On the evaluation of some differential formulations for the pom-pom constitutive model

In recent years, progress has been made in modelling long chain branched polymers by the introduction of the so-called pompom model. Initially developed by McLeish and Larson (1998), the model has undergone several improvements or alterations, leading to the development of new formulations. Some of these formulations however suffer from certain mathematical defects. The purpose of the present paper is to review some of the formulations of the pom-pom constitutive model, and to investigate their possible mathematical defects. Next, an alternative formulation is proposed, which does not appear to exhibit mathematical defects, and we explore its modelling performance by comparing the predictions with experiments in non-trivial rheometric flows of an LDPE melt. The selected rheometric flows are the double step strain, as well as the large amplitude oscillatory shear experiments. For LAOS experiments, the comparison involves the use of Fourier-transform analysis.

Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.

The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Influence of normal stress on creep in tension and compression of polyethylene and rigid polyvinyl chloride copolymer,

At head of title: Interim report no. 1. Investigation of creep behavior of plastics. "EMRL-15."

A theory of the non-linear influence of normal stress on fatigue under combined stresses,

Contract no. DA-19-020-ORD-3520."

Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

In-line rheo-optical microstructural characterization of complex polymer systems

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos.

Serum-Mediane von Placentaprotein-Markern: Relevanz der Unterschiede zwischen spontanen und nach-in-vitro-Fertilisation eingetretenen Schwangerschaften für das fetale Trisomie-Screening.

Trisomy-21 (Down syndrome) is the most frequent chromosomal abnorm- ality but only one third of cases would be detected by amniocentesis based on maternal age alone. Serum screening tests in the early second trimester increase the detec- tion rate to 60-65%, and more recently it was found that such screening was also possible in the first trimester by quantifying a diffe- rent panel of markers. The concen- trations of these placental proteins are strongly dependent on gestatio- nal age; thus control medians must be established and precise dating is essential. Serum chorionic gonado- trophin (HCG) levels were recently found to be increased in IVF preg- nancies compared to spontaneous gestations, leading to a falsely ele- vated trisomy screening risk. The aim of this preliminary study was to find out whether, in the first-trime- ster screening, the markers similarly differed between IVF and spontane- ous pregnancies which would call for the establishment of separate normal medians for IVF patients. We compared 24 pregnancies ob- tained after ovarian stimulation and IVF with six women after thawed embryo transfer (unstimulated cycle) and 63 gestation- and maternal-age matched spontaneously pregnant controls. A single serum was ob- tained between 6 and 16 weeks of gestation and various placental protein levels determined by im- munometric assays. Serum levels of pregnancy-associated plasma protein A (PAPP-A), which is the major marker in the first-trimes- ter screening test, were reduced in IVF pregnancies: after 9 weeks of gestation, multiples of median (MoMs) ranged between 0.23 and 3.58 (logarithmic mean 0.743). For the frozen/thawed transfers, this value was 1.08. In the 9-12 week group containing 6 cases of IVF, three thawed transfers and 25 con- trols, PAPP-A was significantly redu- ced in the stimulated compared to the nonstimulated cycles. In the late first and early second trimester the difference was not significant in our small group but the trend persisted. Pregnancies after IVF will thus show an increased incidence of false positive results in fetal trisomy-21 screening, and special medians should be established for these pati- ents.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Difference variance dispersion graphs for comparing response surface designs with applications in food technology

Variance dispersion graphs have become a popular tool in aiding the choice of a response surface design. Often differences in response from some particular point, such as the expected position of the optimum or standard operating conditions, are more important than the response itself. We describe two examples from food technology. In the first, an experiment was conducted to find the levels of three factors which optimized the yield of valuable products enzymatically synthesized from sugars and to discover how the yield changed as the levels of the factors were changed from the optimum. In the second example, an experiment was conducted on a mixing process for pastry dough to discover how three factors affected a number of properties of the pastry, with a view to using these factors to control the process. We introduce the difference variance dispersion graph (DVDG) to help in the choice of a design in these circumstances. The DVDG for blocked designs is developed and the examples are used to show how the DVDG can be used in practice. In both examples a design was chosen by using the DVDG, as well as other properties, and the experiments were conducted and produced results that were useful to the experimenters. In both cases the conclusions were drawn partly by comparing responses at different points on the response surface.

