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Journal of RheologyVolume 45, Issue 6 (November-December 2001) |
Contents
A simple constitutive equation for entangled polymers with chain stretchGiovanni Ianniruberto and Giuseppe Marruccia) AbstractWe here propose a simple way of including chain stretch effects in CCR theories for entangled polymers. The main idea is that the characteristic time of orientational relaxation depends in a series-parallel way on all three relevant mechanisms, i.e., reptation, constraint release (thermal and convective), and Rouse relaxation. As usual, a separate equation describes chain stretch, which however is assumed not to be affected by constraint release. The model is further simplified by writing the orientational equation in differential form. For step strains, the successful damping function of the Doi-Edwards theory is exactly preserved. Predictions in steady shear also favorably compare with typical data of nearly monodisperse polymers. a) To whom correspondence should be addressed. E-mail: marrucci@unina.it Two-dimensional Fourier transform rheologyDagmar van Dusschotena),
Manfred Wilhelm, and Hans W. Spiess AbstractA two dimensional FT-rheology experiment is presented that separates the relaxation dynamics of different contributions to the stress relaxation, here specifically for entangled polymers. This experiment has the overall form of discrete large amplitude oscillations and consists of multiple step shear experiments. It is called Large Amplitude Step Shear Oscillations, or short, LASSO. The time-dependent non-linear material response follows the discrete periodic excitation and can therefore be Fourier transformed, which results in a spectrum of harmonics for each delay time between the steps. The Fourier Transformation is used here to correlate the different step shear experiments. The method was applied to a slightly entangled, polydisperse PIB solution where a small deviation of the time strain separation is detected, even at times exceeding the Rouse time by orders of magnitude. On the other hand, the Time Temperature Superposition seems to work for all the harmonic decays within the spectrum. When the time window between the shear steps is reduced such that slow relaxation processes still possess memory of prior steps, an increase of the non-linear contributions of the fast, completely relaxed, relaxation modes is observed. This is in qualitative agreement with reptation models where polymer stretching and orienting are considered coupled processes. a) To whom correspondence should be addressed. E-mail: dvd@mpip-mainz.mpg.de Finite element analysis of axisymmetric creeping motion of a deformable non-Newtonian drop in the entrance region of a cylindrical tubeSee Jo Kim Chang Dae Ran AbstractThe finite-element method was employed to analyze axisymmetric creeping motion of a deformable drop in the entrance region of a cylindrical tube. In the present study a non-Newtonian drop suspended in a non-Newtonian medium was considered, for which a truncated power-law model was employed. The penalty function method was used to eliminate the pressure variables from the system equations, considerably reducing the computational time required. In solving the system equations an unstructured mesh generator and auto-remeshing technique were used to describe the shapes of highly deformed drops. The results are in good agreement with experiments of Chin and Ran (1979, 1980), describing the deformation as the drop approaches the inlet from the reservoir section and recoil after it enters the tube. The present study demonstrates the effects of the capillary number and viscosity ratio on the deformation of non-Newtonian drops suspended in non- Newtonian liquids in the entrance region of a cylindrical tube. The effect of droplet extension on the rheology of emulsions of water in alkyd resinM. J. Thompsona), J. R. A. Pearsonb), and M. R. Mackleya) a) Department of Chemical Engineering b) Schlumberger Cambridge Research AbstractWe present experimental findings and matching modelling concerning the effect of water droplets on the rheology of a high viscosity alkyd resin. In the flow regime where significant droplet deformation occurs, the shear viscosity of the fluid containing highly extended filaments was found to be lower than that of the alkyd resin on its own. A theoretical mechanism for this high shear rate viscosity reduction is proposed, and reasonable agreement established with experimental observation. At intermediate shear rates a crossover between viscosity enhancement and viscosity reduction correlates with a capillary number close to one. At low shear rates classic viscosity enhancement was observed. The viscosity of surfactant stabilized emulsionsK. M. B. Jansen, W. G. M. Agterof and J. Mellema AbstractA new scaling parameter for the viscosity of surfactant stabilized emulsions is proposed. We suggest that the attractive force between emulsion droplets is caused by the small surfactant micelles in the continuous phase of an emulsion. The new scaling parameter will be referred to as the depletion flow number, Fld = 4phs(g-dot)a2am/ kTfm, and is defined as the ratio between the viscous energy needed to separate the droplets and the depletion energy which opposes this separation. Here hs, a, am and fm are the solvent viscosity, dispersed phase droplet radius, micelle radius and micelle volume fraction, respectively. Fld is of order unity at the onset of shear thinning and is capable of explaining all previously observed effects of drop size, solvent viscosity and surfactant concentration. With the master curves which are obtained by using Fld as the running parameter, a relatively simple empirical model is constructed which could reproduce the viscosity curves of many previously reported publications. Assessment of the Doi-Ohta theory for co-continuous blends under oscillatory flowI. Vinckiera) and H. M. Launb) a) Chemical Engineering Department b) Polymer Research, Polymer Physics AbstractPredictions of the semi-phenomenological Doi-Ohta theory for the rheology and morphology of immiscible blends are compared to experimental data of a 40/60 blend of PMMA/PaMSAN with a co-continuous structure. As the Doi-Ohta theory actually was developed for co-continuous blends, published comparisons on droplet-matrix blends are not considered as adequate. It is verified how the polymeric constituents contribute to the blend response and it is shown how the phenomenological parameters of the Doi-Ohta theory can be determined. Subsequently, these parameters are used to predict the morphology evolution and rheological response of the blend under oscillatory flow. The evolution of the storage modulus clearly reflects the changes in morphology of the blend with time and strain amplitude in agreement with the theoretical predictions. Below a critical strain amplitude the co-continuous structure will coarsen until a droplet-matrix morphology is generated but large strain amplitudes are effective enough to stop