 |
 |
|
|
 |
Journal of RheologyVolume 46, Issue 6 (November-December 2002) |
Contents
Rouse chains with excluded volume interactions in steady simple shear flowJ. Ravi Prakasha) AbstractViscometric functions for a dilute polymer solution, undergoing steady simple shear flow, are predicted using a modified version of the Rouse model. The presence of excluded volume interactions between different parts of a polymer chain, which is not taken into account in the original fuse model, is incorporated into the present model with the help of a narrow Gaussian repulsive potential, that acts pairwise between the beads of the Rouse chain. Exact results are obtained numerically with the help of Brownian dynamics simulations, since the analytical tractability of the Rouse model is lost due to the modification. The presence of excluded volume effects is shown to cause the viscosity and the first normal stress difference to decrease with increasing shear rate ¾ a feature not predicted by the Rouse model, though commonly observed experimentally. The exact simulation results are used to assess the quality of an approximate solution, obtained by assuming that the non-equilibrium distribution function is Gaussian. The Gaussian approximation is found to be accurate within a certain range of parameter values. By extrapolating data acquired for chains of finite length to the infinite chain length limit, it is shown that the predictions of the Gaussian approximation become universal in this limit, independent of model parameters. The predicted universal dependence of the normalized viscosity, and the normalized first normal stress difference, on a characteristic nondimensional shear rate, is shown to be well represented by the Carreau-Yasuda model. a) Electronic address: ravi.jagadeeshan@eng.monash.edu.au Hindered flotation functions from NMR imagingStephen A. Altobellia) and Lisa A. Mondyb) a) New Mexico Resonance, Albuquerque, NM b) Sandia National Laboratories, Albuquerque, NM AbstractIn bat settling or flotation the velocity of the disperse phase ud = USG(f). US is the terminal velocity of an isolated particle, and G is the hindrance function. Vertical profiles of the fluid fraction in batch flotation experiments, measured with one-dimensional Nuclear Magnetic Resonance (NMR) imaging were input to a new method for extracting G. This simple, explicit calculation was tested on concentrated monodisperse and polydisperse samples. In a single experiment on a 44 ml sample of monodisperse suspension with overall solid fraction fi = 0.2, the hindered flotation function G(f) was measured over the range 0.05 < f < fm, where fm is the maximum packing fraction. This represents a significant simplification compared to observation of the clearing interface in a series of suspensions with varying fi. The hindrance function G was well fit by G(f)=(1 - f)5 as expected for monodisperse samples. In a polydisperse suspension, the NMR hindrance function showed an initial transient, and thereafter was fit coarsely by G(f)=(1 - f)4.4, in the range fi < f < fm. The new procedure is useful for rapidly characterizing settling or flotation of suspensions. Further, only a very small volume of suspension is required to measure G over a range of fi. a) E-mail: salto@nmr.org Rheological implications of completely monotone fading memoryR. S. Anderssena) and R. J. Loyb) a) CSIRO Mathematical and Information Sciences b) Mathematical Sciences Institute AbstractIn the constitutive equation modelling of a (linear) viscoelastic material, the “fading memory” of the relaxation modulus G(t) is a fundamental concept that dates back to Boltzmann (1876). There have been various proposals, that range from the experimental and pragmatic to the theoretical, about how fading memory should be defined. However, if, as is common in the rheological literature, one assumes that G(t) has the following relaxation spectrum representation G(t) = Integral of exp(-t/t) [H(t)/t)] dt from 0 to ¥ t > 0, then it follows automatically that G(t) is a completely monotone function. Such functions have quite deep mathematical properties, that, in a rheological context, spawn interesting and novel implications. For example, because the set of completely monotone functions is closed under positive linear combinations and products, it follows that the dynamics of a linear viscoelastic material, under appropriate stress-strain stimuli, will involve a simultaneous mixture of different molecular interactions. In fact, it has been established experimentally, for both binary and polydisperse polymeric systems, that the dynamics can simultaneously involve a number of different molecular interactions such as the Rouse, double reptation and/or diffusion (Thimm et al. (2000) and Léonardi et al. (2000)). The properties of completely monotone functions either yield new insight into the modelling of the dynamics of real polymers, or they call into question some of the key assumptions on which the current modelling is based, such as the linearity of the Boltzmann model of viscoelasticity and/or the relaxation spectrum representation for the relaxation modulus G(t). If the validity of the relaxation spectrum representation is accepted, the resulting mathematical properties that follow from the complete monotonicity of G(t) allows one to place the classical relaxation model of Doi and Edwards (1987), as a linear combination of exp(-t/t*) relaxation processes, each with a characteristic relaxation time t*, on a more general and rigorous footing. Rheological characterization of ionic bonding in ethylene-ionomer melts with low neutralization degreeAkihiro Nishioka, Tatsuhiro Takahashi, Department of Polymer Science and Engineering AbstractThe roles of ionic bonding in molten ethylene-ionomers without ionic aggregates were rheologically characterized in linear and non-linear regions under shear. We have measured melt rheology of ethylene-methacrylic acid (EMAA) ionomers by means of dynamic shear, step-shear relaxation, and transient shear viscosity. The studied samples were EMAA copolymer (MAA = 5.4 mol%), its sodium and zinc ionomers, in both of which the neutralization degree of total MAA is 20%, where no ionic aggregates exist. The dynamic shear properties revealed that the time-material superposition, i.e., the super-master curve, was applicable among the three samples, suggesting that the ionic bonding only acts as the increase of polymeric chain friction in the linear region. The damping functions from the step-shear relaxation were found to be identical to one another among the three, resulting in that the effect of ionic bonding does not appear. However, the damping property of the zinc ionomer, which was analyzed by the BKZ (Bemstein-Kearskey-Zapas) model in the start up of steady shear viscosity, exhibited unexpectedly much weaker than those of EMAA and the sodium ionomer. It is the first observation that the influence of pseudo cross-linking structure from ionic bonding clearly appears in experimental rheological studies of ethylene-ionomer melts. a) Author to whom all correspondence should be addressed. Tel: 81-238-26-3055; Fax: 81-238-26-3411; E-mail: koyama@yz.yamagata-u.ac.jp Inhomogeneous transient uniaxial extensional rheometeryJonathan P. Rothstein and Gareth H. McKinley AbstractA filament stretching rheometer is used to probe the development of coil-stretch hysteresis in transient non-homogeneous uniaxial elongation of a dilute polymer solution. Laser-Doppler velocimetry measurements are used to measure the steady centerline velocity profile in an elastic test fluid as it flows towards the throat of a 4:1:4 axisymmetric contraction-expansion over a range of Deborah numbers. The corresponding time-varying extension rate experienced by a fluid element as it flows into the contraction is then downloaded to a filament stretching rheometer in order to impose an identical inhomogeneous stretch history. Simultaneous optoelectronic measurements of the flow induced birefringence and mechanical measurements of the total tensile force in the filament allow independent determination of the evolution in the conformational anisotropy and stress. A pronounced stress-conformation hysteresis is observed with the relationship between the polymeric tensile stress and the average anisotropy in the polymer coil conformation evolving differently during the imposed extension and subsequent relaxation. An energy dissipation per unit volume can be calculated from the area enclosed by the stress-conformation hysteresis loop. The critical Deborah number for the onset of hysteresis and the scaling of the energy dissipation with increasing deformation rate are found to correlate closely with the development of the additional pressure drop that is measured macroscopically during viscoelastic flow through the contraction-expansion. These macroscopic and microscopic measurements both support the existence of an additional dissipative contribution to the polymer stress which must be resolved by constitutive models in order to accurately simulate complex flows of elastic polymer solutions. Shear thinning and thixotropy of HMHEC and HEC water solutionsA. Maestroa),
