Showing papers in "Rheologica Acta in 1996"

A rheological study of shear induced crystallization

Abstract: The isothermal crystallization of three isotactic polypropylene (iPP) types, with different molar mass (distributions), was studied after a well defined shear treatment of the melt at an elevated temperature and a subsequent quench to the crystallization temperature. For these experiments a standard rheometer of the cone and plate configuration was used. The development of the crystallization was monitored by dynamic oscillatory measurements. Shearing in the melt was shown to enhance subsequent crystallization at lower temperatures. Not only the total shear at constant rate is of importance, but also the chosen combination of rate and shearing time. Moreover, a pronounced influence of molar mass was detected. The exploration of the melting temperatures and times which are necessary for an erasion of the memory effects showed that the effect of shearing could not completely be erased, possibly as a consequence of mechanical degradation.

Structure and rheology of wormlike micelles

Abstract: In a semi-dilute aqueous solution under certain conditions, surfactant molecules will self assemble to form wormlike micelles. The micelles are dynamic in structure since they can break and reform, providing an additional mode of relaxation. The viscoelastic properties of the wormlike micelles can be predicted using simple theological models. For many surfactant solutions the mechanical data can be related to the optical data by the stress-optical rule. From the viscoelastic data it is possible to estimate the breaking time of the micelle. The techniques of birefringence and small angle light scattering are used to study the microstructure of a surfactant solution under simple shear and extensional flow. The sample under investigation is a solution of cetyltrimethylammonium bromide and sodium salicylate in water, with a salt to surfactant ratio of 7.7. Below a critical shear rate, the birefringence increases linearly with shear rate and the stress-optical rule is valid. The SALS patterns reveal distinctive butterfly patterns indicating that scattering is a result of concentration fluctuations that moderately couple to the flow. However, above a critical shear rate the birefringence plateaus and the stress-optical rule is no longer valid. SALS patterns show both a bright streak and a butterfly pattern. The bright streak is caused by elongated structures aligned in the direction of the flow. The oriented structures occur when the characteristic time of flow is faster than the breaking time of the micelles.

On the development of oblong particles as precursors for polymer crystallization from shear flow: Origin of the so-called fine grained layers

Abstract: Recent studies concerning shear-induced crystallization after isothermal short-term shearing enabled a theoretical explanation for the formation of highly oriented surface layers in isotactic polypropylene. Under these special conditions also an occurrence of so-called fine grained layers was observed but has not been understood, so far. For slightly supercooled melts of polyethylene the formation of oblong crystallites, which were oriented perpendicularly to the flow direction, was recently reported for very slow continuous shear flow. This phenomenon was explained by the rotational component of this flow. The present work describes the growth of similar structures in isotactic polypropylene melts after fast short-term shearing at mild degrees of supercooling. The pertinent crystallites, which are finally formed on transverse precursors, are observed in cross-sections perpendicular to the direction of previous flow. Their anisotropic growth was monitored with the aid of light scattering. The present work also emphasizes that these structures are formed as a consequence of shear rates that occur in industrial processes. In fact, in injection molded parts they are formed in the neighborhood of the highly oriented surface layers. It is suggested that the transverse thread-like particles act as activators for the formation of the precursors of the highly oriented surface layers, as soon as they switch into the flow direction.

Hierarchical models for viscoelasticity : dynamic behaviour in the linear range

Abstract: Viscoelastic elements derived from hierarchical models are introduced into classical models. Some of the resulting “modified” models are shown to yield the fractional differential descriptions of viscoelastic behaviour given previously by Friedrich, and to comply automatically with previously formulated thermodynamic constraints. The reasons underlying the previously observed differences between fractional differential and fractional integral formulations are clarified. The “modified” models are shown to be capable of describing experimentally observed dynamic viscoelastic behaviour over a wide frequency range, including multiple transitions, using a limited number of free parameters.

