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Journal of RheologyVolume 40, Issue 4 (July-August 1996) |
Contents
Transient Rheological Behavior of a Long Discontinuous Fiber-Melt SystemT. S. Creasy, S. G. Advani and R. K. Okine SynopsisThe transient elongational behavior of a highly-aligned 60% fiber volume fraction long-discontinuous-fiber filled poly-ether-ketone-ketone (PEKK) melt system was investigated with a computer controlled extensional rheometer at 370°C. Long discontinuous graphite fibers, 7 µm in diameter, and poly-ether-ketone-ketone (PEKK) thermoplastic constituted the melt system. Experiments conducted under conditions to approximate controlled strain rate and controlled stress produced tau-barE+(t, epsilon-dot-bar) and epsilon-dot-bar-(t, tau-barE) similar to a shear dominated flow of a non-linear viscoelastic fluid. Increasing strain rate resulted in an increasing peak stress and in an increasing ratio between peak stress and plateau stress. Increasing controlled stress level resulted in decreasing elongational viscosity and increasing post-elastic-step strain rate. The ratio of apparent etaE/etaPEKK was 3.67 × 108 to 3.94 × 1010 for average strain rates from 6.81 × 10-7 to 1.49 × 10-3 sec-1. A variable taper shear cell analysis provided the range of expected etaE/eta, which agreed well at high strain rates with the experimental data. Secondary Flow of Entangled Polymer Fluids in Plane Couette ShearVijay R. Mhetar and L. A. Archer AbstractWe report new evidence of secondary flow during plane Couette shearing of entangled polystyrene solutions and an entangled polyisobutylene melt. The secondary flow is shown to be driven by normal stress imbalances at the free edges of the materials, and is accompanied by spatial variations in birefringence. In the polymer solutions, the secondary flow though unmistakable is weak and is only apparent from tracer particle visualization experiments using a video microscopy technique. In the polymer melt, however, secondary flow is much stronger and causes gross shape changes in sheared samples that are easily visualized with the naked eye. We also show that several details of the plane Couette secondary flow are correctly predicted by a simple differential constitutive equation in the narrow gap approximation. Our findings suggest that the secondary flow's effect on sliding plate rheological measurements could be minimized by: (a) using large plates with narrow gaps, i.e. small sample aspect ratios; (b) performing measurements at low Weissenberg numbers (Wi = tauL gamma-dot); and (c) employing measuring techniques such as laser birefringence that permit stresses to be determined close to the center of the shearing surfaces of the plane Couette cell. In addition to secondary flow, we find significant levels of slip during steady shearing of entangled polystyrene solutions. The slip though qualitatively similar to the entangled slip predictions of Brochard and deGennes [Langmuir 8, 3033-3037 (1992)], is unusual because at low slip velocities Vs the slip lengths b = Vs/gamma-dot are of the order of 150 µm, which is much larger than expected for entangled slip. Furthermore, slip in the solutions is shown to be non-isotropic with the slip velocity manifesting a similar shear rate dependence to the birefringence. These findings suggest that the slip law for entangled polymers may be more complex than previously thought. A Bead-Spring Model Incorporating Cyclic Structures, Non-Equal Springs and Beads with Non-Equal Friction CoefficientsA. I. M. Denneman and R. J. J. Jongschaap AbstractA formulation is given for a bead-spring model which possesses the following features simultaneously: (i) the Hookean springs may have different spring moduli, (ii) the friction coefficients belonging to the beads may be different, (iii) preaveraged hydrodynamic interaction may be included and (iv) the geometry of the bead-spring structure may contain cycles. The possible presence of cycles implies that one may use, in principle, three different representations for describing the geometry: one bead position representation and two different connector vector representations: one related to the springs of the entire bead-spring structure and the second related to the springs of a particular sub-structure (the spanning tree) of the entire bead spring structure. For these three representations it was possible to derive the equations of motion and the expressions for the corresponding modified Rouse and Kramers matrices. In case of a dilute solution of equal Hookean bead-spring structures (the spring moduli and friction coefficients may be non-equal, preaveraged hydrodynamic interaction may be included and the geometry may contain cycles) an explicit constitutive equation is obtained. The model is formulated in such a way that further extensions and modifications are relatively simple to incorporate. Shear Thickening in Model Suspensions of Sterically Stabilized ParticlesW. J Frith#†, P d'Haene*, R. Buscall#, and J. Mewis* *Katholieke Universiteit Leuven, Department Chemische
