Showing papers in "Rheologica Acta in 2008"
TL;DR: In this paper, the authors present an idiosyncratic view of the current state of shear banding in complex fluids, including applicability of models that have traditionally been used to model experiments, future directions and challenges for experimentalists, and issues surrounding vorticity banding.
Abstract: In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.
402 citations
TL;DR: In this paper, the authors investigate the use of two distinct and complementary approaches in measuring the viscometric properties of low viscosity complex fluids at high shear rates up to 80,000 s−1.
Abstract: We investigate the use of two distinct and complementary approaches in measuring the viscometric properties of low viscosity complex fluids at high shear rates up to 80,000 s−1. Firstly, we adapt commercial controlled-stress and controlled-rate rheometers to access elevated shear rates by using parallel-plate fixtures with very small gap settings (down to 30 μm). The resulting apparent viscosities are gap dependent and systematically in error, but the data can be corrected—at least for Newtonian fluids—via a simple linear gap correction originally presented by Connelly and Greener, J. Rheol, 29(2):209–226, 1985). Secondly, we use a microfabricated rheometer-on-a-chip to measure the steady flow curve in rectangular microchannels. The Weissenberg–Rabinowitsch–Mooney analysis is used to convert measurements of the pressure-drop/flow-rate relationship into the true wall-shear rate and the corresponding rate-dependent viscosity. Microchannel measurements are presented for a range of Newtonian calibration oils, a weakly shear-thinning dilute solution of poly(ethylene oxide), a strongly shear-thinning concentrated solution of xanthan gum, and a wormlike micelle solution that exhibits shear banding at a critical stress. Excellent agreement between the two approaches is obtained for the Newtonian calibration oils, and the relative benefits of each technique are compared and contrasted by considering the physical processes and instrumental limitations that bound the operating spaces for each device.
220 citations
TL;DR: In this article, the authors summarize the various tools for measuring locally the microstructure and the velocity field under shear, and a few results are extracted from current works to illustrate open questions and directions for future research.
Abstract: Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.
161 citations
TL;DR: In this article, the authors proposed a minimal model for gradient banding, which assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval.
Abstract: "Banded structures" of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the gradient or vorticity direction, the banding transition is referred to as "gradient banding" or "vorticity banding," respectively. The main features of gradient banding can be understood on the basis of a relatively simple constitutive equation. This minimal model for gradient banding will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient banding is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient banding can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity banding is less well understood and less extensively investigated experimentally as compared to gradient banding. Possible scenarios that are at the origin of vorticity banding will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain vorticity banding in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour.
152 citations
TL;DR: In this paper, the basics of Rheo-NMR and summarise its recent application to the study of shear banding are described and summarised, and a particular advantage of NMR is the ability to simultaneously investigate structural ordering and to compare such ordering with local strain rates.
Abstract: The phenomenon of shear banding in complex fluids has been investigated using NMR velocimetry and NMR spectroscopy, mostly in wormlike micelle systems, but more recently in colloidal systems and multilayer vesicles. A particular advantage of NMR is the ability to simultaneously investigate structural ordering and to compare such ordering with local strain rates. In this paper, we describe the basics of Rheo-NMR and summarise its recent application to the study of shear banding.
121 citations
TL;DR: In this paper, the linear and nonlinear rheology of colloidal glasses consisting of hard spheres and soft core-shell particles at several volume fractions was explored to explore the effects of particle softness on the mechanical properties and yielding.
Abstract: We studied the linear and nonlinear rheology of colloidal glasses consisting of hard spheres and soft core-shell particles at several volume fractions to explore the effects of particle softness on the mechanical properties and yielding. Creep and recovery and oscillatory shear measurements were used to determine the shear elastic modulus and the yield strain. Both hard and soft sphere glasses exhibited ‘entropic cage elasticity’ below random close packing, whereas for compressed soft spheres at higher effective volume fractions, the yield strain was determined by shell elasticity. The shear modulus followed a strong increase with volume fraction for hard spheres and a much weaker one for soft particles reflecting their interparticle potential. Nonlinear effects, revealed as strong distortions of the stress signal during yielding, were analyzed via Fourier transform rheology and Lissajous plots. The significant contribution of the nonlinearities was analyzed in terms of strain softening and hardening mechanisms within a cycle of oscillation and discussed in relation to particle softness.
115 citations
TL;DR: In this paper, the yielding of several reversible yield stress fluids was studied during scissometric-like creep experiments and the temporal evolution of the apparent deformation was recorded for applied stresses close and below the usual yield stress.
Abstract: The yielding of several reversible yield stress fluids is studied during scissometric-like creep experiments. The temporal evolution of the apparent deformation is recorded for applied stresses close and below the usual yield stress. Similarly to solids, three main creep regimes are observed. First, a primary creep regime displaying a temporal power law evolution of the deformation rate occurs, followed by a temporal minimum, which leads to an apparent flow of the material. This local minimum, defined as the “transition time,” and the subsequent fluidization can be observed at long times. The evolution of this time as a function of the applied stress appears to follow a universal law reminiscent of fracture behavior in hard solids.
90 citations
TL;DR: In this article, the effect of dispersion on the magnetorheological properties of the suspensions was also studied, and it was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field.
Abstract: In this work, we describe methods for the preparation of suspensions of micron-sized iron particles grafted with different surfactants. The aim is to obtain well-dispersed magnetorheological (MR) fluids. The effectiveness of the surfactants as dispersants was analyzed quantitatively by means of rheological measurements. With this objective, the viscosity of the suspensions was measured, and the results were compared with the prediction of the Batchelor’s formula (Batchelor, J Fluid Mech 83:97–117, 1977). The effect of dispersion on the MR properties of the suspensions was also studied. It was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field. It was also found that the transition from the solid-like state to the liquid-like one happens very smoothly for well-dispersed suspensions, contrarily to the abrupt transition for poorly dispersed suspensions.
70 citations
TL;DR: In this paper, broadband viscoelastic spectroscopy is used to isothermally study polymethylmethacrylate and low-density polyethylene at several temperatures in the glassy region.
Abstract: Many instruments used to measure viscoelastic properties are only capable of subjecting a sample to a limited range of loading frequencies. For thermorheologically simple materials, it is assumed that a change in temperature is equivalent to a shift of the viscoelastic behavior on the log frequency or time axis. For many materials, time–temperature superposition appears to work well for modulus or compliance curves over three decades of time or frequency, but some deviations are known if the window is expanded to five or six decades. To apply a more stringent test of the validity of time–temperature superposition, broadband viscoelastic spectroscopy is used to isothermally study polymethylmethacrylate and low-density polyethylene at several temperatures in the glassy region. Shear modulus and damping (tan δ) are measured isothermally over a wide range (up to 11 decades) of time and frequency. Results indicate that, while modulus curves can be approximately superimposed, the damping (tan δ) curves change in height and shape with temperature.
67 citations
TL;DR: In this article, a modification of the magnetocell, such that the magnetorheological fluid (MRF) sits on a non-magnetic Hall disc of 1.5mm thickness, allowing an online flux density measurement by a FW Bell Hall probe.
Abstract: The apparent shear stress from plate–plate magnetorheometry, using the commercial magnetocell MRD180/1T (Physica/Anton Paar) in standard configuration, is distinctly overestimated. The effect is due to a flux density maximum near the sample rim and radial migration of iron particles towards the rim. Radial magnetic flux density profiles were investigated by finite element simulations using the Maxwell®2D code and by direct Hall probe measurements. The reliability of the finite element method results, both for the empty magnetocell and with magnetorheological fluid (MRF) in the measuring gap, allows conclusions on the true flux density within the MRF, which cannot be accessed by Hall probe measurements. If the MRF sits on top of the bottom yoke (standard configuration), the flux density maximum reaches twice the plateau value (0.74 T for 3 A coil current and 0.3 mm gap height of the investigated MRF). This yields a higher effective flux density and causes radial iron particle migration, resulting in an additional magnetic flux increase near the rim due to augmented MRF magnetisation. As a result, the rotor torque at constant rotary speed increases with time. Reliable results are achieved by a modification of the magnetocell, such that the MRF sits on a non-magnetic Hall disc of 1.5 mm thickness, allowing an online flux density measurement by a FW Bell Hall probe. In this configuration, the radial flux density profile near the rim remains sufficiently flat and no iron particle migration is detected.