C. González, and J. M. Gutiérrez AbstractSteady state viscosity and thixotropy of hydrophobically modified hydroxyethyl cellulose (HMHEC) and non-associative cellulose water solutions is studied. Although all the samples are shear thinning, only the HMHEC is thixotropic, since the migration of hydrophobes to micelles is controlled by diffusion. The Cross model fits steady state curves. The Mewis model, a phenomenological model that proposes that the rate of change of viscosity when the shear rate is suddenly changed is related to the difference between the steady state and current values of viscosity raised to an exponent, fits structure construction experiments when the exponent n is estimated to be around 2. The Newtonian assumption used by Mewis cannot be used here, however. This seems to be related to the fact that the thickening is due to bridged micelles formation, which is a slow process, but also to topological constraints and entanglements, which are rapid processes. The kinetic parameter was redefined to kn in order to make it independent of initial conditions. So, kn depends only on how the shear affects the structure. kn reaches a plateau at shear rates too low to produce structure destruction and decreases at higher shear rates. a) Corresponding author. E-mail: maestro@angel.qui.ub.es Disentanglement of polymer melts flowing through porous medium before entering a capillary dieYannick Goutille and Jacques Guillet Laboratoire de Rhéologie
des Matières Plastiques AbstractTwo random styrene butadiene rubber (SBR) copolymers, one linear and one star-branched, are successively extruded through a porous medium and a capillary die. Porous media consisting of filters stacks are positioned just at the capillary die entrance. First, the effect of the flow history in different porous media on the corrected pressure in the capillary is investigated. In contrast to a previous work [Done et al (1983)], no significant decrease on the pressure loss across the capillary die wall is observed. Thus, extruded rods are submitted to elongational flow at the die exit by means of a Göttfert Rheotens apparatus in quasi isothermal conditions. The melt strength of the polymers is measured to assess the effect of filter stacks on rheological properties. As the response of the extruded polymer melt is characterized by its complex flow prehistory in the porous media, the filtration is found to decrease the melt strength (MS) whereas the breaking stretching ratio (BSR) is not affected. It is clearly shown that the magnitude of the variation depends on the filtering rate. As proposed by Done et al [1983], the decrease in melt strength is also assigned to the disentanglement of macromolecular chains in the porous medium. Quantitative relationship between rheology and morphology in emulsionsWei Yua), M. Bousminaa,e), M. Grmelab), J. F. Paliernec), and C. X. Zhoud) a) Department of Chemical Engineering b) CRASP, Ecole Polytechnique de Montreal c) Laboratoire de Physique URA 1325 du CNRS d) Department of Polymer Science and
Engineering AbstractCalculations based on Grmela, Bousmina and Palierne model (2001) for the simple case of ellipsoidal droplet-type morphology express a direct quantitative relationship between flow and microstructure both in steady and transient regimes. The results of the calculations show that in shear, elongational and planar hyperbolic flows it is possible to extract the morphology (the deformation and the orientation of the drop) from rheological material functions and conversely, rheological material functions can be obtained from in situ morphological observations. e) Corresponding author. Tel: 418-656-2769; Fax: 418-656-5993; E-mail: bousmina@gch.ulaval.ca Modeling of oscillatory shear flow of emulsions under small and large deformation fieldsWei Yua), Mosto Bousminaa,d), Miroslav Grmelab), and Chixing Zhouc) a) Department of Chemical Engineering b) CRASP, Ecole Polytechnique de Montreal c) Department of Polymer Science and
Engineering AbstractA model for a mixture of two Newtonian liquids undergoing oscillatory shear flow is presented. The model expresses qualitatively the relationship between the oscillating stress and the oscillating shape of the drops characterized by a second order symmetric tensor called a morphology tensor. The governing equations of the model are solved analytically in small oscillatory shear flow (SAOS) and, to the second order of the capillary number, in large oscillatory shear flow (LAOS). Maxwell type dynamic moduli under SAOS are found to give quite similar predictions as those of Palierne (1990) and Bousmina (1999) emulsion models. Nonlinear dependence of the shear stress and the first normal stress difference on strain are predicted for LAOS. The predictions of the model are found to be in agreement with the experimental results of Cavallo et al. (2002). d) Corresponding author. Tel: 418-656-2769; Fax: 418-656-5993; E-mail: bousmina@gch.ulaval.ca |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |