Numerical simulation of viscoelastic two-phase flows using openFOAM

In this work a new solver is developed for the OpenFOAM^® CFD toolbox, which handles viscoelastic two-phase flows. A derivative of the volume-of-fluid (VoF) methodology is used to describe the interface. Established constitutive equations derived from kinetic theory, such as Oldroyd-B, Giesekus, FENE-P and FENE-CR, from network theory of concentrated solutions and melts, such as linear and exponential Phan-Thien–Tanner (PTT), and from reptation theory, such as Pom–Pom and XPP models, as well as multi-mode formulations are implemented in OpenFOAM. Validation of the numerical technique is performed by comparing detailed simulation predictions to data from several experimental studies, numerical studies and analytical models found in the literature. Two well-known viscoelastic free-surface effects, namely the Weissenberg and the Die Swell effect, are simulated. Furthermore, transient and steady-state droplet flow in shear and elongational flows is examined.     

Estimation of rheological parameters using velocity measurements

In the present investigation, we develop a method for estimating rheological parameters of viscoelastic fluids using velocity measurement in a square straight channel. It is believed that a somewhat complicated patterns of secondary flows due to the non-zero second normal stress difference are more useful than the simple viscometric flows traditionally adopted in the determination of rheological parameters. The inverse problem of determining the rheological parameters from a set of velocity measurements is solved using a conjugate gradient method. When applied to a general constitutive equation encompassing the UCM model, the Oldroyd-B model and the PTT model, the present method is found to yield a reasonably accurate estimation of five rheological parameters simultaneously even with noisy velocity measurements.     

Synergistic Influence of pH and Temperature on Rheological Behavior of Adhesive Emulsions Stabilized with Micelle Dispersion of an Anionic Surfactant

The influence of emulsion pH and temperature on the rheological behavior of adhesive oil-in-water (o/w) emulsions stabilized with an anionic surfactant (sodium dodecyl benzene sulfonate, SDBS) was studied. The flow properties of emulsions as a complex fluid were investigated using steady and dynamic rheometry for characterization of non-Newtonian behavior. Emulsion pH was varied from 2 to 12 and temperature was varied from 20 to 50 °C, respectively. The influences of the above-mentioned variables on the rheology of o/w emulsion were studied using steady-shear and dynamic oscillatory experiments. Various viscosity models (2, 3, and 4 parameter rheological model) were used to predict the rheological parameters. An increase in the pH of the emulsion led to an increase in the emulsion stability, viscosity, and viscoelastic properties ( G′ , G″ , η* , and tan δ ), and a decrease in the mean droplet size of the emulsion. A decrease in the temperature yields higher values of steady-shear viscosity and viscoelastic properties upon a decrease in droplet size. Emulsions were characterized as flocculated structured liquid exhibiting a characteristic crossover frequency ( ω* ) within the range of angular frequency studied in oscillatory measurements. Overall, emulsions exhibited non-Newtonian shear-thinning behavior and the synergy of pH and temperature significantly influences the emulsion rheology.     

The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres

A study on the interaction of particles settling in non-Newtonian fluids of shear-thinning, thixotropic and viscoelastic characteristics has been conducted. Key aspects of the rheological characteristics of the fluids that influence the interaction of the particles were examined by analysing the trajectories of two particles that are initially placed side-by-side in the fluid medium.The interaction of the particles was found to be highly dependent on the separation distance that is initially set between them. If the initial distance is smaller than a critical value, the spheres would tend to attract and converge. In cases where the initial distance is greater than this critical value, the two spheres would tend to diverge, resulting in a slight (∼20%) increase in their separation distance over their course of settling. This tendency to diverge was found to diminish as the initial distance is increased further from the critical value.The magnitude of the critical separation distance was found to be primarily dependent on the normal stresses of the fluids. A correlation was thus proposed based on this observation. In cases where the two spheres do attract and converge, it was found that the spheres tend to follow a non-symmetrical trajectory, where one of the spheres possesses a slightly lower settling velocity than the other. As a result, the spheres appear to re-arrange themselves into a vertically aligned configuration. Once aligned, the shear-thinning and thixotropic characteristics of the fluid causes the lagging sphere to accelerate and collide with the leading sphere.     