Relaxation and viscoelastic properties of complex polymer systems

Abstract: Dynamic behavior of various polymer melts is studied on the basis of a comparison of viscoelastic properties with the information obtained from dielectric spectroscopy. The experimental observations are compared with results of computer simulation of corresponding systems. The studies include simple melts of linear chains, block copolymer systems of miscible components, as well as the behavior of melts with molecular objects of complex topology-like stars or microgels. In the case of polyisoprene linear chain melts an equivalence of terminal relaxation times determined from mechanical and dielectric measurements is demonstrated. Using linear block copolymers of isoprene and butadiene, relaxation times of chain fragments (isoprene blocks) in relation to relaxation times of whole copolymer chains are determined and compared with theory and simulation. Both the experimentally determined block relaxation times and relaxation times of chain fragments in simulated linear chain melts show a disagreement with predictions of the reptation theory. In the case of multiarm star polymers and microgel melts, the slow relaxation modes observed in viscoelastic spectra are assigned to cooperative translational motions detected in corresponding simulated systems in which an ordering of such molecules is demonstrated. This suggests that the terminal relaxation in multiarm star or microgel melts is governed by another relaxation mechanism than in linear chain melts. High efficiency of the Cooperative Motion Algorithm in simulation of dense systems of complex molecules is demonstrated.

A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime

Abstract: The dynamic mechanical behavior of a series of monodisperse polybutadienes has been investigated from the flow regime to the glassy state. Assuming a linear superposition of the entanglement and glass behavior a mathematical model of the spectrum of relaxation times is developed. It consists in a self-similar spectra for the entanglement contribution and a Fractional Maxwell Fluid (FMF) for the glassy contribution. The model closely represents the master curves of dynamic moduli over 15 logarithmic decades of frequency with three parameters for the flow regime (GN 0 N η0 and a cut-off parameter λmax) and four parameters for the FMF. It is shown that one of the parameter of the FMF is similar to the power-law exponent of a self-similar spectra previously proposed in the literature to model the transition to glass.

Rheometry on magnetorheological (MR) fluids I. steady shear flow in stationary magnetic fields

Abstract: Test fixtures of a commercial concentric cylinder rheometer (Physica Rheolab MC 20) were modified to enable measurements under magnetic inductions up to 0.5 Tesla in a shear rate range of 0.1 up to 1000 s −1 and temperatures 0° to 150°C. In the 2 x90°-cups only two 90° sectors of the stationary part of the double concentric cylinder arrangement are submitted to the magnetic field which is created outside the test tools by an electromagnet. A prototype of a 360°-cup contains the electromagnet within the cup and avoids the correction necessary for the sector geometry. Measurements are shown for a carbonyl iron MR fluid and two nano MR fluids. An encouraging comparison of the viscosity function and MR effect (shear stress changes due to the field) measured by using the various cups is presented. The detailed investigation of the magnetic field distribution in the tools yields a distinct radial field gradient and also stray fields that make the quantification of the effective field in the gap difficult. The change of the field when the gap is filled with MR fluid is addressed. MR effects up to 13 000 Pa have been found, the limited torque range of the rheometer making it necessary to use relatively small gap dimensions which introduce errors due to edge effects. Shear rates up to 40000 s−1 as typical for the application in dampers were investigated by a piston-driven capillary rheometer making use of a thermostated rectangular slit with superimposed magnetic field. A satisfactory agreement of the magnetorheological data with the concentric cylinder results is found in the overlapping shear rate range.

Rheology/morphology/flow conditions relationships for polymethylmethacrylate/rubber blend

Abstract: Viscoelastic behavior, phase morphology and flow conditions relationships in polymer/rubber blends have been investigated. The importance of such correlations is illustrated on polymethylmethacrylate (PMMA)/rubber blends subjected to different flow conditions both under small and large deformations. In small-amplitude oscillatory shear (the morphology does not change during the flow) the elastic modulus G′ of the concentrated blends shows a secondary plateau, G′ p , in the low frequency region. This solid-like behavior appears for rubber particle contents beyond the percolation threshold concentration (15%). Morphological observations revealed that for concentrations higher than 15%, the particles are dispersed in a three-dimensional network-type structure. In capillary flow it was found that the network-type structure was destroyed and replaced by an alignment of particles in the flow direction. This morphological modification resulted in a decrease in both viscosity and post-extrusion swell of the blends. Morphological observations revealed that the ordered structure in the flow direction was concentrated only in the skin region of the extrudate, where the shear stress is higher than the secondary plateau, G′ p . A simple kinetic mechanism is proposed to explain the observed morphology. Similarly, steady shear measurements performed in the cone-and-plate geometry revealed alignment of particles in the flow direction for shear stress values higher than G′p.

Ultrasonic devulcanization of waste rubbers: Experimentation and modeling

Abstract: Continuous ultrasonic devulcanization of ground tire rubber (GRT) and styrene-butadiene rubber (SBR) is considered. Experiments are performed under various processing conditions. Two recipes of SBR with different amounts of polysulfidic linkages are utilized. Gel fraction and crosslink density of devulcanized rubbers are measured and a unique relationship between them is established. Die characteristics with and without imposition of ultrasonic waves are determined. Devulcanized samples are revulcanized and mechanical properties are measured. In some cases, properties of revulcanized SBR samples exceeded those of virgin vulcanizates. This is explained based on the presence of a double network in the revulcanized rubber. A modification of acoustic cavitation and flow modeling of ultrasonic devulcanization of SBR and GRT is proposed using a concept of effective viscosity characterizing the flow of vulcanized particles before devulcanization combined with a shear rate, temperature and gel fraction-dependent viscosity of devulcanized rubber. Velocity, shear rate, pressure, and temperature field along with gel fraction, crosslink density and number of bonds broken are simulated. Predicted data on gel fraction, crosslink density, and pressure using the present modification of the model are found to be closer to experimental data then previously reported.

Nonlinear rheological behavior of a concentrated spherical silica suspension

Abstract: Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain γ(≤0.2) while the nonlinear relaxation modulus G(t, γ) characterizing strong stress damping behavior was obtained for large γ(>0.2). G(t, γ) obeyed the time-strain separability at long time scales, and the damping function h(γ) (−G(t, γ)/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity η(γ) for small shear rates γ( τ−1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, η + (t, γ) and η− (t, γ). In the shear-thinning regime, the γ and τ dependence of η+(t,γ) and η−(t,γ) as well as the γ dependence of η(γ) were well described by a BKZ-type constitutive equation using the G(t) and h(γ) data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.

Experimental observations on the pressure-dependent polymer melt rheology of linear low density polyethylene, using a multi-pass rheometer

Abstract: We report experimental data for a linear low density grade of polyethylene at elevated temperatures using a newly designed Multi-Pass Rheometer This rheometer is capable of measuring oscillatory viscoelastic data and steady shear capillary measurements on the same test fluid within an enclosed environment Data presented in this paper show that at low pressures there is reasonable self-consistency between the Multi-Pass data and separate oscillatory data obtained by using a Rheometrics Mechanical Spectrometer and steady shear data obtained from a Rosand capillary rheometer In addition, we report experimental data on the pressure dependence for both viscoelastic and steady shear data over the range of 1–230 bar The steady shear results appear to be consistent with previously published data The apparent viscosity and the viscoelastic data both show a linear increase of about 20% over the pressure range tested

Rheology of critical LCST polymer blends: poly(styrene-co-maleic anhydrite)/poly(methyl methacrylate)

Abstract: The shear rheology of a binary polymer blend exhibiting a lower critical solution temperature (LCST) phase diagram and a small dynamic asymmetry (difference of glass transition temperatures between its constituents) has been investigated in the vicinity of phase separation; it is a mixture of a random copolymer of styrene and maleic anhydrite and poly(methyl methacrylate). In the linear viscoelastic regime, the material functions are sensitive to phase separation, and the effects of critical concentration fluctuations, which dominate the mechanical response, are quantified, yielding both the binodal and spinodal curves. The weak dynamic asymmetry is apparently responsible for the reduced magnitude of the observed effects, compared to blends exhibiting much larger contrast in glass transition; therefore, this property affects to some degree the accuracy of the rheologically determined phase diagram. The steady shear properties are weakly sensitive to phase separation, and suggest that shear-induced demixing may be possible. They also indicate the importance of the amount of strain energy introduced to the blend in controlling the effects of flow on phase behavior.

Rheotens-mastercurves and elongational viscosity of polymer melts

Abstract: In a Rheotens experiment, the tensile force needed for elongation of an extruded filament is measured as a function of the draw ratio. For thermo-rheologically simple polymer melts, the existence of Rheotens-mastercurves was proved by Wagner, Schulze, and Gottfert (1995). Rheotens-mastercurves are invariant with respect to changes in melt temperature and changes in the average molar mass. By use of purely viscous models, we convert Rheotens-mastercurves of a branched and a linear polyethylene melt to elongational viscosity as a function of strain rate. The resulting elongational viscosity from constant force extension experiments is found to be in general agreement with what is expected as steady-state viscosity of polyethylene melts measured in either constant strain-rate or constant stress mode.

Simultaneous measurement of viscoelastic changes and cell opening during processing of flexible polyurethane foam

Abstract: A parallel-plate rheomete was constructed and used to study the development of dynamic shear modulus and cell opening under forced adiabatic conditions for a series of flexible slabstock polyurethane foams. Typical industrial formulations were used. The plates were heated to follow the adiabatic temperature profile of a real foam bun during foaming. The rheometer overcomes difficulties encountered in other methods such as heat loss and bubble damage caused by the probe.

On the spin coating of viscoplastic fluids

Abstract: The spin coating of a viscoplastic material is studied using a continuous viscosity function. Thus, the transient model requires the calculation of only velocity, pressure and the moving-free surface of the liquid film, but not the calculation of the yield surface within the liquid. A Finite Element/Newton-Raphson method is presented for solving this moving boundary problem after mapping the deforming domain onto a fixed one. Assuming axial symmetry, the effect of the Bingham, Reynolds, Capillary and gravitational Bond numbers is examined. The magnitude of the first two parameters affects significantly the flow field and the shape of the film as well as the required spinning time in order to produce a film of uniform thickness. Depending on their values, large departures from the corresponding Newtonian solution may be obtained. In these cases the film does not thin out uniformly, but a maximum in its profile is created at the center of the disk. Then, the magnitude of the Capillary number also affects the size of this maximum. The gravitational Bond number affects the film thickness and its profile to a lesser extent.

The relaxation of concentrated polymer solutions

Abstract: The focus of this paper is on the viscoelastic properties of concentrated polymer solutions and polymer melts. Dynamic mechanical measurements were performed on various polystyrene/ethylbenzene solutions with polymer concentrations ranging from 40% up to 100% and temperatures from Tg+30°C up to 70°C (230°C for polymer melts). The basis polymers are two commerical grade polystyrenes (BASF) with M W = 247 kg/mol and 374 kg/mol, respectively. To avoid solvent loss due to evaporating during the measurements, a special sealing technique was used. A phenomenological model which describes quantitatively the relaxation spectrum of concentrated polymer solutions from the flow regime up to the glass transition regime is developed. The relaxation data of the respective polymer melt and the glass transition temperature of the solution are the only input parameters needed. The temperature dependence is described by a universal, concentration invariant WLF-equation. The relaxation spectra are divided into two parts accounting for the entanglement and the segmental relaxation modes, respectively. The relaxation strength related to the flow and entanglement regime scale with c 2.3, whereas the segmental relaxation strength does not alter with concentration. All relaxation times change with concentration proportional to c 3.5. Flow curves can be calculated from these relaxation spectra and thus, our results are useful for engineering applications.

Excess pressure losses in the capillary flow of molten polymers

Abstract: The excess pressure losses due to end effects in the capillary flow of a linear low-density polyethylene resin (LLDPE) were studied both experimentally and numerically. First, they were determined experimentally by using two methods: i) by extrapolating experimental data of pressure drop versus length-to-radius ratios (L/R) to zero capillary length and ii) by means of using orifice dies (L/R ≈ 0). Both methods resulted in about the same end corrections. Numerical simulation was also used to model this important aspect of experimental rheology. The constitutive equation used in the simulations is a multimode K-BKZ equation proposed by Papanastasiou et al. (1983, J. Rheol. 27:387) and further modified by Luo and Tanner (1988, Int. J. Num. Meth. Eng., 25:9). It was found that the numerical predictions agreed qualitatively, but underestimated the experimental data for the various geometries used to determine the end effects.

Temporal and spatial instability of an inviscid compound jet

Abstract: This paper examines the linear hydrodynamic stability of an inviscid compound jet. We perform the temporal and the spatial analyses in a unified framework in terms of transforms. The two analyses agree in the limit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analysis, there are two growing modes, stretching and squeezing. Thin film asymptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstable for small jet velocities and admits a convectively growing instability for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spatial growth rate. Predictions of both the temporal and the spatial theories compare well with experiment.

New ill-posed problems in rheology

Abstract: Many methods of material characterization by rheological methods lead to ill-posed problems. The nature of ill-posedness is discussed. In this light, some such new problems appearing in molecular weight characterization of homopolymers as well as in the characterization of size distribution of dispersed phases in polymer blends by rheological techniques are analyzed. The working capability of a nonlinear regularization method is demonstrated with examples of blend rheology. The role of Professor Meissner in motivating the research in the field of ill-posed problems as well as his important contribution to rheology of polymer blends is outlined.

Nonisothermal model of glass fiber drawing stability

Abstract: Draw resonance is caused by a constant speed winder that leads to non-constant axial forces (Schultz, 1984). The well studied isothermal Newtonian fiber drawing predicts very modest critical draw ratios (around 20, much less than the typical production draw ratios for glass fibers of 103 – 105). The nonisothermal fiber drawing model presented here shows that cooling along the spin line strongly stabilizes the process. However, we show that the conclusion of Shah and Pearson (1972a,b) that non-isothermal Newtonian fiber spinning is unconditionally stable is based on non-converged numerical results. The choice of viscosity-temperature correlation function has a strong influence in determining the stability of the process. While viscoelasticity generally has an adverse effect on the stability, low viscoelasticity in the presence of extensional thinning helps to slightly improve the maximum critical draw ratio.

On the relative magnitudes of viscous, elastic and texture stresses in liquid crystalline PBG solutions

Abstract: The relative contributions of the viscous, elastic, and texture stresses in flows of modestly concentrated liquid crystalline solutions of poly(γ-benzyl glutamate) or PBG, at low shear rates are assessed by comparing published experimental rheological and light-scattering data to theoretical predictions The data considered include ratios of Leslie-Ericksen viscosities, the shear viscosity jump at the transition from the isotropic to the liquid-crystalline state, the dependence of the shear viscosity on concentration, and the fraction of slowly relaxing stress after cessation of shearing flow We quantify the relative contributions of viscous and elastic stresses by estimating from these data a value for the parameter s*V≡ζstrD*r/kT, where ζstr, is the solvent-polymer friction coefficient and Dr*is the rotary diffusivity in the isotropic phase at the concentration where the isotropic phase becomes unstable to liquid crystalline order The experimental evidence suggests a value \*v ≈ 003, five times lower than the value, 015, for dilute solutions The relative contributions of elastic and texture stresses can be quantified by a parameter e in the mesoscopic theory for polydomain nematics; a value of e≈003 gives reasonable agreement with transient shearing experiments, and predicts that the shear viscosity will show an upturn at high polymer concentrations, in agreement with experiments