65 citations
TL;DR: In this article, a Ziegler-Natta, LLDPE (LL3001.32) was blended with four LDPEs having distinctly different molecular weights, and the weight fractions of the LDPE used in the blends were 1, 5, 10, 20, 50, and 75%.
Abstract: The thermorheological behavior of a number of linear low-density polyethylene and low-density polyethylene (LLDPE/LDPE) blends was studied with emphasis on the effects of long chain branching. A Ziegler–Natta, LLDPE (LL3001.32) was blended with four LDPEs having distinctly different molecular weights. The weight fractions of the LDPEs used in the blends were 1, 5, 10, 20, 50, and 75%. Differential scanning calorimetry (DSC) analysis has shown that all blends exhibited more than one crystal type. At high LDPE weight fractions, apart from the two distinct peaks of the individual components, a third peak appears which indicates the existence of a third phase that is created from the co-crystallization of the two components. The linear viscoelastic characterization was performed, and mastercurves at 150 °C were constructed for all blends to check miscibility. In addition, Van Gurp Palmen, zero-shear viscosity vs composition, Cole–Cole, and the weighted relaxation spectra plots were constructed to check the thermorheological behavior of all blends. In general, good agreement is found among these various methods. The elongational behavior of the blends was studied using a uniaxial extensional rheometer, the SER universal testing platform from Xpansion Instruments. The blends exhibit strain-hardening behavior at high rates of deformation even at LDPE concentrations as low as 1%, which suggests the strong effect of branching added by the LDPE component.
TL;DR: The aging behavior of neat laponite systems over the course of 1,000 or more days was observed in this article, where the aging behavior was predicted by models of soft glassy systems.
Abstract: We observe aging behavior of neat laponite systems over the course of 1,000 or more days. Under basic conditions, low laponite concentrations (1 wt%) slowly evolve from a viscoelastic liquid to a glass made of clusters acting as constituent elements interacting via long-range repulsion. Higher concentrations of laponite (3 wt%) quickly form a glass of individual particles. Intermediate concentrations of laponite form a glass that is a combination of clusters and individual particles. The aging rheological response and upturn of the loss modulus at low frequencies are well predicted by models of soft glassy systems (Fielding et al., J Rheol, 44(2):323–369, 2000; Sollich, Phys Rev E, 58(1):738–759, 1998). If low amounts of high-molecular-weight (Mn ≥ 163 kg/mol) poly(ethylene oxide) (PEO) are added, the aging behavior follows the dynamical response of the clay. Above a critical ratio, φ, of the free polymer chains in solution to the total laponite surface area, the PEO dynamics dominate at high frequencies. It appears that the dynamics of these complex laponite-PEO systems are governed by the parameter φ.
TL;DR: In this paper, the effects of 2.7-μm-diameter hydrophobic silica particles added to droplet-matrix blends of polyethylene oxide (PEO) and polyisobutylene (PIB) were investigated.
Abstract: We consider the effects of 2.7-μm-diameter hydrophobic silica particles added to droplet–matrix blends of polyethylene oxide (PEO) and polyisobutylene (PIB). The particles adsorb on the surface of the PEO drops but protrude considerably into the PIB phase. Hence, it is possible for a single particle to adsorb onto two PEO drops simultaneously. Such particles are called “bridging” particles, and they the glue drops into noncoalescing clusters. Flow visualization studies show that shearing the sample promotes bridging-induced clustering of drops and that the structure of the clusters depends on the shear rate. Rheologically, the most significant consequence of bridging-induced drop clustering appears to be a plateau in G′ at low frequencies characteristic of gel-like behavior. The gel-like behavior develops fully after shearing the sample, and the kinetics of gel formation are faster with increasing shear stress or increasing drop volume fraction. The gel-like behavior suggests that the bridging-induced drop clusters form a weak network. Apart from particle bridging, optical microscopy also reveals that particles can organize into a hexagonal lattice on the drops’ surfaces, a phenomenon that has only been noted in aqueous systems previously. Finally, rheology and flow visualization both suggest that particles promote coalescence of drops. This is surprising in light of much past research that shows that particles that are preferentially wetted by the continuous phase generally hinder coalescence in droplet–matrix systems.
TL;DR: In this article, the effect of carbon black particles on morphological processes (coalescence and break-up) in polyamide and ethylene-ethylene-metylacrylate copolymers was studied using rheological methods.
Abstract: The effect of low-volume fractions of nanoparticles on the morphological processes and the rheological properties of immiscible blends are dis cussed. For blends of poly-isobutylene and poly-dimethylsiloxane stabilized by silica particles, particles help to suppress coalescence. Yet, particle bridging of different droplets has also been reported and leads to a slow build up of a gel-like structure, which could interfere with the morphology evolution under flow. We first investigated the importance of this effect under relevant conditions. To further assess the relative importance of the different processes in technically relevant polymer–polymer blends, the effect of carbon black particles on morphological processes—coalescence and break-up—in polyamide and ethylene–ethylene–metylacrylate copolymers will be studied using rheological methods. It will be shown that particles affect coalescence and break-up, suggesting that the effect of particles is linked to their effect on interfacial dynamics.
TL;DR: In this paper, two constitutive equations have been applied, namely a viscoplastic Herschel-Bulkley model and a viscoelastoplastic K-BKZ model with a yield stress.
Abstract: Bread dough (a flour–water system) has been rheologically characterized using a parallel-plate, an extensional, and a capillary rheometer at room temperature. Based on the linear and nonlinear viscoelastic and viscoplastic data, two constitutive equations have been applied, namely a viscoplastic Herschel–Bulkley model and a viscoelastoplastic K–BKZ model with a yield stress. For cases where time effects are unimportant, the viscoplastic Herschel–Bulkley model can be used. For cases where transient effects are important, it is more appropriate to use the K-BKZ model with the addition of a yield stress. Finally, the wall slip behavior of dough was studied in capillary flow, and an appropriate slip law was formulated. These models characterize the rheological behavior of bread dough and constitute the basic ingredients for flow simulation of dough processing, such as extrusion, calendering, and rolling.
TL;DR: In this article, the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources was dealt with by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps.
Abstract: Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.
TL;DR: In this paper, the effect of interfacial area on the rheological behavior of a multilayered polyamide (PA6)/polyethylene grafted with glycidyl methacrylate was investigated.
Abstract: The rheological behavior of multilayered reactive polymers was investigated. Dynamic mechanical experiments were performed to probe the effect of the interfacial area on the rheological behavior of a multilayered structure as compared to that of a droplet-type morphology. Polyamide (PA6)/polyethylene grafted with glycidyl methacrylate was used as a model system, and in the molten state, such a system generated a reaction between amine, carboxylic, and epoxy groups. Multilayer structures containing various amounts of both interfacial area and volume fractions of the two components were studied. Relationships between viscoelastic material functions and compositions were used to analyze the effects of bulk and reactive functions in the polyolefin phase at the interface with PA. The contribution of the interface/interphase effect was investigated along with the increase in the number of layers, and the results showed that the variation in dynamic modulus of the multilayer system was a result of both diffusion and chemical reaction. Specific experiments were carried out to separate the thermodynamic effects from the kinetic ones, and the results were rationalized by comparing the obtained data with theoretical models. Finally, the effect of the interface/interphase triggered between the neighboring layers was quantified at a specific welding time and shear rate.
TL;DR: In this paper, the authors observed evidence of reentrant behavior in dispersions of a discotic clay, laponite, with added poly(ethylene oxide) with added polymer.