Extensional flow of wormlike micellar solutions

We consider the inhomogeneous extensional response of a new constitutive model, the VCM model [Vasquez, et al., 2007. A network scission model for wormlike micellar solutions I: model formulation and homogeneous flow predictions. J. Non-Newt. Fluid Mech. 144, 122-139] that has been developed to describe concentrated solutions of wormlike micelles. The time dependent numerical analysis is carried out in a simplified slender filament formulation appropriate for transient elongational flows of complex fluids. The simulations show that, beyond a critical extension rate, elongating filaments of a micellar fluid described by the VCM model exhibit a dramatic and sudden rupture event as a result of the scission of the entangled wormlike chains. The computations capture many of the features of the high-speed rupture process observed experimentally [Bhardwaj, et al., 2007. Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions. J. Rheol. 51, 693-719] in filament stretching experiments with wormlike micelle solutions. The highly localized rupture predicted by the VCM model and the corresponding evolution in the tensile force within the filament is contrasted with the familiar and more gradual necking responses predicted by the upper convected Maxwell and Giesekus models under equivalent kinematic boundary conditions.     

Fluidization with viscoelastic polymer solutions in the transition flow region

Fluidization of spherical and non-spherical particle beds with shear thinning viscoelastic polymer solutions was investigated experimentally in the transition flow region. It was observed that the influence of elasticity on the anomalous expansion course weakens with the increasing value of Reynolds number. After exceeding a critical value of Reynolds number, which depends on the measure of liquid elasticity, the effect of elasticity vanishes and the expansion curves have the same linear shape as for fluidization with Newtonian (or purely viscous non-Newtonian) fluids. Semi-empirical equations based on the Carreau viscosity model were proposed for predicting the critical value of Reynolds number and the bed expansion in the region of diminishing elasticity effects.     

Simulation of the polymeric fluid flow in the feed distributor of melt blowing process

The polymeric fluid flow in the feed distributor of melt blowing process is simulated using three‐dimensional finite element method. The numerical results are experimentally verified quantitatively and qualitatively using laser Doppler velocimetry and particle image velocimetry respectively. The effects of the distributor's geometric parameters on the uniformity of the transverse flow distribution are investigated. As the manifold angle increases, the flow distribution curve appears to transform gradually from a “hill” shape to a “bone” shape. The uniformity of flow distribution at distributor outlet, especially the fluctuation at the central part, will be improved by increasing the land height. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 1570–1574, 2006     

A level set based immersed boundary method for simulation of non-isothermal viscoelastic melt filling process

In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the non-isothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with differ-ent Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress differ-ence, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.     

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR=2.4, 4, 8 and 12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streak line photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at De≈200, 300, 70 and 450 for CR=2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments.     

Rheological behavior of new melt compounded copolyamide nanocomposites

In this paper the rheological behavior of new polyamide-based nanocomposites produced by melt compounding using three different silicate loadings and screw speeds was investigated. The thermoplastic matrices selected were a polyamide 6 and its statistical copolymer having partially aromatic structure, whereas the clay was a commercial organo-modified montmorillonite. Hybrid systems were prepared by means of a laboratory-scale twin screw extruder and were submitted to rheological and structural investigations. The rheological experiments (dynamic frequency sweep, steady rate sweep and stress relaxation tests) were performed to evaluate the effect of both system composition (kind of matrix and clay content) and extrusion rate on the flow behavior of the nanocomposites. Rheology, that is highly sensitive to the nanoscale structure of the materials, put out a pseudo-solid like flow behavior at long times in the hybrids with silicate content higher than 6 wt% and produced with high extrusion rate; this response was related to the formation of an extended structural network across the polymer matrix due to strong polymer-silicate interactions that slow the relaxation times of the macromolecules. Corresponding to this behavior, TEM micrographs have shown a quite uniform dispersion of clay particles on micron-scale and a fair level of silicate exfoliation on nanoscale with a macroscopic preferential orientation of the layers in samples. The rheological measurements also reveal that this flow response is more marked for nanocomposites based on the copolyamide matrix, suggesting that this resin may have a higher silicate affinity respect to polyamide 6 homopolymer.     

Polypropylene blends with potential as materials for microporous membranes formed by melt processing

Novel microporous membranes with pore size ranging from 2 to 25 nm were produced from immiscible polypropylene blends via melt processing and post-extrusion treatments. Systems containing polystyrene and polyethylene terephthalate as the minor phase components were employed as starting membrane materials at concentrations not exceeding 15 wt%. The blends were first compounded in a co-rotating twin-screw extruder and subsequently extruded through a sheet die to obtain the non-porous precursor films. These were uniaxially drawn (100-500%) with respect to the original dimensions at a temperature below the glass transition temperature of the minor phase to induce a microporous structure and then post-treated at elevated temperatures to stabilize the porous structure, which consisted of uniform microcracks in the order of a few nanometers in width. The effects of dispersed phase concentration and component melt rheology on the solid and microporous blend morphologies are presented. Finite element modeling of the stretching operation in the solid state yielded a successful interpretation of the blend response to uniaxial tension that resulted in microcrack formation. The processes developed in this work may be considered as solventless alternatives to phase inversion manufacturing practices for membranes containing mesopores.     

Conversion of Recycled Polymers/Fibers Into Melt-Blown Nonwovens

Being a simple one-step process for converting polymer directly into a nonwoven fabric, melt blowing is ideally suited for processing of several recycled plastics. The process uses hot air to draw the fibers and does not require precise, individual control of each filament as in the conventional fiber-spinning processes. Recycled polypropylenes (PPs) from several sources were investigated as candidates for melt blowing. Waste from spun-bond line and spun-bond-melt-blown-spun-bond (SMS) fabrics were pelletized and then melt blown at our facility. The feasibility of using a melt-blowing line with an extruder gear pump unit to remelt the waste fibers/web and feed it with the molten virgin polymer stream coming from the main extruder was explored. A 1000 MFR virgin PP resin and fabrics produced from that polymer were used for this investigation. Fabrics were characterized in all the cases for their performance properties. Some of the relevant data are reported here. It was observed that in most of the cases, fabrics with good properties could be produced at high throughputs, thus demonstrating that most of the plant waste can be reused.     

Sensitivity analysis of low-speed melt spinning of isotactic polypropylene

Linearized sensitivity analysis of fiber spinning has been studied using a two-phase constitutive model that includes the effects of crystallization. The analysis focuses on sensitivity predictions for the low-speed melt spinning of isotactic polypropylene and comparison to the experimental results of Young and Denn [1989, Disturbance propagation in melt spinning. Chemical Engineering Science 44, 1807-1818]. Modifications in an earlier-developed two-phase model enable comparisons of two different constitutive equations for the melt phase, namely the Giesekus and extended pom-pom models. Comparisons with sensitivity data for low-speed spinning conditions demonstrate that the incorporation of crystallization effects leads to improved predictions of the magnitude and trends of the perturbation frequency dependence for both constitutive equations. At low spin speeds where flow-enhanced crystallization effects are negligible, the sensitivity is predicted to decrease with increasing cooling and this trend is also shown to be consistent with increased crystallinity.     

The melt grafting preparation and rheological characterization of long chain branching polypropylene

To study the rheological properties of long chain branching (LCB) polypropylene (PP), long chain branches (LCB) were grafted onto the linear PP by melt grafting reaction in the presence of a novel chain extender, poly(hexamethylendiamine-guanidine hydrochloride) (PHGH). The branching reactions between the functionalized PP and PHGH were confirmed by transient torque curves and FTIR. By differential scanning calorimetry (DSC) and polarized microscope measurements, the presence of long chain branching structures was further confirmed. Also, the viscoelastic properties of the LCB PP and linear PP under shear flow were investigated for distinguishing LCB PP from linear PP. It was found that the elastic response of LCB PP at low frequencies was significantly enhanced in comparison with that of the linear PP, implying a presence of a long relaxation time mode that was not revealed in linear PP. Moreover, the branching levels of LCB PP were quantified using a detailed method, which was in correspondence with the molar amount of PHGH grafted on PP.     

The effect of melt viscosity on thermal efficiency for single screw extrusion of HDPE

In this work, a highly instrumented single screw extruder has been used to study the effect of polymer rheology on the thermal efficiency of the extrusion process. Three different molecular weight grades of high density polyethylene (HDPE) were extruded at a range of conditions. Three geometries of extruder screws were used at several set temperatures and screw rotation speeds. The extruder was equipped with real-time quantification of energy consumption; thermal dynamics of the process were examined using thermocouple grid sensors at the entrance to the die. Results showed that polymer rheology had a significant effect on process energy consumption and thermal homogeneity of the melt. Highest specific energy consumption and poorest homogeneity was observed for the highest viscosity grade of HDPE. Extruder screw geometry, set extrusion temperature and screw rotation speed were also found to have a direct effect on energy consumption and melt consistency. In particular, specific energy consumption was lower using a barrier flighted screw compared to single flighted screws at the same set conditions. These results highlight the complex nature of extrusion thermal dynamics and provide evidence that rheological properties of the polymer can significantly influence the thermal efficiency of the process.     

Considère reconsidered: Necking of polymeric liquids

We review the Considère construction and discuss its applicability to the prediction of the inception of necking in extensional flow. The behaviour of simple fluid models is used to illustrate the importance of fully specifying the flow conditions. Even for a Newtonian liquid there is a marked difference in the prediction of necking under the application of a constant force and the imposition of a constant rate of strain.     

Rheological Behavior and Structure of a Commercial Esterquat Surfactant Aqueous System

Aqueous dispersions of a commercial esterquat‐type surfactant widely used in fabric softeners were rheologically characterized. While at 4 wt % esterquat concentration, a Newtonian response was observed; non‐Newtonian (Sisko) flow behavior and viscoelastic properties were found at 12 wt % and higher concentrations. The onset of nonlinear viscoelasticity in oscillatory shear provided interesting information on the strength of quiescent surfactant aggregates. Mechanical spectra corresponded to the plateau zone and the onset of the transition zone. The plateau modulus and the characteristic slopes of the relaxation spectra depended on the strength of the interactions among the aggregates. Start‐up at the inception of the shear experiments were carried out to obtain information on the time‐dependent shear behavior. Cryo‐SEM micrographs demonstrated the occurrence of a dispersion of vesicles embedded into a bilayer matrix.     

A model for the two-layer blown film process with flow-enhanced crystallization

A 2-D model for non-isothermal bi-layer film blowing is developed based on the 1-D film blowing model of Henrichsen and McHugh [2007a. Analysis of film blowing with flow-enhanced crystallization: part 1. Steady-state behavior. International Polymer Processing XXII (2), 179-189] that accounts for viscoelasticity and flow-enhanced crystallization. Numerical results demonstrate the role of rheological, thermal, and crystallization properties on the development of crystallinity and stresses in a bi-layer system consisting of two crystallizable polymers. For a two-layer film consisting of the same materials, the evolution of the stress in an individual layer can be significantly different due to the temperature difference. Varying the material properties in a given layer, such as the plateau modulus and the maximum crystallization rate, not only leads to the corresponding responses in its own layer, but also influences stresses and crystallinity in the other layer through heat transfer between two layers. Results further demonstrate that stresses in the film after the frost line will be borne primarily by the layer that solidifies first, while the second, molten component will have a tendency to relax. The layer arrangement is also shown to have direct impact on the stresses and semi-crystalline phase orientation at the freeze point which will impact the final properties of the film.     

Modeling of melt electrospinning for semi-crystalline polymers

A comprehensive model for the stable jet region in electrospinning of crystallizing polymer melts has been presented. First, the conventional flow-induced crystallization (FIC) model by Ziabicki was coupled with the non-isothermal melt electrospinning model. The modeled initial jet profiles were compared to digitized experimental images of the stable Nylon-6 melt jet near the spinneret. The final jet diameters were also compared to the average thickness of collected fibers. The results were in good agreement with the flow visualization experiments for various melt temperatures and flow rates. The modeled crystallinity predictions were also in agreement with experimental data from collected fiber mats. Then, a new FIC model that can provide microstructure information, such as crystallite number density and average size, has been proposed and validated under isothermal and non-isothermal conditions in the bulk as well as in the confined geometry of the polymer melt jet in electrospinning. Nylon-6,6 was used as the model polymer in this crystallization study, and the results are in good agreement with the widely-used Ziabicki FIC model.     

The engineering rheology of liquid explosives as highly concentrated emulsions

Rheological properties of liquid explosives are summarized and discussed in this paper. Liquid explosives are highly concentrated emulsions by their physical nature. During the internal phase, it is an aqueous supersaturated solution of mainly ammonium nitrate which is a useful component of a multi-component system, and at the continuous phase it is a solution of emulsifier in hydrocarbon oils. Liquid explosives demonstrate a complex set of properties characteristic for highly concentrated emulsions, such as visco-plasticity, existence of the yield stress, thixotropy (or time-dependent behavior), non-Newtonian flow at stresses exceeding the yield stress. Rheological properties depend on the concentration of internal phase, size of droplets, and the nature of the used surfactant. Stability of these materials is determined mainly by the tendency of an aqueous solution to crystallization at prolonged storage, though shearing does not influence on phase separation. Wall slip is absent in flow of liquid emulsions through tubes. Therefore, it allows us to make reliable predictions on the output vs. pressure dependence for real technological practice.