends investigated were made from.

A transient-network model describing the rheological behaviour of concentrated dispersions

Abstract: Attractive forces acting between particles in dispersions may cause a three-dimensional structure to be built up. A temporary-network model is postulated that describes the rheological behaviour of such systems. Chains of particles are assumed to be created and broken by thermal actions and by applied deformation. The relation between the network structure and the macroscopic stress tensor is deduced. One of the main model features is that no use is made of the common assumption of affinity of the motion of the chain vectors with the gradient of the macroscopic velocity field. Instead, the chain deformations are assumed to depend on the forces acting on them, i.e. their deformations depend on their stiffness and on the applied deformation, whereas fracture of chains may cause stress relaxation in the rest of the network. The chains may behave as highly non-linear springs, whereas the probability that the chains will break in some time interval may be an explicit function of the chain length itself. Integral equations are derived, from which the stress-tensor components can be calculated in any flow experiment, that obeys creeping-flow conditions. Analytical expressions are obtained for the relaxation spectrum of such systems in terms of the microscopic parameters.

Effects of body shape and viscoelasticity on the slow flow around an obstacle

Abstract: A study was made of the motion of axisymmetrical objects in viscous and viscoelastic fluids within a cylindrical tank with the assumption of negligible inertial effects. A numerical treatment based on the Stokes equations of motion and an optimization technique enabled the details of the velocity and rate-of-deformation fields for a Newtonian fluid to be predicted. The influence of the shape of various bodies, some even with concave surfaces, was examined. The corresponding experiments were carried out with viscous and viscoelastic fluids using a visualization technique. A correlation between the main flow characteristics and the rheological behaviour of the fluids was established.

Stagnation flows for the Oldroyd-B fluid

Abstract: Exact solutions to the plane and axi-symmetric stagnation flows of an Oldroyd-B fluid are reported. It is found that a steady flow is possible if the Weissenberg numberWi, defined by the product of the Maxwellian relaxation time and the shear rate at infinity, satisfies − 1/2

Non-linear behaviour of asphalts in steady and transient shear flow

Abstract: Steady-state and transient shear stress and normal stress data were obtained for four asphalts with a modified Weissenberg Rheogoniometer. Interest was specially related to non-linear behaviour at high shear-rates. The time-temperature superposition principle was found to hold in non-linear behaviour. Moreover, steady-state and transient data could be plotted as master curves irrespective of the nature of the asphalts. In particular, the master curve of steady-state viscosity could be extended to results published in the literature. In the nonlinear region the shear stress relaxation after cessation of a steady shear rate $$\dot \gamma$$ becomes a function of $$\dot \gamma$$ t only and is related to the primary normal-stress coefficient, as predicted by the Yamamoto equation. In the shear stress growth experiment an overshoot is obtained at a constant strain close to 1.5, independent of the rate of strain.