Abstract: We observe evidence of re-entrant behavior in dispersions of a discotic clay, laponite, with added polymer. Under basic conditions, neat laponite forms a disordered colloidal glass. Rheologically, this phase behaves as a viscoelastic solid, and dynamic light scattering shows evidence of non-ergodic behavior. Addition of low molecular weight poly(ethylene oxide) (PEO) melts the glass, resulting in a low-viscosity liquid with fast dynamics. We believe this is due to a depletion force caused by excess PEO chains in solution. A viscoelastic solid is re-formed with the addition of high molecular weight PEO, which we believe to be caused by polymer chains bridging between laponite particles. The physics in our system is quite different from the hard sphere/nonadsorbing polymer systems for which re-entrant glass transitions have been reported in the literature; however, we believe there may be similarities between these phenomena. To our knowledge, this is the first evidence of a type of re-entrant behavior in anisotropic colloids.
TL;DR: In this article, the rheological behavior of block copolymers with different morphologies (lamellar, cylindrical, spherical, and disordered) and their clay-containing nanocomposites was studied using small amplitude oscillatory shear.
Abstract: In this work, the rheological behavior of block copolymers with different morphologies (lamellar, cylindrical, spherical, and disordered) and their clay-containing nanocomposites was studied using small amplitude oscillatory shear. The copolymers studied were one asymmetric starblock styrene–butadiene–styrene copolymer and four styrene–ethylene/butylenes–styrene copolymers with different molecular architectures, one of them being modified with maleic anhydride. The nanocomposites of those copolymers were prepared by adding organophilic clay using three different preparation techniques: melt mixing, solution casting, and a hybrid melt mixing–solution technique. The nanocomposites were characterized by X-ray diffraction and transmission electron microscopy, and their viscoelastic properties were evaluated and compared to the ones of the pure copolymers. The influence of copolymer morphology and presence of clay on the storage modulus (G′) curves was studied by the evaluation of the changes in the low frequency slope of log G′× logω (ω: frequency) curves upon variation of temperature and clay addition. This slope may be related to the degree of liquid- or solid-like behavior of a material. It was observed that at temperatures corresponding to the ordered state, the rheological behavior of the nanocomposites depended mainly on the viscoelasticity of each type of ordered phase and the variation of the slope due to the addition of clay was small. For temperatures corresponding to the disordered state, however, the rheological behavior of the copolymer nanocomposites was dictated mostly by the degree of clay dispersion: When the clay was well dispersed, a strong solid-like behavior corresponding to large G′ slope variations was observed.
TL;DR: In this article, the authors extended the simple phenomenological model developed by Maffettone and Minale for the deformation of a single ellipsoidal drop in a viscous flow to predict the drop deformation in confined viscous flows.
Abstract: The simple phenomenological model developed by Maffettone and Minale (J Non-Newt Fluid Mech 78:227–241, 1998) for the deformation of a single ellipsoidal drop in a viscous flow is extended here to predict the drop deformation in confined viscous flows. The model is capable of describing the transient evolution of an ellipsoidal drop subjected to a generic flow field. The steady-state predictions are analytical and recover the theoretical limits of Shapira and Haber (Int J Multiph Flow 16:305–321, 1990) for steady small deformation of a drop in a confined simple shear flow. Model predictions are compared with data available in the literature that cover a wide range of parameter values, and the agreement is good.
TL;DR: In this paper, a combination of low-frequency loss tangent and light attenuation coefficient provides a potentially sensitive method for the characterization of the degree of clay dispersion in melt-processed nanocomposites.
Abstract: Nanobiocomposites of poly(lactic acid) (PLA) with 3–5 wt% organically modified montmorillonite (OMMT) were prepared by melt compounding in two different mixers, miniature twin-screw extruder and internal batch mixer, leading to different degrees of dispersion. The progress of dispersion was characterized by melt rheology coupled with light attenuation. Processed PLA/OMMT samples showed percolating networks in the melt, detected by a step increase in low-frequency elastic moduli. The melt elasticity of nanocomposites increased, while the light attenuation coefficient and the loss tangent decreased progressively with mixing energy and reached saturation that can be attributed to the maximum level of clay dispersion achieved in the present experimental conditions. Results showed that a combination of low-frequency loss tangent and light attenuation coefficient provides a potentially sensitive method for the characterization of the degree of clay dispersion. The direct correlation between light attenuation coefficient and loss tangent follows linear dependence and may open an approach for the rapid inline analysis of the degree of dispersion in melt-processed nanocomposites.
TL;DR: In this paper, the authors investigated the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO2) nanoparticles and polypropylene.
Abstract: We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO2) nanoparticles and polypropylene. Above a critical volume fraction, Φ
c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition, the elasticity of the hybrids shows critical behavior around Φ
c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters. For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G′, scaling with frequency, ω, as G′∼ω
0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of the components could be superimposed.
TL;DR: In this article, a filament stretching protocol for the study of the extensional rheology of both treated and untreated carbon nanotubes (CNT) suspended within an epoxy resin is described.
Abstract: This paper reports the application of a recently developed filament stretching protocol for the study of the extensional rheology of both treated and untreated carbon nanotubes (CNT) suspended within an epoxy resin. It was experimentally observed that filaments formed by treated and untreated CNT suspensions behaved differently after initial stretching. The filament thinning process of the base epoxy was consistent with a simple Newtonian fluid, whilst the filament of treated CNT suspensions also thinned in a Newtonian way but with an enhanced extensional viscosity. Filaments formed with untreated CNT suspensions behaved in a non-uniform way with local fluctuation in filament diameter, and it was not possible to obtain reliable extensional viscosity data. Irregularity of the untreated CNT filaments was consistent with coupled optical images, where spatial variation in CNT aggregate concentration was observed. In the case of treated CNT suspensions, the enhanced extensional viscosity was modelled in terms of the alignment of CNTs in the stretching direction, and the degree of alignment was subsequently estimated using a simple orientation model.
TL;DR: In this paper, a mesoscopic rheological model was developed for suspensions of fibers in viscoelastic fluids, and the results were interpreted with the help of a mesoscale rheology model.
Abstract: Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.
TL;DR: In this article, a phenomenological extension of linear viscoelastic suspension models into the nonlinear regime is proposed, focusing on their possibilities in the context of polymer crystallization, and the predictions of the most suitable model are compared to direct numerical simulation results and experimental data.
Abstract: The applicability of suspension models to polymer crystallization is discussed. Although direct numerical simulations of flowing particle-filled melts are useful for gaining understanding about the rheological phenomena involved, they are computationally expensive. A more coarse-grained suspension model, which can relate the parameters in a constitutive equation for the two-phase material to morphological features, such as the volume fractions of differently shaped crystallites and the rheological properties of both phases, will be more practical in numerical polymer processing simulations. General issues, concerning the modeling of linear and nonlinear viscoelastic phenomena induced by rigid and deformable particles, are discussed. A phenomenological extension of linear viscoelastic suspension models into the nonlinear regime is proposed. A number of linear viscoelastic models for deformable particles are discussed, focusing on their possibilities in the context of polymer crystallization. The predictions of the most suitable model are compared to direct numerical simulation results and experimental data.
TL;DR: The relaxation spectrum is estimated from dynamic experiments using Bayesian analysis and a new regularization constraint and the information content in a given set of experimental data can be quantified.
Abstract: The relaxation spectrum is estimated from dynamic experiments using Bayesian analysis and a new regularization constraint. In the Bayesian framework, a probability can be calculated for each estimate of the spectrum. This offers several advantages; (1) an optimal estimate of the relaxation spectrum may be calculated as the mean of a large number of estimates, and (2) reliable errors for the optimal estimate can be provided using the deviation of all estimates from the mean. Furthermore, the Bayesian approach (3) gives an estimate of the overall noise level of the experiment, which is usually an important but unknown parameter for the calculation of relaxation spectra from dynamic experiments by indirect methods (determining the regularization parameter), and finally, (4) the information content in a given set of experimental data can be quantified. The validity of the Bayesian approach is demonstrated using simulated data.
TL;DR: In this paper, the axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls.
Abstract: The axisymmetric and plane extrusion flows of a liquid foam are simulated assuming that the foam is a homogeneous compressible Newtonian fluid that slips along the walls. Compressibility effects are investigated using both a linear and an exponential equation of state. The numerical results confirm previous reports that the swelling of the extrudate decreases initially as the compressibility of the fluid is increased and then increases considerably. The latter increase is sharper in the case of the exponential equation of state. In the case of non-zero inertia, high compressibility was found to lead to a contraction of the extrudate after the initial expansion, similar to that observed experimentally with liquid foams and to decaying oscillations of the extrudate surface. The time-dependent calculations show that the oscillatory steady-state solutions are stable. These steady-state oscillatory solutions are not affected by the length of the extrudate region nor by the boundary condition along the wall.