Ingenieurstechnieken #ICI Wilton Research Centre, P.O. Box 90, Wilton TS6 8JE, United Kingdom AbstractThe onset of shear thickening (dilatancy) has been studied in submicron model suspensions of sterically stabilized spherical particles. Stress controlled rheometers have been used for this purpose, so that measurements can be performed beyond the onset of sudden shear thickening. Systematic data are presented for the effect of particle size, particle concentration and the nature of the suspending medium on the onset of shear thickening. As a first approximation the critical shear-rate changes inversely proportional with the medium viscosity. The changing solvency of the medium for the stabilizer polymer introduces additional changes through effects on the thickness and stiffness of the steric barrier. Thinner, stiffer barriers cause lower critical shear-rates. In the softer systems the critical shear stress becomes independent of particle concentration in dense suspensions. This does not seem to be the case for the harder systems. The effect of particle radius a could shed some light on the underlying mechanisms of shear thickening. The data do not, however, enable us to decide between a scaling for the critical shear-rate with a2 or one with a3. The latter seems more appropriate for harder systems, the former for softer ones. †Present Address: Unilever Research Colworth Laboratory, Colworth House, Sharnbrook, Bedford MK44 1LQ, United Kingdom Rheology of Long-Chain Randomly Branched PolybutadieneLeo J. Kasehagen, Christopher W. Macosko Dave Trowbridge, and Fred Magnus SynopsisThe rheology of a series of long-chain randomly branched polybutadienes has been investigated. Branched samples were made through a hydrosilation reaction between a small difunctional crosslinker and the 1,2 groups distributed on the backbone of near-monodisperse PBD (Mw = 56,000, 137,000; Mw/Mn = 1.04). The resulting samples have both dispersity in molecular weight and architecture. The species distribution has been studied using size exclusion chromatography and has been found to agree with the Flory-Stockmayer distribution for the random branching of monodisperse chains. Sinusoidal oscillation and creep/creep recovery experiments were done to determine dynamic moduli, zero shear viscosity and equilibrium creep compliance. The observation that branching is random allows structural parameters to be calculated such as weight fractions and average molecular weights of free chains, arms and interior chains. These parameters are used in existing rheology models whose results are compared to experimental observation. In particular, qualitative agreement is found for zero shear viscosity as a function of branching content by applying the model proposed by McLeish and O'Connor for star/linear blends. Thixotropic Colloidal Suspensions and Flow Curves with Minimum: Identification of Flow Regimes and Rheological ConsequencesFrederic Pignon, Albert Magnin, and Jean-Michel Piau SynopsisSome colloidal suspensions with a thixotropic behavior and yield stress also display a minimum stress in their flow curves. One of these is an aqueous suspension of synthetic clay, consisting of anisotropic particles of nanometric size, forming a transparent thixotropic gel. Four flow regimes corresponding to four different states of strain field were defined by combining visualization techniques and rheometric measurements in cone-plate geometry Links with the microstructure of the suspension are suggested. Flow instabilities such as localized shear and stick-slip were identified in the falling branch of the flow curve and in the minimum stress area. Two regimes involving the bulk properties of the sample were identified. Consequently, proper procedures for characterizing the thixotropy of the suspensions are proposed. Component Predictions and the Relaxation Spectrum of the Double Reptation Mixing Rule for Polydisperse Linear Flexible PolymersD.W. Mead AbstractGeneral, experimentally verifiable predictions of individual component behavior of linear flexible polymer in arbitrary molecular weight distributions are derived from the double reptation mixing rule. The distribution of stress/orientation amongst the different components of the molecular weight distribution during steady deformation and constrained elastic recovery are developed for the case of a single exponential monodisperse relaxation function. The des Cloizeaux "double reptation" model and the Tsenoglou network model are shown to be equivalent and the precise relationship between the model parameters is determined. Distinct contributions to the relaxation process from the separate mechanisms of reptation and matrix relaxation (constraint release) are identified. Experimental relaxation spectra of bidisperse blends of nearly monodisperse polybutadienes reveal a cascade of discrete peaks in the terminal zone that are in qualitative agreement with theoretical predictions from the double reptation mixing rule with a Doi-Edwards monodisperse relaxation function. The ability to accurately calculate experimental relaxation spectra for complex blends of nearly monodisperse materials is a powerful tool in developing, discriminating and evaluating new mixing rules. How Copolymers Promote Mixing of Immiscible HomopolymersScott T. Milner and Haowen Xi AbstractCopolymers and stirring are commonly used to produce fine dispersions of immiscible homopolymers. Recent experiments call into question the classical view that copolymers promote the mixing by reducing the interfacial tension, suggesting rather that copolymers induce repulsive interactions between droplets and thus inhibit collision-induced coalescence events. We present a dynamical theory of the breakup and coalescence of polymer droplets in a mixing shear flow, including hydrodynamic and repulsive interactions between droplets. We find that a low surface coverage of copolymers, of order one chain per square radius of gyration, is sufficient to inhibit collisions between submicron-sized droplets, while giving a negligible reduction in inter-facial tension. Relationship between Rheology and Morphology of Model Blends in Steady Shear FlowI. Vinckier, P. Moldenaers, and J. Mewis SynopsisImmiscible polymer blends display a complex flow behaviour caused by the coupling between morphology and rheology. The flow induced microstructure has been studied on model systems of nearly inelastic polymers. For these systems, the elastic properties of the blend are mainly governed by the interface. Measurements of the storage modulus and of the first normal stress difference, both reflecting this enhanced elasticity, have been used to probe the blend morphology. From oscillatory measurements after cessation of flow the mean diameter of the disperse phase, as generated by the previous flow, has been calculated using the model of Palierne. A procedure based on a direct fitting of the dynamic moduli with the model is compared with one that uses a weighted relaxation spectrum. The steady state normal stress data, on the other hand, have been related to the morphology of the blend by means of the model of Doi and Ohta. Since this model predicts a direct proportionality between the contribution of the interface to the normal stress and the specific interfacial area, the size of the droplets can be calculated once the proportionality constant is known. The conditions for which the model is valid have been determined and the required constant is obtained by comparing the results with those from the dynamic moduli. The resulting droplet sizes have been used to develop a data reduction scheme: the specific interfacial area is found to be inversely proportional to the ratio of interfacial tension over shear stress for several blends with various concentrations and viscosity ratios. Transient Extensional Viscosity from a Rotational Shear Rheometer Using Fiber-Windup TechniqueMahesh Padmanabhan*, Leo J. Kasehagen, and Chris Macosko
AbstractThe fiber-windup technique, developed by Macosko and Lorntson (SPE Tech. Papers, 19, 461-467, 1973) for rotational shear rheometers, was re-examined to obtain transient uniaxial extensional viscosity data. Macosko and Lorntson used a special force transducer to measure the tension in the filament being pulled. In contrast, in this study commercial rotational shear rheometers (Rheometrics Mechanical Spectrometer-800 and Rheometrics Fluids Spectrometer II) with torque transducers were used to obtain the extensional viscosity. One end of the sample is clamped, while the other end is wound around a drum at a constant rotational speed, to achieve a given extension rate. Tests were conducted with a polyisobutylene sample at room temperature to verify reproducibility and compared with published studies. Results for polyisobutylene and IUPAC-X low density polyethylene were found in good agreement with published results. Hencky strains of up to 6 could be achieved. The technique can provide valuable extensional viscosity data for high viscosity liquids. * Present address: Adhesives Division, National Starch and Chemical Company, 10 Finderne Ave., Bridgewater, NJ 08807. Entrance Length and Pulsatile Flows of a Model Concentrated SuspensionN. Phan-Thien and Z. Fang AbstractThe flow behaviour of Phillips et al.'s suspension model (1991) in channel and pulsatile flows is investigated by a combination of analytical and numerical methods (using an unstructured finite volume method). In the channel flow, we found that the kinematics develop faster than the concentration, with an entrance length of 0.2 H3/a2, where H is the channel half width, and a is the particles' radius. The corresponding entrance length for the concentration is 0.5 H3/a2. In time-periodic flows, the steady-state kinematics and the stresses are periodic in time, and yet the steady-state concentration (and thus the viscosity) is time-independent. This feature is perhaps a critical test of the model, and indeed of any model in which the flux is quasi-linear in the generalized strain rate. Flow of a Yield Stress Fluid in a Long Domain Application to Flow on an Inclined PlaneJ. M. Piau AbstractComplex isochoric flows in a domain of space which is long compared to its width are studied for a visco-plastic and perfectly rigid Herschel-Bulkley model. It is argued here that no continuous yield surface can exist along the flow direction in these either confined or open channel flows. A similarity analysis is performed which shows that normal stresses cannot be neglected. For open channel flows the influence of normal stresses can be estimated through comparison of the yield stress value to the hydrostatic pressure value at the channel bed. Generalized Barré de Saint Venant one-dimensional equations are obtained. The influence of the yield stress value on wave velocity and on gradually varied flows and critical depth has been deduced. Rheological Characterization of Hanford Neutralized Current Acid Waste Simulant SlurriesC. Chang, P. A. Smith, and E. M. Tracey SynopsisUsing a Couette viscometer, we investigated the dependence of the steady shear viscosity of simulated neutralized current acid waste on pH and different acids. For a fixed weight percent of waste solids, the relative viscosity decreased as pH was lowered. The magnitude of the relative viscosity varied for the different acids. The values of random maximum packing for these different slurries were obtained using a floc-agglomerate structural model proposed by Tsutsumi et al. (1994). As the weight percent of waste solids is normalized by the value of maximum packing, the relative viscosity data approximately fall onto a single master curve for a specific shear rate. A direct relationship between the macroscopic rheological properties (steady shear viscosity) and the suspension microstructure was established through the packing behavior of a suspension. A comparison of the strongly flocculated and non-colloidal suspensions indicates that besides the normalized weight fraction, the dependence of shear rate must be considered to estimate the relative viscosity for strongly flocculated suspensions. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |