In this thesis, the seminal work of Stokes concerning the ow of a Navier-Stokesuid due to a suddenly accelerated or oscillating plate and the ow due to torsionaloscillations of an innitely long rod in a Navier-Stokes uid is extended to a uid withpressure dependent viscosity. The viscosity of many uids varies signicantly withpressure, a fact recognized by Stokes; and Barus, in fact, conducted experiments thatshowed that the variation of the viscosity with pressure was exponential. Given sucha tremendous variation, we study how this change in viscosity aects the nature of thesolution to these problems. We nd that the velocity eld, and hence the structureof the vorticity and the shear stress at the walls for uids with pressure dependentviscosity, are markedly dierent from those for the classical Navier-Stokes uid.

In this thesis, the seminal work of Stokes concerning the ow of a Navier-Stokesuid due to a suddenly accelerated or oscillating plate and the ow due to torsionaloscillations of an innitely long rod in a Navier-Stokes uid is extended to a uid withpressure dependent viscosity. The viscosity of many uids varies signicantly withpressure, a fact recognized by Stokes; and Barus, in fact, conducted experiments thatshowed that the variation of the viscosity with pressure was exponential. Given sucha tremendous variation, we study how this change in viscosity aects the nature of thesolution to these problems. We nd that the velocity eld, and hence the structureof the vorticity and the shear stress at the walls for uids with pressure dependentviscosity, are markedly dierent from those for the classical Navier-Stokes uid.

This dissertation is devoted to the finite element (FE) approximation of equations describing the motion of a class of non-Newtonian fluids. The main focus is on incompressible fluids whose viscosity nonlinearly depends on the shear rate and pressure. The equations of motion are discretized with equal-order d-linear finite elements, which fail to satisfy the inf-sup stability condition. In this thesis a stabilization technique for the pressure-gradient is proposed that is based on the well-known local projection stabilization (LPS) method. If the viscosity solely depends on the shear rate, the well-posedness of the stabilized discrete systems is shown and a priori error estimates quantifying the convergence of the method are proven. In the shear thinning case, the derived error estimates provide optimal rates of convergence with respect to the regularity of the solution. As is well-known, the Galerkin FE method may suffer from instabilities resulting not only from lacking inf-sup stability but also from dominating convection. The proposed LPS approach is then extended in order to cope with both instability phenomena. Finally, shear-rate- and pressure-dependent viscosities are considered. The Galerkin discretization of the governing equations is analyzed and the convergence of discrete solutions is...

A lot of technologically relevant incompressible fluids exhibit a substantial variaton of viscosity with the pressure;a falling cylinder viscometer is frequently used for the measurements, determining the viscosity indirectly from the time it takes the sinker to fall a given distance. The relation between the sinker fall velocity and the fluid viscosity is, however, derived under the constant viscosity assumption. The objective of the present thesis is to perform a numerical simulation of the viscometric experiment, assuming an explicit form of the pressure-viscosity dependence and realistic parameter values and to quantitatively assess the difference in body motion to the Navier- Stokes model. The computational method proposed, handling both the nonlinear constitutive relation and the body motion, was tested on simple problems with analytical solutions. The semianalytical relation for the Navier-Stokes model, also re-derived here, is compared to the computational results.The validity of the assumptions used in the theoretical derivation, based on the results of the numerical simulation, is discussed regarding the geometry of the viscometer. Powered by TCPDF (www.tcpdf.org)

Investigation of material behaviour in a squeeze flow geometry provides an impor- tant technique in rheology and it is relevant also from the technological point of view (some types of dampers, compression moulding). To our best knowledge, the sque- eze flow has not been solved for fluids-like materials with pressure-dependent material moduli. In the main scope of the present thesis, an incompressible fluid whose visco- sity strongly depends on the pressure is studied in both the perfect-slip and the no-slip squeeze flow. It is shown that such a material model can provide interesting departures compared to the classical model for viscous (Navier-Stokes) fluid even on the level of analytical solutions, which are obtained using some physically relevant simplificati- ons. Numerical simulation of a free boundary problem for the no-slip squeeze flow is then developed in the thesis using body-fitted curvilinear coordinates and spectral collocation method. An interesting behaviour is expected especially in the corners of the computational domain where the stress singularities are normally located. Unfor- tunately, numerical results reveal some fundamental drawbacks related to the physical model and its possible improvement is discussed at the end of the thesis.