Experimental investigation into the effect of stress on dissolution and growth of very soluble brittle salts in aqueous solution

Das Studium der Auflösungs- und Wachstumsprozesse an Feststoff-Flüssigkeits-Grenzflächen unter nicht-hydrostatischen Beanspruchungen ist wesentlich für das Verständnis von Defor-mationsprozessen, die in der Erde ablaufen. Unter diesen genannten Prozessen gehört die Drucklösung zu den wichtigsten duktilen Deformationsprozessen, von der Diagenese bishin zur niedrig- bis mittelgradigen metamorphen Bedingungen. Bisher ist allerdings wenig darüber bekannt, welche mechanischen, physikalischen oder chemischen Potentialenergie-Gradienten die Drucklösung steuern. I.a. wird angenommen, daß die Drucklösung durch Un-terschiede kristallplastischer Verformungsenergien oder aber durch Unterschiede der Normal-beanspruchung an Korngrenzen gesteuert wird. Unterschiede der elastischen Verformungs-energien werden dabei allerdings als zu gering erachtet, um einen signifikanten Beitrag zu leisten. Aus diesem Grund werden sie als mögliche treibende Kräfte für die Drucklösung vernachlässigt. Andererseits haben neue experimentelle und theoretische Untersuchungen gezeigt, daß die elastische Verformung in der Tat einen starken Einfluß auf Lösungs- und Wachstumsmechanismen von Kristallen in einer Lösung haben kann. Da die in der Erdkruste vorherrschenden Deformationsmechanismen überwiegend im elastischen Verformungsbereich der Gesteine ablaufen, ist es sehr wichtig, das Verständnis für die Effekte, die die elastische Verformung verursacht, zu erweitern, und ihre Rolle während der Deformation durch Drucklösung zu definieren. Die vorliegende Arbeit beschäftigt sich mit Experimenten, bei denen der Effekt der mechanisch kompressiven Beanspruchung auf Lösungs- und Wachstumsprozesse von Einzelkristallen unterschiedlicher, sehr gut löslicher, elastisch/spröder Salze untersucht wurde. Diese Salze wurden als Analoga gesteinsbildender Minerale wie Quarz und Calcit ausgewählt. Der Einfluß von Stress auf die Ausbildung der Oberflächenmikrostrukturen in einer untersättigten Lösung wurde an Kaliumalaun untersucht.Lösungsrillen (20 – 40 µm breit, 10 – 40 µm tief und 20 – 80 µm Abstand) entwickelten sich in den Bereichen, in denen die Beanspruchung im Kristall am größten war. Sie verschwanden wieder, sobald der Kristall entlastet wurde. Diese Rillen entwickelten sich parallel zu niedrig indizierten kristallographischen Richtungen und sub-perpendikular zu den Trajektorien, die der maximalen, lokalen kompressiven Beanspruchung entsprachen. Die Größe der Lösungsrillen hing von der lokalen Oberflächenbeanspruchung, der Oberflächenenergie und dem Untersättigungsgrad der wässrigen Lösung ab. Die mikrostrukturelle Entwicklung der Kristalloberflächen stimmte gut mit den theoretischen Vorhersagen überein, die auf den Modellen von Heidug & Leroy (1994) und Leroy & Heidug (1994) basieren. Der Einfluß der Beanspruchung auf die Auflösungsrate wurde an Natriumchlorat-Einzelkristallen untersucht. Dabei wurde herausgefunden, daß sich gestresste Kristalle schneller lösen als Kristalle, auf die keine Beanspruchung einwirkt. Der experimentell beobachtete Anstieg der Auflösungsrate der gestressten Kristalle war ein bis zwei Größenordnungen höher als theoretisch erwartet. Die Auflösungsrate stieg linear mit dem Stress an, und der Anstieg war um so größer, je stärker die Lösung untersättigt war. Außerdem wurde der Effekt der Bean-spruchung auf das Kristallwachstum an Kaliumalaun- und Kaliumdihydrogenphosphat-Ein-zelkristallen untersucht. Die Wachstumsrate der Flächen {100} und {110} von Kalium-alaun war bei Beanspruchung stark reduziert. Für all diese Ergebnisse spielte die Oberflächenrauhigkeit der Kristalle eine Schlüsselrolle, indem sie eine nicht-homogene Stressverteilung auf der Kristalloberfläche verursachte. Die Resultate zeigen, daß die elastische Verformung eine signifikante Rolle während der Drucklösung spielen kann, und eine signifikante Deformation in der oberen Kruste verursachen kann, bei Beanspruchungen, die geringer sind, als gemeinhin angenommen wird. Somit folgt, daß die elastische Bean-spruchung berücksichtigt werden muß, wenn mikrophysikalische Deformationsmodelle entwickelt werden sollen.