Consistency tests for start-up and cessation deformations of viscoelastic fluids

The time-dependent shear stress and first normal stress difference were measured for a polystyrene solution for start-up and cessation-flow experiments over a relatively wide range of shear rate. Consistency tests for the K-BKZ model were applied to the data, and it was concluded that the K-BKZ equation generally does not satisfactorily describe the start-up and cessation data. Modified consistency tests were developed using a strain-coupling constitutive equation, and the evidence suggests that most of the differences between the predictions of the K-BKZ theory and experiment can be explained by including a strain-coupling effect in the rheological constitutive equation.     

Elongational rheology of polyethylene melts — temporary network constitutive laws

The uniaxial elongational properties of various polyethylenes have been evaluated using an elongational rheometer and a melt-strength apparatus. It is possible to derive the data obtained in elongation from the distribution of relaxation times obtained from oscillatory shearing measurements (linear viscoelasticity), using a Wagner constitutive equation. The effects of the molecular parameters of the samples have been studied, in particular the effect of polydispersity on the shape of the damping function.     

Viscometric flows of polymeric melts treated according to the rational theory of Eckart's continuum. I. General theory

The purely rational theory of Eckart continua (i.e. elastic bodies with a variable relaxed state) is applied to viscometric flows of polymeric melts. The main assumptions are thermodynamic non-interaction of inelastic behaviour and of non-elastic stress, as well as elastic isotropy. After establishing the time-dependent differential equations of viscometric flow, these equations are simplified to a set of algebraic equations describing steady-state flow. From this we deduce two general equations connecting the three elastic steady-state viscometric functions which do not depend upon the elastic behaviour. The law of rubber elasticity used in this paper is described in the Appendix.     

Rheological properties of service weathered road bitumens

A study was carried out of the rheological properties of service weathered bitumens and their properties were compared with road performance. Bitumen from 39 test sites was recovered from the uppermost layer of stone particles covering the road surfacing and tested under dynamic and transient loading. Dynamic testing was carried out under forced sinusoidal loading. Testing under transient loading was mainly with a viscosity test conducted at 45°C, but some creep testing in compression was conducted at 0°C. From the results of dynamic testing, master curves of modulus and loss angle were constructed, spanning over ten decades in loading frequency. The hyperbolic expressions of Dickinson and Witt successfully described the frequency dependence of bitumen modulus and loss angle. The Williams, Landel and Ferry (WLF) equation, with newly derived coefficients, described the temperature dependence of the shift factor (or Newtonian viscosity) for the temperature range –10 to 60°C. Attempts were made to compare the measured transient response with that calculated from dynamic results. The result of the viscosity test conducted at 45°C as an indicator of modulus at low temperatures was assessed. Surfacing distress increased as the bitumen viscosity or modulus increased, however service performance of the bitumens was best correlated with the modulus calculated at conditions representative of traffic stressing and lowest site temperature. The changes in the rheological properties of bitumens induced by weathering is discussed.     

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.     

Shrinkage effect on polyethylene based blends

An experimental study of the shrinkage effect in low density-high density polyethylene blends, high density-high density polyethylene blends and low density polyethylene-ethylene vinyl acetate copolymer blends is presented. Viscosity measurements are also included.The strain recovery is analysed as the addition of the interfacial tension effect and the elastic recoverable strain. The results are compared with those obtained for other polyolefin blends observing that in the case of compatible systems as low density-high density polyethylene and high density-high density polyethylene blends the strain recovery and the viscosity follow approximately the additive rule. In the case of more incompatible systems like polyethylene-ethylene vinyl acetate copolymer, polyethylene-polypropylene and others very large recoveries were observed. The formation of minifibres of the dispersed phase during the preparation of the samples is suggested as responsible for the obtained results.     

Correlation between interfacial interactions and internal stresses in filled high density polyethylene

The stress relaxation and the creep behaviour of high density polyethylene (HDPE) filled with glass fibres, clay (plate-like particles) or CaCO₃ (particles with irregular shape) were measured in uniaxial extension at room temperature. It was observed that the addition of filler increased the internal stress level, as evaluated from stress relaxation data. This increase was larger than the corresponding increase in the (short-term) elastic modulus. This behaviour may be attributed to a reduced macromolecular mobility in the matrix material close to the filler surface, i.e. to formation of an interphase region in the HDPE-matrix. From the internal stress values, the thickness of this interphase region around each filler particle was estimated, assuming a uniform coverage of the particles. It was suggested that the amount of matrix material with reduced mobility (or the thickness of the interphase region) reflected the degree of adhesion between the filler and HDPE. The change in the internal stress level due to the incorporation of different fillers, which were surface treated in some cases, was also consistent with the observed creep behaviour.     

The time-dependent stress-optical behavior of polycarbonate in the glass transition region

The mechanical and stress-optical behavior of Bisphenol-A polycarbonate was investigated in the glass-transition region. For this purpose, optical creep experiments were carried out in shear and elongation on a tensile tester specially designed for use on a microscope state. A Kohlrausch Williams Watts equation (KWW) with a temperature-independent parameter could successfully be applied to the curves describing the time-dependent values of the stress-optical coefficient for several temperatures. The temperature dependence of the corresponding retardation time could be established and described by the WLF equation. For variable stresses the time-dependent birefringence is obtained from a generalized linear stress-optical rule as modeled according to linear superposition. The time-temperature superposition principle was applied to all measurements. With the dynamic moduli some deviations were observed at the transition from the rubbery plateau to the relaxation. The strain-optical coefficient was found to decrease with increasing time and strain. The strain dependence was found to be independent of temperature at constant stress.     

Comparison between uniaxial and biaxial elongational flow behavior of viscoelastic fluids as predicted by differential constitutive equations

Behavior of polymer melts in biaxial as well as uniaxial elongational flow is studied based on the predictions of three constitutive models (Leonov, Giesekus, and Larson) with single relaxation mode. Transient elongational viscosities in both flows are calculated for three constitutive models, and steady-state elongational viscosities are obtained as functions of strain rates for the Giesekus and the Larson models.Change of elongational flow behavior with adjustable parameter is investigated in each model. Steady-state viscosities _E and _B are obtained for the Leonov model only when the strain-hardening parameter is smaller than the critical value _cr determined in each flow. In this model, uniaxial elongational viscosity _E increases with increasing strain rate , while biaxial elongational viscosity _B decreases with increasing biaxial strain rate _B . The Giesekus model predictions depend on the anisotropy parameter . _E and _B increase with strain rates for small _B while they decrease for large . When is 0.5, _E in increasing, but _B is decreasing. The Larson model predicts strain-softening behavior for both flows when the chain-contraction parameter > 0.5. On the other hand, when is small, the steady-state viscosities of this model show distinct maximum around = _B = 1.0 with relaxation time . The maximum is more prominent in _E than in _B .     

A boundary element simulation of the unsteady motion of a sphere in a cylindrical tube containing a viscoelastic fluid

A boundary element method is used to simulate the unsteady motion of a sphere falling under gravity along the centreline of a cylindrical tube containing a viscoelastic fluid. The fluid is modelled by the upper-convected Maxwell constitutive equation. Results show that the viscoelasticity of the liquid leads to a damped oscillation in sphere velocity about its terminal value. The maximum sphere velocity, which occurs in the first overshoot, is approximately proportional to the square root of the Weissenberg number when the ratio of the sphere radius to the tube radius is sufficiently small. Particular attention is also paid to the wall effects. It is shown that a closer wall reduces the oscillatory amplitude of the sphere velocity but increases its frequency. The results suggest that the falling-ball technique, which is now widely used for viscosity measurement, might also be used for the determination of a relaxation time for a viscoelastic fluid.     

A theoretical model for the prediction of thermal expansion behaviour of particulate composites

The thermal expansion coefficient of particle-reinforced polymers was evaluated using a theoretical model which takes into account the adhesion efficiency between the inclusions and the matrix — an important factor affecting the thermomechanical properties of a composite. To measure the adhesion efficiency a boundary interphase, i.e. a layer between the matrix and the fillers having a structure and properties different from those of the constituent phases, was considered. This layer is assumed to have varying properties.To obtain information concerning the properties and extent of the interphase, an experimental study of the thermal behaviour of aluminium-epoxy composites was undertaken. Differential Scanning Calorimetry (DSC) measurements were performed to evaluate heat capacity with respect to temperature. In addition, the effects of different factors, such as heating rate and filler concentration on the glass transition temperature of the composite, were examined. The sudden changes in heat capacity values in the glass transition region were used to estimate the extent of the boundary interphase according to an existing theory.Finally, the values of the thermal expansion coefficient, predicted by this model, were compared with theoretical results obtained by other authors and with experimental results.     

Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^–1. The elongational strain rates are similar at a low shear rate of 5 s^–1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.     

Ein rheometer zur untersuchung von flüssigen polymermaterialien in einachsiger und zweiachsiger Dehnung