Predicting the rheology of linear with branched polyethylene blends

Abstract: A series of melt blended commercial linear and branched polyethylenes are used to explore the generality of blending laws. The measured relaxation modulus G(t), and zero shear viscosity η0 for each blend and blend fraction, have been compared with prediction for miscible blends, particularly using equations derived by Tsenoglou (1987). Plus or minus deviation between theory and measurement is dependent on the relative molecular weights of the blend components. We have found empirically that a generalised form of the blending law for G(t) and for η0, with a floating index C, provides an improved prediction of the blend fraction data. In particular the function defining C is non-symmetrical, from which we infer the significance of branching as well as molecular weight. The optimum value of the index differs for each of our blends, in the range 1.25 to 4, the variability being accounted for by the different degrees to which branched and linear polymers relax co-operatively in the melt. Blends of two near linear polymers do not fit the floating index prediction and conform more closely, though not precisely, to the original Tsenoglou rule.

Normal stress difference in liquid lubricants sheared under high pressure

Abstract: Although normal stress differences in liquids have conventionally been associated with polymers, aspects of rheological behavior in lubricated concentrated contacts suggest that normal stress difference may be significant in even low molecular weight liquids sheared under high pressure and high shear stress. A torsional flow rheogoniometer was constructed for use at high (300 MPa) pressure. Four typical liquid lubricants were investigated, including one polymer/mineral oil solution. Shear stress and N2-N2 are reported as functions of shear rate. The effect of pressure variation is reported for two liquids. Results are compared with predictive techniques and a molecular dynamics simulation. Simple low molecular weight lubricant base oils can generate measurable and significant normal stress differences when sheared at high shear stress.

On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall

Abstract: In this paper we solve the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. We use a non-linear slip model relating the shear stress to the velocity at the wall and exhibiting a maximum and a minimum. We assume that the material parameters in the slip equation are such that multiple steady-state solutions do not exist. The stability of the steady-state solutions is investigated by means of a one-dimensional linear stability analysis and by numerical calculations. The instability regimes are always within or coincide with the negative-slope regime of the slip equation. As expected, the numerical results show that the instability regimes are much broader than those predicted by the linear stability analysis. Under our assumptions for the slip equation, the Newtonian solutions are stable everywhere. The interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model. Perturbing an unstable steady-state solution leads to periodic solutions. The amplitude and the period of the oscillations increase with elasticity.

Experimental and numerical study of entry flow of low-density polyethylene melts

Abstract: The present work deals with experimental and numerical features of entry flows of two polyethylene melts, namely a linear low-density polyethylene (LLDPE) and a low-density polyethylene (LDPE) in an axisymmetric converging geometry. The study also involves rheological characterization of the polymers and determination of flow parameters, at 160°C. For both fluids, the data are fed into a viscoelastic integral Wagner constitutive equation. The numerical flow simulations are performed by using a stream-tube mapping analysis. Consideration of a sub-domain of the total flow domain, the “peripheral stream tube”, close to the wall of the converging duct permits to relate the results of the numerical simulation to experimental flow characteristics as total and entrance pressure drops. The agreement is good for the total pressure losses, but, concerning LDPE, a lack of consistency remains for the entrance pressure drop.

Transient rheological behaviour of poly-para-henylenetherephthalamide (PpPTA) in sulphuric acid

Abstract: Nearly all the available information on the transient flow behaviour of liquid crystalline polymers has been obtained on model systems, especially on solutions of polybenzylglutamate (PBG) and hydroxypropylcellulose (HPC). The assessment of rheological models has been based almost entirely on these model systems. It is not clear how much of the available theoretical and experimental knowledge can be applied to systems of industrial relevance, which have quite different molecular structures. Here, an industrial lyotropic system, poly(p-phenylenetherephthalamide) (PpPTA) in sulphuric acid (TWARON from AKZO), is investigated. Various techniques to study transient behaviour are used, these include measurements of transient shear and normal stresses after sudden changes in shear rate, dynamic moduli and stress relaxation after cessation of flow and elastic recoil. At all shear rates studied the PpPTA solution is shear thinning, and the first normal stress difference remains positive. For the stress transients a strain scaling applies reasonably well as it did in model systems. The moduli increase with time upon cessation of flow, indicating that the molecules become less oriented in the previous flow direction. This particular behaviour is similar to that of HPC. Transients also resemble more closely those of HPC rather than those of PBG. This latter difference might be attributed to the higher flexibility of HPC and PpPTA chains as compared with PBG molecules.

