Yes / A recent development of the Molecular Stress Function constitutive model, the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model has been shown to fit a large range of rheometrical data with accuracy, for a large range of polymer melts. We develop a 3D simulation of the HMMSF model and compare it to experimental data for the flow of Lupolen 1840H LDPE through an abrupt 3D contraction flow. We believe this to be the first finite element implementation of the HMMSF model. It is shown that the model gives a striking agreement with experimental vortex opening angles, with very good agreement to full-field birefringence measurements, over a wide range of flow rates. A method to give fully-developed inlet boundary conditions is implemented (in place of using parabolic inlet boundary conditions), which gives a significantly improved match to birefringence measurements in the inlet area, and in low stress areas downstream from the inlet. Alternative constitutive model parameters are assessed following the principle that extensional rheometer data actually provides a ‘lower bound’ for peak extensional viscosity. It is shown that the model robustly maintains an accurate fit to vortex opening angle and full-field birefringence data, provided that both adjustable parameters are kept such that both shear and extensional data are well fitted.

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J.L. White, A. Kondo, Flow patterns in polyethylene and polystyrene melts during extrusion through a die entry region: measurement and interpretation, J. Non-Newtonian Fluid Mech. 3 (1977) 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

Constitutive models that conform to separable KBKZ specification have been shown to fit steady-state strain hardening rheological data in planar and uniaxial elongational flows, but with inaccuracy in the rate of strain hardening. The single parameter Molecular Stress Function model of Wagner [Rheol. Acta, 39 (2000), 97-109] has been shown to accurately fit the rise-rate in experimental data for a number of strain hardening and strain softening materials. We study this models accuracy against the well characterised IUPAC LDPE data, and present a method for full implementation of this model for flow solution which is suitable for incorporating into existing separable KBKZ software. A new method for particle tracking in arbitrarily aligned meshes, which is efficient and robust, is given. The Quadratic Molecular Stress Function (QMSF) model is compared to existing separable KBKZ based models, including one which is capable of giving planar strain hardening; the QMSF is shown to fit experimental rheological and contraction flow data more convincingly. The issue of `negative correction pressures¿ notable in some Doi-Edwards based models is addressed. The cause is identified, and leads to a logical method of calculation which does not give these anomalous results.

Yes / The Molecular Stress Function (MSF) constitutive model with convective constraint release mechanism has been shown to accurately fit a large range of viscometric data, and also shown to give strong vortex growth in flows of LDPE through planar and axisymmetric contractions. This work compares simulation and experimental results for 3-D flows of Lupolen 1840H LDPE through a contraction slit; 3-D effects are introduced by using a slit with a low upstream aspect ratio of 5:3. Comparisons are made with vortex opening angles obtained from streak photography, and also with stress birefringence measurements. The comparisons are made with two versions of the convective constraint release (CCR) mechanism. The simulated vortex angles for one version of the CCR mechanism are found to approach what is seen experimentally. The best-fit value for the stress optical coefficient was found to vary between CCRs and to decrease with flow rate. This is partially explained by different centreline elongational rates with the two CCRs, which in turn is related to different opening angles. A 3-D simulation is compared to the corresponding 2-D simulation. It is shown that both velocity vectors and birefringence show only small changes to around 60% of the distance to the side wall.

Depuis quelques années, la microplasturgie est un secteur en plein développement. Cependant, le comportement rhéologique des matériaux polymères dans des géométries très minces (dimension inférieure à 100 µm) n’est pas bien caractérisé. Peu de travaux ont été entrepris à ce sujet, en particulier en ce qui concerne les écoulements de Poiseuille qui sont pourtant les plus représentatifs des conditions de mise en œuvre usuelles. Ainsi, ce travail a pour but la mise au point d’une méthode expérimentale permettant d’obtenir des données pertinentes afin de caractériser de façon approfondie le comportement des matériaux polymères en écoulement de Poiseuille dans des géométries micrométriques. Afin de décrire au mieux la physique de tels écoulements, nous avons également cherché à les simuler numériquement, soit en utilisant des lois de comportement classiques, soit à l’aide de modèles se référant à la dynamique moléculaire. Pour atteindre ces objectifs, une filière à fente plate instrumentée avec des capteurs de pression et température, d’entrefer variant entre 50 et 200µm, a été conçue afin d’effectuer des mesures à l’aide d’un rhéomètre capillaire. Ce dispositif a été validé en confrontant les mesures à celles obtenues par d’autres méthodes (rhéométrie capillaire en filière classique et rhéométrie dynamique). Le glissement à la paroi a également été étudié, selon la méthode de Mooney. La simulation numérique de l’écoulement a d’abord été réalisée à l’aide de POLYFLOW®. L’effet de la pression sur la géométrie ainsi que sur le matériau polymère a été étudié. Puis, l’écoulement a également été simulé sous MATLAB® en utilisant des lois constitutives de type moléculaire basées sur le modèle du tube de Doï-Edwards ainsi que sur le concept de « Molecular Stress Function » introduit par Wagner pour rendre compte des effets d’orientation des molécules (variation du diamètre du tube) dans le champ de contraintes. L’écart constaté entre ces calculs et les résultats expérimentaux est expliqué et discuté à la lumière des simulations sous POLYFLOW®. Il modifie les perspectives d’étude de ce type d’écoulements. / The rheological behavior of polymer melts in microscale geometries is not really understood yet. In such processes which involve gaps thinner than 100µm (e.g. micro-injection molding), the material behaves differently compared to macroscopic flows. Besides, most polymer processing techniques involve pressure flows and only very few studies can be found about pressure flows in such thin geometries. The aim of this study was, first, to develop an experimental method which can provide relevant data about the rheological behavior of polymer melts in pressure flow taking place in microscale geometries. In order to get better descriptions of the physics involved in such flows, numerical simulation with commercial and home-made softwares was also implemented, especially with molecular dynamics constitutive models. Thus, a modular rheometrical slit die equipped with pressure and temperature transducers was designed to be adapted to a capillary rheometer, with different gap dimensions available, between 50µm and 200µm. The device was assessed by comparing to usual rheological ones, and wall slip was investigated according to Mooney’s method. Then, simulation of the flow was performed with POLYFLOW®. The pressure effect on the geometry and on the polymer material was investigated. Besides, simulation was also conducted with MATLAB® by implementing the Doi-Edwards’ tube model (reptation theory) and the Molecular Stress Function concept of Wagner to take into account the enhanced orientation of the molecules due to the very close vicinity of the die walls. Experimental results were compared to calculations, and the discussion of the discrepancies was supported by POLYFLOW® simulations. The conclusions somewhat modify the prospects for future studies of such flows.