domain growth. Design of an orifice die to measure entrance pressure dropSeungoh Kim and John M. Dealya) AbstractThe entrance pressure drop (DPEnt) associated with the flow from a cylindrical reservoir into a capillary is of great importance in melt rheology. First, it is required in order to determine the true wall shear stress in a capillary rheometer when only the overall pressure drop is measured. In addition, it is used to calculate an average extensional viscosity at strain rates that are not accessible using a true extensional rheometer. We recommend the use of a specially designed orifice die, in place of a Bagley plot, for the determination of this entrance pressure drop. This orifice has the following characteristics: its length to diameter ratio (L/D) is no more than 0.5, its entrance angle is greater than 90°, and the exit of the orifice is designed to prevent melt from touching the die wall. a) Author to whom correspondence should be addressed. The molecular stress function model for polydisperse polymer melts with dissipative convective constraint releaseM. H. Wagnera), P. Rubiob), H. Bastianb) a) Technische Universität Berlin b) Universität Stuttgart AbstractThe Molecular Stress Function (MSF) theory for polymer melts is extended to include a new, dissipative convective constraint release process. First the Helmholtz Free Energy of tube segments with strain-dependent tube diameter is established neglecting constraint release, and it is demonstrated that the molecular stress is a function of the average logarithmic stretch under these conditions. Then convective constraint release is introduced as a dissipative process in the energy balance of tube deformation, which leads to a strain-dependent evolution equation for the molecular stress function. Constraint release is considered to be the consequence of different convection mechanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasises that tube kinematics is fundamentally different for rotational and irrotational flows, and therefore distinguishes explicitly between simple shear and pure shear (planar extension). For start-up of simple shear and extensional flows, the predictions of our set of constitutive equations consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress function with only two non- linear material parameters, are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, stress relaxation after a step-shear strain is described for both the HDPE and the LDPE melt. Role of lubricated contacts in concentrated polydisperse suspensionsChristophe
Ancey AbstractThis paper presents experimental results concerning the bulk behavior of concentrated suspensions of coarse and fine (colloidal) particles in a Newtonian fluid (water). Different rheological behaviors can be observed depending on both the solid concentrations in fine and coarse particles and the shear velocity. For suspensions concentrated in coarse particles that are poor in fine particles, bulk behavior is frictional for low shear velocities and viscous for sufficiently large shear velocities. In the converse case, for mixtures rich in fine particles, bulk behavior is viscoplastic. A more complex time-dependent behavior can be observed when the viscoplastic force exerted by the dispersion on coarse particles roughly balances the force of gravity. The diversity in bulk behavior is explained by the specific role played by the contact between coarse particles. Time-strain non-separability in viscoelastic constitutive equationsYoungdon Kwona,c) and Kwang Soo Chob) a)
Department of Textile Engineering b)
Department of Materials Science & Engineering AbstractThe time-strain separability in viscoelastic systems is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood [Archer (1999)]. In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. It is shown that the Hadamard-type instabilities of the Wagner, Luo- Tanner, Papanastasiou and K-BKZ models with Larson-Monroe or Mooney potential, as well as the dissipative instability of the Lodge model (all proven previously) [Kwon and Leonov (1995)] are all caused by the separability hypothesis inherent in their equations. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamard-type instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. c) Corresponding author: ydkwon@yurim.skku.ac.kr Determination of viscosity from drop deformationY. T. Hua) and A. Lips AbstractA novel technique for measuring viscosities of droplets is described. This technique uses the transient and steady state deformation of a droplet suspended in an immiscible fluid. Drop viscosities are derived from small deformation theory as hd = (-5(g-dot)/2Dsa - 1.5)hs for hyperbolic flow, and hd = (-5(g-dot)/4Dsa - 1.5)hs for shear flow. Here g-dot is the flow rate, Ds is the steady state deformation, a is the exponent obtained from deformation growth or relaxation, and hs is the suspending fluid viscosity. Drop viscosities measured using this technique as implemented on a 4-roll mill apparatus are compared with bulk viscosities measured using a conventional rheometer. The measurement scope of the new technique, with respect to capillary number, drop size and viscosity ratio, is defined. a) Author to whom correspondence should be addressed; e-mail: thomas.hu@unilever .com Unstable flow and non-monotonic flow curves of transient networksEric Michel,
Jacqueline Appell, François Molino, AbstractWe have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated. The phase behavior is characterized which comprises a liquid-gas phase separation and a percolation threshold. The rheological measurements are performed in the one phase region above the percolation line. Shear thinning is observed for all samples, leading in most cases to an unstable stress response at intermediate shear rates. We built up a very simple mean field model which involves the reduction of the residence time of the stickers in the droplets due to the chain tensions at high shear. The computed flow curves are non-monotonic with a range where the stress is a decreasing function of the rate, a feature that indeed makes homogeneous flows unstable. The computed the flow curves compare well to the experiments. a) To whom correspondence should be addressed. Electrorheological properties of a mixture of two immiscible fluids having the same viscosityHiroshi Orihara, Akio Taki, and Masao Doi Akio Inoue AbstractWe investigated the electrorheological (ER) properties of a mixture of two immiscible fluids having the same viscosity, but different permittivity and conductivity. In this mixture droplets were dispersed; when subjected to an electric field they became elongated. We observed an ER effect, i.e., an increase of apparent viscosity following the application of an electric field. It was seen from microscopic observation that the ER effect in the present mixture is brought about by a morphological change, with the interfacial tension between the two fluids playing a crucial role. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |