Showing papers in "Rheologica Acta in 2005"

Shear and extensional rheology of carbon nanofiber suspensions

Abstract: The morphology and rheology of carbon nanofiber (CNF) suspensions were studied. The CNFs, produced by decomposing organic vapors at elevated temperature in the presence of metal catalysts, have characteristic diameter and length of 100 nm and 20–100 μm, respectively. The CNFs, as delivered, have a strong tendency to clump into mm-sized agglomerates. The efficacy of CNF/glycerol-water suspensions was studied vs. two processing parameters: mechanical sonication and chemical treatment. Experimental measurements revealed that sonication alone reduces the size of CNF clumps from millimeter to micrometer scale, but cannot achieve uniform dispersion. The chemically untreated sonicated suspensions contain clumps of nanofibers with a characteristic size of 20×50 μm, together with smaller aggregations of partially dispersed nanofibers. In response to this unsatisfactory dispersion, the effect of acid treatment before dispersion was investigated. This acid treatment, which makes the surface of the CNFs more hydrophilic, greatly improves dispersion in the aqueous solution: treatment followed by sonication results in a uniform dispersion of individual nanofibers. At the same time, however, we observed that surface treatment and subsequent sonication greatly shorten the nanofibers. The rheology of CNF/glycerol-water suspensions is highly non-Newtonian both in shear and extensional flows, with strong dependence on the dispersion, particle length, and concentration of the CNFs. As the solvent is Newtonian, all of the elastic and strain-rate dependent behavior in the CNF/aqueous suspensions derives from the addition of nanofibers. The steady shear viscosity of the untreated-sonicated (poorly dispersed, with longer fibers) suspensions is highly shear thinning with a viscosity that increases three orders of magnitude as concentration varies from 0.5 wt% to 5 wt%. Beyond 5 wt% the suspensions are too viscous to be effectively mixed by sonication. When the CNFs are chemically treated and then sonicated (resulting in much better dispersion but shorter fibers), the viscosity exhibits little shear thinning, and only varies by a factor of two from pure solvent to 5 wt%. In small amplitude oscillatory shear measurements, we found strong indications of elastic behavior in both the treated and untreated suspensions, with elastic modulus G′ greater than loss modulus G′′. In particular, for both systems G′ exhibits a low-frequency plateau when nanofiber concentration is 3 wt% or above, a characteristic of elastic solidlike response. Again, there is a strong dependence on CNF dispersion and fiber length: At low frequencies, the elastic modulus of the 5 wt% untreated suspension (with agglomerates and longer fibers) is four orders of magnitude larger than that of the 5 wt% treated suspension (with uniformly dispersed, shorter fibers). In addition, G′ of untreated suspensions is a much stronger function of concentration than that of treated suspensions, indicative of network formation. The rheology and morphology of nanofiber suspensions were related by identifying morphology of the suspensions with the assumptions of the kinetic theory-based elastic and rigid dumbbell constitutive models; the approach is to specify the parameters in the kinetic theory models in terms of microscale morphological features measured in the SEM. Of those investigated, the elastic dumbbell model with anisotropic hydrodynamic drag is the most successful, effectively modeling the small amplitude oscillatory shear and steady shear behavior of the treated sonicated suspensions. As for the treated unsonicated and untreated sonicated suspensions, which contain mesoscale agglomerates not present in the underlying assumptions of the dumbbell models, it is discovered that the elastic dumbbell with parameters assigned from morphological measurements predicts the correct trends in the steady shear experiments, but fails to accurately predict the small amplitude oscillatory shear experiments.

A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching

Abstract: The “hierarchical model” proposed earlier [Larson in Macromolecules 34:4556–4571, 2001] is herein modified by inclusion of early time fluctuations and other refinements drawn from the theories of Milner and McLeish for more quantitative prediction. The hierarchical model predictions are then compared with experimental linear viscoelastic data of well-defined long chain branched 1,4-polybutadienes and 1,4-polyisoprenes using a single set of parameter values for each polymer, which are obtained from experimental data for monodisperse linear and star polymers. For a wide range of monodisperse branched polymer melts, the predictions of the hierarchical model for monodisperse melts are very similar to those of the Milner–McLeish theories, and agree well with experimental data for many, but not all, of the branched polymer samples. Since the modified hierarchical model accounts for arbitrary polydispersity in molecular weight and branching distributions, which is not accounted for in the Milner–McLeish theories, the hierarchical algorithm is a promising one for predicting the relaxation of general mixtures of branched polymers.

Correlation between rheological behaviour in uniaxial elongation and film blowing properties of various polyethylenes

Abstract: Six various low density polyethylenes and one blend were rheologically characterized in elongation. Their different strain-hardening behaviour could qualitatively be related to their molecular structure. All the materials were blown to films on laboratory equipment under various conditions. The take-up force and the film homogeneity were determined quantitatively, the bubble stability was visually assessed. The bubble stability increased with growing take-up force. The take-up force was found to be the stronger the higher the elongational viscosity was. The homogeneity of film thickness is not related to the bubble stability but to the occurrence of strain hardening in the uniaxial elongational experiment at high Hencky strains. Measurements of the uniaxial elongational behaviour of polyethylene melts are a valuable and promising way to assist the development and optimisation of film blowing materials.

Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution

Abstract: Tensile stress and flow-induced birefringence have been measured during uniaxial elongation at a constant strain rate of two polystyrene melts with narrow molecular weight distribution. For both melts, the stress- optical rule (SOR) is found to be fulfilled upto a critical stress of 2.7 MPa, independent of strain rate and temperature. Estimation of the Rouse times of the melts, from both the zero-shear viscosity and the dynamic-shear moduli at high frequency, shows that the violation of the SOR occurs when the strain rate multiplied by the Rouse time of the melt exceeds by approximately 3. The presented results indicate that in contrast to current predictions of molecular theories, the regime of extensional thinning observed by Bach et al. (2003) extends well beyond the onset of failure of the SOR, and therefore the onset of chain stretch in the non-Gaussian regime.

Influence of M w of LDPE and vinyl acetate content of EVA on the rheology of polymer modified asphalt

Abstract: Asphalt binder was modi- fied by low-density polyethylene (LDPE) and ethyl vinyl acetate (EVA) polymers to investigate the structure-property relationships of polymer-modified asphalt (PMA). The PMA was prepared in a high- shear blender at 160 � C. The opti- mum blending time (OBT) for each polymer was determined following a separate investigation. OBT was influenced by Mw, MWD, and polymer structure. The influence of Mw of LDPE and vinyl acetate (VA) content of EVA on PMAs was studied by rheological tools. Poly- mer modification improved the rhe- ological properties of base asphalt. EVA-PMAs were found to be less temperature sensitive than LDPE- modified asphalts. LDPE modifica- tion increased flow activation energy (Ea) but EVA modification de- creased Ea. Both VA content and Mw of LDPE have influenced the storage stability of PMAs. The low- temperature properties of PMAs and short ageing tests were not influ- enced by polymer type. On the other hand, the high-temperature proper- ties of PMAs were strongly influ- enced by Mw of LDPE and VA content of EVA. Overall, EVA with low VA content showed the best temperature resistance to high- temperature deformations, the highest upper service temperature as well as the best storage stability.

Suspensions of Semiflexible Fibers in Polymeric Fluids: Rheology and Thermodynamics

Abstract: A mesoscopic rheological model of suspensions of semiflexible fibers in polymeric fluids is formulated. Consequences of the model are compared with results of experimental observations of the rheological properties in a simple shear flow. The model takes into account the fiber-fiber and fiber-polymer interactions (in the free energy and the mobility coefficients) and the semiflexible nature of the fibers (in the choice of the Khokhlov-Semenov entropy).

Influence of medium viscosity and adsorbed polymer on the reversible shear thickening transition in concentrated colloidal dispersions

Abstract: The influence of medium viscosity on the onset of shear thickening of silica dispersions is investigated with two different methods. In the first method, the sample temperature is varied over a narrow range for two different suspensions. For the first suspension, the stress at the onset of shear thickening, or the critical stress, was found to be independent of sample viscosity, and the shear viscosity scaled with Peclet number, as expected. The critical stress for the second suspension was not independent of sample viscosity, and the Peclet number scaling was only moderately successful. The differences were attributed to changes in particle interactions with temperature. In the second method, the molecular weight of an oligomeric silicone oil medium is varied. In principle, this method should maintain constant chemical interactions as medium viscosity varies; however the polymer is found to adsorb onto the silica surface and delay shear thickening to higher stresses with increasing molecular weight. The critical stress for the highest molecular weight systems, which is highly dependent on particle loading, overlays with an effective volume fraction based on the hydrodynamic diameter of the polymer-stabilized colloids. The results of both methods suggest that if all other properties of the dispersion are held constant, critical stress is independent of medium viscosity.

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Abstract: Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.

Characterization of polyacrylamide gels as an elastic model for food gels

Abstract: Serving as an elastic model system for food gels, characteristics of polyacrylamide (PAAm) gels were investigated using small amplitude and large deformation rheological tests. The PAAm gels displayed elastic or viscoelastic behavior depending on network crosslink density. For elastic PAAm gels, the rheological properties obeyed the theory of rubber elasticity; whereas for viscoelastic PAAm gels, shear modulus depended on temperature. The elastic PAAm gel fracture parameters did not change with deformation rate (0.2–5.5 s−1), indicating insignificant viscous flow during deformation. Fracture stress was correlated with gel monomer concentration, whereas the fracture strain remained constant regardless of the monomer concentration. In addition, the stress was linearly proportioned with strain up to fracture, indicating that PAAm gels did not experience finite network chain extensibility during large deformation. Consequently, the fracture of PAAm gels did not result from the extensional limitation of network chains, nor did gel fracture result from the nonlinear force–distance relationship between polymer connections. Purportedly, the fracture of PAAm gels was caused by external force overcoming the gel cohesive forces, and low strength of PAAm gels compared to rubbers caused fracture prior to experiencing nonlinear stress-strain deformation.

The effect of slip in the flow of a branched PP melt: experiments and simulations

Abstract: In this paper visualisation and direct velocity profile measurement experiments for a branched polypropylene melt in a 10:1 axisymmetric contraction demonstrate the onset of wall slip. Video processing of the flow shows the formation of vortices and their diminution with increasing flow rate. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model—both of them incorporating a nonlinear slip law—were used to predict the flow kinematics and dynamics as well as to deduce the slip velocity function by performing fitting to the velocity profiles. It was found that the numerical predictions agree well with the experimental results for the velocity profiles, and vortex formation, growth and reduction. It is suggested that such experiments (visualisation of entrance flow and direct velocity profile measurement) can be useful in evaluating the validity of constitutive equations and slip laws in the flow of polymer melts through processing equipment.

A model system for thixotropy studies

Abstract: Many constitutive equations have been proposed for thixotropic materials but the supporting experimental evidence has usually been rather fragmentary. To a large extent this is due to the difficulties involved in measuring thixotropic systems. These systems normally display various phenomena that result in poor accuracy and poor reproducibility of the measurements. Therefore, it has been attempted here to formulate a robust thixotropic system that allows accurate measurements and that would be suitable for detailed studies of thixotropy. The system that has been developed is based on a matrix liquid that consists of a high boiling paraffin oil and a low molecular weight poly(isobutylene). A suitable type of fumed silica is used as the dispersed phase. The various rheological parameters of the material can be altered by varying the concentration of the components and, if necessary, the molecular weight of the polymer. The relative humidity around the sample turns out to be an important factor in controlling the yield stress, and its effect is shown to be reversible. The selected system can be measured accurately over a wide range of measurement conditions. These include stress jump measurements, which can be used to separate viscous and elastic contributions. The highest possible shear rate is limited by the occurrence of a peculiar phenomenon that shows up in the normal stresses.

The role of shear and elongation in the flow of solutions of semi-flexible polymers through porous media

Abstract: The rheological behavior of hydrophobically modified hydroxyethyl cellulose (HMHEC) and xanthan gum solutions has been characterized in simple shear flow, opposed-jets flow, and flow through porous media. Both polymers exhibit shear thinning in simple shear flow and apparent shear thinning in flow through porous media. Analysis of the results shows there is a direct correspondence between shear viscosities determined in simple shear experiments and apparent viscosities in porous media flow at relatively low shear rates. At high shear rates the extensional component of the flow in porous media appreciably increases the apparent viscosity over the simple shear values. This increase is shown to correlate with results obtained in opposed-jets experiments, and is attributed to formation of transient entanglements.

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites

Abstract: The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.

A regularization-free method for the calculation of molecular weight distributions from dynamic moduli data

Abstract: There are several models for the determination of molecular weight distributions (MWDs) of linear, entangled, polymer melts via rheometry. Typically, however, models require a priori knowledge of the critical molecular weight, the plateau modulus, and parameters relating relaxation time and molecular weight (e.g., k and α in τ=kMα). Also, in an effort to obtain the most general MWD or to describe certain polymer relaxation mechanisms, models often rely on the inversion of integral equations via regularization. Here, the inversion of integral equations is avoided by using a simple double-reptation model and assuming that the MWD can be described by an analytic function. Moreover, by taking advantage of dimensionless variables and explicit analytic relations, we have developed an unambiguous and virtually parameter-free methodology for the determination of MWDs via rheometry. Unimodal MWDs have been determined using only a priori knowledge of the exponent α and dynamic moduli data. In addition, the uncertainty in rheological MWD determinations has been quantified, and it is shown that the reliability of the predictions is greater for the high-molecular-weight portion of the distribution.

Nonlinear viscoelasticity of PP/PS/SEBS blends

Abstract: The nonlinear viscoelastic behavior of polypropylene/polystyrene (PP/PS) blends compatibilized or not with the linear triblock copolymer (styrene-ethylene-/butylene-styrene, SEBS) was investigated. Start-up of steady-shear at rates from 0.1 to 10 s−1 was carried out using a controlled strain rotational rheometer and a sliding plate rheometer for strain histories involving one or several shear rates. The shear stress and first normal shear stress difference were measured as functions of time, and the morphologies of the samples before and after shearing were determined. For each strain history except that involving a single shear rate of 0.1 s−1 the blends showed typical non-linear viscoelastic behavior: a shear stress overshoot/undershoot, depending on the history, followed by a steady state for each step. The first normal stress difference increased monotonically to a steady-state value. The values of the stresses increased with the addition of SEBS. The shear stress overshoot and undershoot and the times at which they occurred depended strongly on the strain history, decreasing for a subsequent shear rate step performed in the same direction as the former, and the time at which stress undershoot occurred increased for a subsequent shear rate step performed in the opposite direction, irrespective of the magnitude of the shear rate. This behavior was observed for all the blends studied. The time of overshoot in a single-step shear rate experiment is inversely proportional to the shear rate, and the steady-state value of N1 scaled linearly with shear rate, whereas the steady-state shear stress did not. The average diameter of the dispersed phase decreased for all strain histories when the blend was not compatibilized. When the blend was compatibilized, the average diameter of the dispersed phase changed only during the stronger flows. Experimental data were compared with the predictions of a model formulated using ideas of Doi and Ohta (1991), Lacroix et al. (1998) and Bousmina et al. (2001). The model correctly predicted the behavior of the uncompatibilized blends for single-step shear rates but not that of the compatibilized blends, nor did it predict morphologies after shearing.

Comparative yield stress determination for pure and interstratified smectite clays

Abstract: Different experimental devices and operative procedures were used to obtain the main properties of suspensions of two purified clays, a pure smectite and an interstratified illite-smectite natural clay, at different concentrations. The yield stress values derived from flow and creep tests were found to be very consistent, while those derived from dynamic tests were observed to be much more sensitive to experimental conditions. Qualitatively, the two clays exhibit the same rheological behaviour, which can be modelled using the Herschel-Bulkley model; their yield stress increases with clay concentration and they present a thixotropic character for low concentrations, with an inversion of the curves when the clay concentration increases. However, significant differences were observed when considering numerical values. For the same clay concentration in the suspension, the yield stress of the pure smectite is distinctly higher than that of the interstratified one. The rheological properties of the pure smectite clay can be related to the swelling properties and the organisation of the minerals in water, leading to three-dimensional strong but deformable structures. On the other hand, the presence of a small percentage of illite in the natural clay gives it a brittle behaviour which collapses more easily under stress.

Strain hardening behavior of polymer blends with fibril morphology

Abstract: We investigate the rheological behavior of the polymer blends with fibril morphology, with special focus on the effect of fibril morphology on the extensional properties under uniaxial extension. We add a small amount of the dispersed phase to the matrix, and control the blend morphology by changing the viscosity ratio. When the fibril morphology is maintained, the blend shows not only a significant increase of the extensional viscosity but the strain hardening behavior. The extensional viscosity increases depending on the aspect ratio of the fibers, while the strain hardening behavior originates from the restricted stretching of deformable fibers, which has been confirmed theoretically by introducing the concept of rigidity of the fiber. It suggests a way to induce the strain hardening behavior by introducing deformable fibrils into the matrix, that is, by the design of polymer blends with a small amount of dispersed phase such that the fibril structure is maintained.

Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory

Abstract: The strain hardening of blends of polystyrene (PS) and ultra-high molecular weight polystyrene (UHMW-PS) in elongational flow is modeled by the molecular stress function (MSF) theory. Assuming that the ratios of strain energies stored in polydisperse and monodisperse polymers are identical for linear and nonlinear deformations, the value of the only non-linear parameter of the theory in extensional flows, the maximum molecular stress fmax, can be determined and is shown to be related to steady-state compliance Je0. Using only linear-viscoelastic data, the elongational viscosity of PS/UHMW-PS blends is consistently predicted by the MSF theory.

Modeling of diffusion through polymeric membranes

Abstract: Diffusion, coupled with rheology, of a simple fluid through a complex polymeric membrane is modeled using the Poisson and dissipation bracket formalism. A set of governing equations describing the time evolution of concentration, flux, and internal structure of the complex polymeric membrane is obtained. Two parameters, which characterize the importance of elasticity and mixing properties, appear in the governing equations. An extension of Fick’s second law is derived for the flux evolution. The model describes the diffusion process quantitatively quite well.

Viscous dissipation and completely monotonic relaxation moduli

Abstract: The connection between weak dissipativity and positive definiteness of the relaxation function as well as between monotone energy decay and complete monotonicity of the relaxation function of a linear viscoelastic system is discussed. Some theorems about the composition of completely monotonic functions relevant for polymer rheology are presented.

Rheological properties of branched polystyrenes: linear viscoelastic behavior

Abstract: Oscillatory shear measurements on a series of branched graft polystyrenes (PS) synthesized by the macromonomer technique are presented. The graft PS have similar molar masses (Mw between 1.3×105 g/mol and 2.4×105 g/mol) and a polydispersity Mw/Mn around 2. The molar masses of the grafted side chains Mw,br range from 6.8×103 g/mol to 5.8×104 g/mol, which are well below and above the critical entanglement molar mass Mc of linear polystyrene. The average number \({\ifmmode\expandafter\bar\else\expandafter\fi{p}}\) of side chains per molecule ranges from 0.6 to 6.7. The oscillatory measurements follow the time–temperature superposition principle. The shift factors do not depend on the number of branches. The zero-shear viscosities of all graft PS are lower than those of linear PS with the same molar mass, which can be attributed to the smaller coil size of the branched molecules. It is shown that the influence of branching on the frequency dependence of the dynamic moduli is weak for all graft PS that were investigated, which can be explained by the low entanglement density.

On the rheology of ethylene-octene copolymers

Abstract: It has previously been shown that the plateau modulus, G N p , and thus the entanglement molecular weight, M e, of flexible polymers can be correlated to the unperturbed chain dimension, o/M, and mass density, ρ, via the use of the packing length, p. For polyolefins, a method was recently proposed whereby knowledge of the average molecular weight per backbone bond, m b, allows o/M and consequently G N o and M e to be estimated. This is particularly valuable for polyolefin copolymers since the melt chain dimensions are often unknown. This work corroborates these theoretical predictions by studying the rheology of a series of carefully synthesized ethylene/octene copolymers with varying octene content (19–92 wt%). Furthermore, the results reported herein also allow the advancement of rheological characterization techniques of polymer melts. For instance, based on the analysis of the linear viscoelastic properties of these copolymers, it has been found that several rheological parameters scale with the copolymer comonomer content. Analysis of the viscoelastic material functions in terms of the evolution of the phase angle, δ, as a function of the absolute value of the complex modulus, |G*|, (the so-called van Gurp-Palmen plots), provides a fast and reliable rheological means for determining the composition of ethylene/α-olefin copolymers. The crossover parameters, G co(=G′=G″) and gco(=1/ω co) also scale with copolymer composition.

Classification of model topologies using the δ versus G* plot

Abstract: Most studies dealing with the quantitative characterization of long-chain branching (LCB) concentrate only on the degree of branching as the characteristic measure. A more complete description of branching structure requires knowledge of the topology, meaning position and length of every single branch. Topology is a vital factor in rheological behavior. However, it is not easy to isolate the influences of the molecular weight distribution (MWD) from LCB effects. To overcome this limitation, we combine MWDs with linear viscoelastic measurements to give a more comprehensive fingerprint of branched samples. The δ versus G* plot proves highly beneficial as part of the method, representing all samples on one comparable scale, eliminating fundamental differences between samples that are not due to LCB. We use the obtained datasets for evaluation of a classification algorithm aimed at assigning unknown samples to one of several known topological classes. Classification is based on a phenomenological observation of the samples’ characteristics, emphasizing the departure of rheological behavior from the expected data for completely linear topologies. We attempt to evaluate the applicability of linear viscoelastic data for the identification of topology. Our work starts out from a novel idea to treat these data and presents first results. The method is promising but requires more working data to reach its full potential. Without this, classification success remains limited.

Headgroup effect on drag reduction and rheological properties of micellar solutions of quaternary ammonium surfactants

Abstract: Two sets of cationic surfactants each with essentially the same alkyl chains but different headgroup structures were studied to investigate the effects of surfactant headgroup structure on micelle microstructures, drag reduction (DR) and rheological properties at certain counterion and surfactant concentrations. Cetyldimethylethylammonium bromide (CDMEAB) was compared with alkyltrimethyl ammonium bromide (CnTAB) and benzyldimethyl(hydrogenated tallow)ammonium chloride (DMHTB) was compared with alkyltrimethylammonium chloride (CmTAC), respectively. Surfactants with larger headgroups showed lower high temperature limits for DR. CDMEAB systems have better DR abilities than CnTAB below room temperature but the opposite is true at higher temperatures. DMHTB has stronger counterion binding ability than CmTAC, giving better DR properties than CmTAC at low counterion concentration, but has a lower upper temperature limit for DR. These results provide further understanding of the self-assembly nature of threadlike micelles of cationic surfactants and guidance for design of effective surfactant structures to meet particular DR requirements.

Development characteristics of fluctuating velocity field of drag-reducing surfactant solution flow in a duct

Abstract: Development behavior of the fluctuating velocity of surfactant solution in a duct has been studied experimentally. The concentration of surfactants was kept constant at 1,000 ppm, mean velocity at 0.78 m/s and fluid temperature at 15 °C. Using laser Doppler velocimetry, the fluctuating streamwise velocity distributions at six cross sections, which ranged from 14 to 112 times of hydraulic diameter of the duct, were measured. From the results, the fluctuating structures of surfactant solution flow are observed to have structures different from that of turbulent water flow in the developing field. The wavelet analysis reveals that the high-level fluctuation of surfactant solution flow is characterized by periodicity rather than irregularity around the position where the fluctuation intensity takes a peak value and that the period and the scale of periodic flow structures are related to the relaxation times of the fluid. This indicates that the high-level fluctuation is deeply related to the elastic instability and has a different generation mechanism from that of turbulence observed in a Newtonian turbulent flow.

Enhanced melt strength and stretching of linear low-density polyethylene extruded under strong slip conditions

Abstract: The influence of extrusion under strong slip conditions on the extensional properties of linear low-density polyethylene was studied in this work. The material was extruded at two different temperatures under strong slip and no slip conditions, and was subsequently subjected to uniaxial elongational flow by means of a Rheotens device. Strong slip was evident through the elimination of sharkskin distortions and the stick-slip instability, as well as by the electrification of the extrudates. The extrudate swell was smaller in the presence of slip when comparing with no slip conditions at constant apparent shear rate, but it was found to be a unique function of the shear stress if comparison was performed at constant stress. The draw ratio and melt strength of the filaments obtained under slip conditions were larger compared to those without slip. In addition, draw resonance was postponed to higher draw ratios during the extrusion with strong slip at constant apparent shear rate. It is suggested that slip of the polymer at the die wall decreases the shear stress in the bulk, and therefore, restricts the disentanglement and orientation of macromolecules during flow, which subsequently produces the increase in draw ratio and melt strength during stretching.

Stress–strain behaviour of poly(ethylene terephthalate) (PET) during large plastic deformation by plane strain compression: the relation between stress–strain curve and thermal history, temperature and strain rate

Abstract: This study presents an experimental investigation of the large plastic deformation of poly(ethylene terephthalate) (PET) submitted to plane strain compression. PET samples, obtained by injection moulding, annealed and non-annealed, were deformed using a specific compression device developed for this purpose. The obtained stress–strain curves at different temperatures and strain rates are useful for engineering applications and show a significant temperature dependence and a minor dependence on the strain rate. A softening temperature as a minimum temperature necessary to initiate deformation when a minimum, almost zero, stress is applied is introduced. This temperature, at the zero stress and strain limit, we denominate “Stress–Strain independent softening Temperature (TSOF)”. The TSOF values, 104 and 113°C for non-annealed and annealed PET, respectively, have been obtained using three different strain rates, indicating that the property is sensitive to the thermal history of the material.

On the fiber orientation in steady recirculating flows involving short fibers suspensions

Abstract: In this work we present a new numerical strategy to treat the 3D Fokker–Planck equation in steady recirculating flows. This strategy combines some ideas of the method of particles, with a more original treatment of the periodicity condition, which characterizes the steady solution of the FP equation in steady recirculating flows, as usually encountered in some rheometric devices. Using this numerical technique the fiber orientation distribution can be computed accurately in any steady recirculating flow. The simulation results can be used to identify some rheological parameters of the suspension, using an inverse technique, as well as to analyze the validity of some simplified models widely used, which require a closure relation. Thus, in this paper several closure relations of the fourth-order orientation tensor will be discussed in the context of a numerical example involving a steady recirculating flow.

A general method for obtaining shear stress and normal stress functions from parallel disk rheometry data

Abstract: The problems of converting the torque and normal force versus rim shear rate data generated by parallel disk rheometers into shear stress and normal stress difference as functions of shear rate are formulated as two independent integral equations of the first kind. Tikhonov regularization is used to obtain approximate solutions of these equations. This way of handling parallel disk rheometer data has the advantage that it is independent of the rheological constitutive equation and noise amplification is kept under control by the user-specified parameter in Tikhonov regularization. If the fluid under test exhibits a yield stress, Tikhonov regularization computation will simultaneously give an estimate of the yield stress. The performance of this method is demonstrated by applying it to a number of data sets taken from the published literature and to laboratory measurements conducted specifically for this investigation.

A correlation for yield stress fluid flow through packed beds

Abstract: Relatively few correlations are available for non-Newtonian fluid flows through packed beds, even though such fluids are frequently used in industry. In this paper, a correlation is presented for yield stress fluid flow through packed beds. The correlation is developed by introducing the yield stress model in place of the Newtonian model used in deriving Ergun’s equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to Ergun’s equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers and can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. Conditions for flow or no-flow are also determined in the correlation. Comparison of model calculations, between a Newtonian and a yield stress fluid for flow penetration into a packed bed of spheres, shows the yield stress fluid initially performs similar to the Newtonian fluid, at large Reynolds numbers. At lower Reynolds numbers the yield stress effect becomes important and the flow rate significantly decreases when compared to the Newtonian fluid.