Submitted by RODRIGO KOITI ISHIZAKA (rodrigo_ishizaka@hotmail.com) on 2018-04-09T20:10:27Z No. of bitstreams: 1 Dissertação Final PDF.pdf: 10461391 bytes, checksum: a78974d2db3d166540e03d4cee7def37 (MD5) / Rejected by ALESSANDRA KUBA OSHIRO ASSUNÇÃO (alessandra@fct.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: - Número de página das referências no sumário está incorreto (consta p.86 quando é p.87); - No sumário consta Apêndices, porém no trabalho não. É finalizado nas referências. Agradecemos a compreensão. on 2018-04-10T12:44:45Z (GMT) / Submitted by RODRIGO KOITI ISHIZAKA (rodrigo_ishizaka@hotmail.com) on 2018-04-10T16:09:35Z No. of bitstreams: 1 Dissertação Final PDF.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) / Approved for entry into archive by ALESSANDRA KUBA OSHIRO ASSUNÇÃO (alessandra@fct.unesp.br) on 2018-04-10T20:02:48Z (GMT) No. of bitstreams: 1 ishizaka_rk_me_prud.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) / Made available in DSpace on 2018-04-10T20:02:48Z (GMT). No. of bitstreams: 1 ishizaka_rk_me_prud.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) Previous issue date: 2018-02-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho de mestrado consiste em apresentar uma modelagem para escoamentos isotérmicos viscoelásticos em que a viscosidade varia de acordo com a pressão e estudos numéricos para alguns problemas bidimensionais, como escoamentos entre placas paralelas e expansão planar 1:4. Para este trabalho é utilizado o modelo viscoelástico Oldroyd-B e uma modelagem linear da viscosidade com relação a pressão. O método numérico desenvolvido é baseado no método da projeção para desacoplar velocidade e pressão nas equações de Navier-Stokes e depois calcula os tensores pela equação constitutiva com a informação da viscosidade variando com a pressão. As equações são discretizadas em uma malha deslocada pelo método de diferenças finitas. Os resultados numéricos são obtidos das simulações de escoamentos em um canal e expansão planar 1:4 bidimensional, cujo foco é destacar algumas diferenças entre o modelo Oldroyd-B Standard e o modelo Oldroyd-B sob influência da viscosidade que varia linearmente com a pressão. Este trabalho de mestrado também tem por objetivo resolver problemas, com fluidos viscoelásticos, em que haja regiões com variações da pressão e estudar estes resultados numéricos comparando-os com o modelo Oldroyd-B Standard. / The present master's work consists in presenting a model for viscoelastic isothermal flows with pressure-dependent viscosity and numerical studies for some two-dimensional problems, such as channel flow and planar expansion 1:4. In this work will be considered the Oldroyd-B viscoelastic model and a linear modeling viscosity with a linear relationship between viscosity and pressure. The numerical method developed is based on the projection method to decouple velocity and pressure in the Navier-Stokes equations and then calculates the tensor from the constitutive equation taking account the pressure-dependent viscosity. The equations are discretized on a staggered grid by using the finite diference method. The numerical results are obtained for two problems: two-dimensional channel and planar expansion 1:4 flows, whose focus is to highlight some diferences between the standard Oldroyd-B model and the Oldroyd-B model under the influence of viscosity that varies linearly with pressure. This master's work aims to solve problems of viscoelastic fluids in which there exist regions where pressure varies and to study these numerical results comparing them with the standard Oldroyd-B model.

Experimental data convincingly show that viscosity of a fluid may change significantly with pressure. This observation leads to various generalizations of well-known models, like Darcy's law, Stokes' law or the Navier-Stokes equations, among others. This thesis investigates three such models in a series of three published papers. Their unifying topic is development of existence theory and finding a weak solution to systems of partial differential equations stemming from the considered models.

La rhéologie à hauts taux de cisaillement pour deux polymères, le PEHD semi-cristallin et le PMMA amorphe a été étudiée. Des outils de rhéométrie classique, un rhéomètre plan-plan en mode dynamique, et un rhéomètre capillaire, ont été utilisés dans des conditions extrêmes (avec des filières pour la rhéométrie capillaire de diamètres allant jusqu'à 0,3 mm) mais les dépouillements de ces résultats ont été fait suivant les hypothèses conventionnelles en négligeant les instabilités et les phénomènes physiques qui interviennent lors de ces écoulements.Nous avons par la suite développé un modèle mathématique de l'écoulement dans un capillaire pour rendre compte de l'importance des différents phénomènes physiques qui peuvent avoir lieu dans des écoulements extrêmes, à savoir l'échauffement et la piezodépendance de la viscosité, la compressibilité et le glissement à la paroi. Les résultats du modèle développé ont été comparés avec les résultats expérimentaux.Nous avons aidé au développement d'une presse de microinjection originale et nous l'avons testée avec un moule de plaque instrumenté d'épaisseur allant jusqu'à 0,2 mm. Nous avons montré qu'il était possible de réaliser des pièces de qualité ce qui est avéré par des mesures de pression, vitesse et de température bien reproductibles. Nous avons exploité les données rhéologiques expérimentales dans la modélisation de la phase de remplissage avec le logiciel de calcul Rem3D. Des corrélations entre les mesures expérimentales et les calculs ont été réalisées en comparant l'évolution des pressions dans le système d'alimentation et dans l'empreinte. / Rheology at high shear rate for both polymers, semi-crystalline HDPE and amorphous PMMA was studied. Classical rheometry tools, plane-plane dynamic mode rheometer and capillary rheometer, were used in extreme conditions (with channels diameters for capillary rheometry up to 0.3 mm). However, analyses of these results were made following conventional assumptions neglecting instabilities and physical phenomena involved in these flows.We then developed a mathematical model of a capillary flow in to reflect the importance of different physical phenomena that can occur in extreme flows, namely heating, pressure dependency of viscosity, compressibility and the wall slip. The results of the developed model were compared with experimental results.We helped develop a press microinjection original and we tested it with instrumented plate mold with thickness up to 0.2 mm. We have shown that it is possible to make quality parts which are proven by well reproducible pressure, speed and temperature measurements. We used the experimental rheological data in filling phase modeling with the calculation software Rem3D. Correlations between experimental measurements and calculations were carried out by comparing the pressure in the filling system and the cavity.