TL;DR: The sensitivity of principal stress difference profiles to material viscoelasticity is demonstrated for two flow geometries using three different polyethylenes in this article using both experimental optical techniques and computational simulations, in the latter case to evaluate the ability to model these complex flows.
Abstract: The sensitivity of the principal stress difference (PSD) profiles to material viscoelasticity is demonstrated for two flow geometries using three different polyethylenes. Studies were performed using both experimental optical techniques and computational simulations, in the latter case to evaluate the ability to model these complex flows. The materials were characterised using linear and extensional rheology which was fitted to a multimode POM-POM model implemented in the Lagrangian–Eulerian code flowSolve. A contraction–expansion (CE) slit geometry was used to create a mixed, but primarily simple shear flow, whilst a cross-slot geometry provided a region of high extensional shear and high strain. In both flows, the PSD developed from an initial Newtonian profile to increasing levels of asymmetry between the inlet and the outlet flow. More specific phenomena, such as downstream stress fangs in the CE slit and the formation of centreline cusps and “W”-shaped cusps in the cross-slot, were also observed. The simulations of PSD development within the CE slit geometry quantitatively captured the experimental results. In the case of the cross-slot geometry, the qualitative features of the PSD development were well captured, although the results were quantitatively less accurate.
TL;DR: In this paper, a filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow, and the integral molecular stress function formulation within the 'interchain pressure' concept agreed qualitatively with the experiments.
Abstract: A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as $\epsilon(t) = \dot{\epsilon}_0 t + \Lambda [1 - \cos( 2 \pi \Omega \dot{\epsilon}_0 t )]$
where e is the Hencky strain, $\dot{\epsilon}_0$
is a constant elongational rate for the base elongational flow, Λ the strain amplitude (Λ ≥ 0), and Ω the strain frequency. A narrow molecular mass distribution linear polystyrene with a molecular weight of 145 kg/mol was subjected to the oscillative flow. The onset of the steady periodic regime is reached at the same Hencky strain as the onset of the steady elongational viscosity ( Λ = 0). The integral molecular stress function formulation within the ‘interchain pressure’ concept agrees qualitatively with the experiments.
TL;DR: Pattamaprom et al. as discussed by the authors used the dual-constraint model to predict the linear viscoelasticity of polydisperse linear and star-branched polymers.
Abstract: Although multiple models now exist for predicting the linear viscoelasticity of a polydisperse linear polymer from its molecular weight distribution (MWD) and for inverting this process by predicting the MWD from the linear rheology, such inverse predictions do not yet exist for long-chain branched polymers. Here, we develop and test a method of inverting the dual-constraint model (Pattamaprom et al., Rheol Acta 39:517–531, 2000; Pattamaprom and Larson, Macromolecules 34:5229–5237, 2001), a model that is able to predict the linear rheology of polydisperse linear and star-branched polymers. As a first step, we apply this method only to polydisperse linear polymers, by comparing the inverse predictions of the dual-constraint model to experimental GPC traces. We show that these predictions are usually at least as good, or better than, the inverse predictions obtained from the Doi–Edwards double-reptation model (Tsenoglou, ACS Polym Prepr 28:185–186, 1987; des Cloizeaux, J Europhys Lett 5:437–442, 1988; Mead, J Rheol 38:1797–1827, 1994), which we take as a “benchmark”—an acceptable invertible model for polydisperse linear polymers. By changing the predefined type of molecular weight distribution from log normal, which has two fitting parameters, to GEX, which has three parameters, the predictions of the dual-constraint model are slightly improved. These results suggest that models that are complex enough to predict branched polymer rheology can be inverted, at least for linear polymers, to obtain molecular weight distribution. Further work will be required to invert such models to allow prediction of the molecular weight distribution of branched polymers.