Oscillatory measurements of silicone oils : Loss and storage modulus master curves

Abstract: The work describes a way to obtain loss modulus and storage modulus master curves from oscillatory measurements of silicone oils. The loss modulus master curve represents the dependence of the viscous flow behavior on ω·η 0 * and the storage modulus master curve — the dependence of the elastic flow behavior on ω·η 0 * . The relation between the values of the loss modulus and storage modulus master curves (at a certain frequency) is a measurement of the viscoelastic behavior of a system. The G′/G″-ratio depends on ω·η 0 * which leads to a viscoelastic master curve. The viscoelastic master curve represents the relation between the elastic and viscous oscillatory flow behavior.

The effects of salts on the rheological characteristics of a drag-reducing cationic surfactant solution with shear-induced micellar structures

Abstract: The effect of the counterion salt sodium salicylate (Nasal) on the transient rheological properties of a drag-reducing surfactant system tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) has been studied with both rheometric and rheo-optical methods. Three types of transient behavior for N1 and viscosity were identified in 5 mM TTAA solutions depending on the counterion concentration: induction and growth (below equimolar concentration); overshoot and growth (above equimolar concentration); and overshoot then plateau (at high concentrations of Nasal). The transient flow birefringence and orientation angle show trends similar to those of the viscosity and N1. The second type of transient behavior suggests a two-stage alignment and shear thickening process. The SIS buildup time from the quiescent state, the rebuilding time after a strong preshear, and the relaxation time were also obtained from N1 measurements, and show a maximum around equimolar conditions. The initial N1 and viscosity immediately after the flow startup, on the other hand, show a maximum around a ratio of 2.5 to 3 Nasal/TTAA. For solutions with a Nasal concentration in the ratio 1.5 to 3, the steady state values of N1 and viscosity do not show much variation with Nasal concentration over the shear rate range covered, however. The effect of an addition of sodium chloride (NaCI) to an equimolar Nasal/TTAA solution on the characteristic times and steady state values was also quantified. These rheological results provide us with tools to determine the optimal concentration ratio for practical drag reduction applications.

Brownian dynamics simulations of shear-thickening in dilute polymer solutions

Abstract: A versatile model describing the shear thickening behaviour of dilute polymer solutions in high shear flows is presented. The polymer macromolecules are modelled as Hookean elastic dumbbells which deform affinely during flow. In addition, the dumbbells feel a retractive anisotropic hydrodynamic drag and an isotropic Brownian force. Furthermore, it is assumed that high shear rate increases the probability of molecules forming associations and this is described through expressions for the frequencies of association and dissociation, without explicitly accounting for finite extensibility, hydrodynamic interaction or excluded volume effects. Thus, a reversible kinetic process is incorporated into the model, which results in two diffusion equations for the associated and dissociated dumbbells. Numerical simulations predict shear thickening for specific range of parameters, which are physically meaningful and related to molecular characteristics of the polymer. A comparison against experimental data reported in the literature revealed very promising results, thus confirming the ability of this model to predict shear thickening under a wide range of conditions, for various polymer models.

Extrudate swell through an orifice die

Abstract: The extrudate swell of a viscoelastic fluid through an orifice die is investigated by using a mixed finite element and a streamline integration method (FESIM), using a version of the K-BKZ model. The free surface calculation is based on a local mass conservation scheme and an approximate numerical treatment for the contact point movement of the free surface. The numerical results show a vortex growth and an increasing swelling ratio with the Weissenberg number. Convergence with mesh refinement is demonstrated, even at a high Weissenberg number of O(587), where the swelling ratio reaches a value of about 360%. In addition, it is found that the effective flow channel at the entrance region next to the orifice die is reduced due to the enhanced vortex growth, which may be a source of flow instability.