Zusammenfassung Wir stellen ein neues Dehnrheometer vor, mit dem sowohl einachsige als auch zweiachsige Dehnexperimente an flüssigen Polymermaterialien durchgeführt werden können. Bei der Apparatur wird das Prinzip der atmenden Blase verwendet: Über eine Düse wird in das zu untersuchende Material eine kugelförmige Blase aus einer niederviskosen, inkompressiblen, unmischbaren Flüssigkeit injiziert. Wachstum bzw. Schrumpfen dieser Blase führt zu einer zweiachsigen bzw. einachsigen Dehndeformation der umgebenden Polymerflüssigkeit. Der Injektionsdruck dient als Meßgröße zur Bestimmung der viskoelastischen Eigenschaften des Probenmaterials. Bei vergleichsweise niederviskosen Silikonölen gelingt die Messung der Nullviskosität bzw. der linear viskoelastischen Eigenschaften in guter Übereinstimmung mit Scherexperimenten. Bei Materialien mit ausgeprägt nichtlinear viskoelastischem Verhalten kann unter Anwendung des Wagner-Modells die Dämpfungsfunktion für ein- und zweiachsige Dehnung ermittelt werden. Unsere Ergebnisse für das Polyisobutylen Oppanol B 15 stimmen mit Messungen von Demarmels und Meißner überein, die mit der Methode der Rotierenden Klemmen durchgeführt werden. Für drei Polyisobutylene unterschiedlichen Molekulargewichts ergibt sich im Rahmen der Meßgenauigkeit die gleiche Dämpfungsfunktion.Vortrag auf der Jahrestagung 1991 der Deutschen Rheologischen Gesellschaft e.V. in Berlin.     

Molecular interpretation of the behaviour of polyisobutylene in different solvents

The effects of solvent environment on the behaviour of a high molecular weight polyisobutylene dissolved in kerosene and various grades of poly-1-butene solvent mixtures are investigated. The dependence of various molecular parameters such as zero-shear viscosity, intrinsic viscosity, specific viscosity, relaxation time and molecular expansion factor, on the polymer concentration, type of solvent and solvent viscosity is studied in the vicinity of dilute and semidilute regions (near the critical concentrationc ^*). The dependence of these parameters on solvent environment follows qualitatively Zimm's molecular model. The dependence on the polymer concentration deviates from this dilute solution theory. The effects of temperature on the zero-shear viscosity and the Maxwell relaxation time are also presented for two PIB solutions.     

Physiology,mechanics, and rheology

Biological systems possess rather specialized mechanical properties, acquired as part and parcel of the evolutionary development of the system as a whole. Their optimization permits the system to function physiologically in the context of a biologically essential, but mechanically often widely varying environment with adequate efficiency. The system's environment is its source of food and shelter; it represents the space in which it forages or preys on other creatures and in which it has to defend itself against still others. Thus, the system has to develop an adequately pliant, rheologically matched, energy-use efficient, mechanical interface between it and its surroundings. This must be an interface that both effectively excludes, but also effectively admits, the external. Internally, as well, it has to adapt the mechanical properties of cell and connective tissue to physiological function and the efficient performance of useful work. This will be illustrated by way of examples. Blood rheology is briefly discussed and put into the context of clinical hemorheology and epithelial protection; and function, by way of a mucus coating or a mucociliary clearance system, is reviewed in some detail. The importance of all aspects of rheological matching is demonstrated.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Evolution of time constants during sol-gel transition

In developing a rheological constitutive equation for crosslinking polymers the determination and explanation of time constants are of great importance. For stoichiometrically balanced and imbalanced reactions of polydimethylsiloxane and polyurethane model polymers with appropriate cross-linkers, it is shown that the experimental data for the storage and loss moduli are well fitted within a large frequency range by a linear rheological constitutive equation with a truncated power law relaxation function.Special attention is given to the problem of estimating the different time constants. A method is proposed for the determination of the terminal relaxation time (in the case below the gel point) and a characteristic retardation time (in the case above the gel point) from the intersection points of the high and low frequency asymptotes of the storage modulus.     

Fragile networks and rheology of concentrated suspensions

Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic -Fe₂O₃ and non-magnetic -Fe₂O₃ particles in mineral oil are interpreted with the model proposed.Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G was found to follow a scaling law of the type G ( _f - _f ^c ) ^f , where _f is the volume fraction of flocs in suspension, and _f ^c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.     

Rheological behavior of water-creosote and creosote-water emulsions

The effect of temperature on the steady-shear viscosity of two base emulsions (water-in-creosote (w/o) and creosote-in-water (o/w)) and a pigment emulsified creosote (PEC) was investigated. The PEC is a water-in-creosote emulsion which contains also a solid, micronised pigment, and is used industrially as a wood preservative. All three emulsions exhibited shear thinning characteristics at different temperatures. The viscosity-shear rate relationships follow a modified Quemada model. A temperature-superposition method using the reduced variables / and t _c was applied to yield a master plot for each of these emulsions at different temperatures. The effect of creosote concentration on the viscosity of four other o/w emulsions at different temperatures was also studied. The same reduced variables were able to produce a temperature-concentration superposition plot for all of the o/w emulsion results.The effective (average) radius of the globules (dispersed phase) was found to increase with increasing temperature for the base w/o and the PEC emulsion. The collision theory could be used to explain the increase in the droplet size. However, while little overall variation in globule size was observed for the o/w emulsions, microscopic observation indicated an increase in the proportion of large diameter droplets with temperature at the highest creosote concentration (60%). A creaming effect (phase concentration) was observed with these emulsions at higher temperatures, precluding an accurate estimate of droplet size based on collision theory.Seconded from Koppers Coal Tar Products, Newcastle, N.S.W., Australia.     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.