1. Principles of Continuum Mechanics. Basic Concepts. Material Derivative. Deformation Rates. Rivlin-Ericksen Tensors. Strain Tensor. Kinematics of Steady Shear Flows. Continuity Equation. Stress and Volume Force. Equations of Motion. Energy Equation for Fluid Flow. 2. Material Properties Occurring in Steady Shear Flows. The Flow Function. The Normal Stress Functions. 3. Processes that are Controlled by the Flow Function. Rotational Viscometer. Pressure-Drag Flow in a Straight Channel. Radial Flow between Two Parallel Planes. Pipe Flow. Helical Flow. 4. Effect of Normal Stress Differences. Cone-and-Plate Flow. Weissenberg Effect. Die-Swell. Axial Shear Flow. 5. Simple Unsteady Flows. Linear Viscoelasticity. Non-Linear Effects in Unsteady Pipe Flow. 6. Nearly Viscometric Flows. Shear Flows with a Weak Unsteady Component. Plane Steady Boundary Layer Flows. Stability of Plane Shear Flows. 7. Extensional Flows. Theoretical Principles. Applications. 8. Special Rheological Laws. Fluids Without Memory. Integral Models. Differential Models. Approximation for Slow and Slowly Varying Processes. 9. Secondary Flows. General Theory. Rotational Symmetric Flows. Plane Flows. Steady Flow through Cylindrical Pipes. Periodic Pipe Flow. Appendix: Set of Formulas for Special Curvilinear Coordinates. References. Index.

Non-Newtonian Fluid Mechanics

Numerical modelling is increasingly supporting the analysis and optimization of manufacturing processes in the production industry. Even if being mostly applied to multistep processes, single process steps may be so complex by nature that the needed models to describe them must include multiphysics. On the other hand, processes which inherently may seem multiphysical by nature might sometimes be modelled by considerably simpler models if the problem at hand can be somehow adequately simplified. In the present article, examples of this will be presented. The cases are chosen with the aim of showing the diversity in the field of modelling of manufacturing processes as regards process, materials, generic disciplines as well as length scales: (1) modelling of tape casting for thin ceramic layers, (2) modelling the flow of polymers in extrusion, (3) modelling the deformation process of flexible stamps for nanoimprint lithography, (4) modelling manufacturing of composite parts and (5) modelling the selective la...

/pdf/multiphysics-modelling-of-manufacturing-processes-a-review-15bdtre5jn.pdf

Multiphysics modelling of manufacturing processes: A review

Drop impact onto a dry surface: Role of the dynamic contact angle

The simulation of flows of viscoelastic fluids is a very challenging domain from the theoretical as well as the numerical modelling point of view. In particular, all the existing methods have failed to solve the high Weissenberg number problem (HWNP). It is therefore clear that new tools are necessary. In this thesis we propose to tackle the problem of the simulation of viscoelastic fluids presenting memory effects, which is the first attempt of applying the lattice Boltzmann method (LBM) to this field for non-trivial flows. A theoretical development of the discrete models corresponding to the equations of mass, momentum conservation and of the constitutive equation is presented as well as the particular treatment of the associated boundary conditions. We start by presenting a simplified case where no memory but shear-thinning or shear-thickening effects are present : simulating the flow of generalized Newtonian fluids. We test the corresponding method against two-dimensional benchmarks : the 2D planar Poiseuille and the 4:1 contraction flows. Then we propose a new model consisting in solving the constitutive equations that account for memory effects, by explicitly including an upper-convected derivative, using the lattice Boltzmann method. In particular, we focus on the polymer dumbbell models, with infinite or finite spring extension (Oldroyd-B and FENE-P models). Using our model, we study the periodic (simplified) 2D four-roll mill and the 3D Taylor-Green decaying vortex cases. Finally, we propose an approach for simulating flat walls and show the applicability of the method on the 2D planar Poiseuille case. Two of the advantages of the proposed method are the ease of implementation of new viscoelastic models and of an algorithm for parallel computing.

/pdf/lattice-boltzmann-method-for-the-simulation-of-viscoelastic-2jw0th3d08.pdf

Lattice Boltzmann method for the simulation of viscoelastic fluid flows

The measurement of cell stiffness is an important part of biological research with diverse applications in biology, biotechnology and medicine. Real-time deformability cytometry (RT-DC) is a new method to probe cell stiffness at high throughput by flushing cells through a microfluidic channel where cell deformation provides an indicator for cell stiffness (Otto et al. Real-time deformability cytometry: on-the-fly cell 725 mechanical phenotyping. Nat. Methods 2015, 12, 199–202). Here, we propose a full numerical model for single cells in a flow channel to quantitatively relate cell deformation to mechanical parameters. Thereby the cell is modeled as a viscoelastic material surrounded by a thin shell cortex, subject to bending stiffness and cortical surface tension. For small deformations our results show good agreement with a previously developed analytical model that neglects the influence of cell deformation on the fluid flow (Mietke et al. Extracting Cell Stiffness from Real-Time Deformability Cytometry...

Numerical Simulation of Real-Time Deformability Cytometry To Extract Cell Mechanical Properties

This work deals with the development of a numerical method for simulating viscoelastic axisymmetric free surface flow of an Oldroyd B fluid. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries and on the symmetry axis. The full free surface stress conditions are employed. The resulting governing equations are solved by finite differences on a Marker-and-cell (MAC) type grid. Validation is provided by simulating a pipe flow problem. The classical die-swell problem is solved and swelling ratios are provided. The height of the splash caused by a falling liquid drop for various Reynolds and Weissenberg numbers is then studied, and the height of the splash is shown to diminish with increasing viscoelasticity.

Die-swell, splashing drop and a numerical technique for solving the Oldroyd B model for axisymmetric free surface flows

O objetivo deste trabalho e o desenvolvimento de um metodo numerico capaz de simular escoamentos viscoelasticos de um fluido Oldroyd-B para o problema da contracao planar 4:1. Simulacao numerica de escoamentos de fluidos viscoelasticos atraves de uma contracao e propensa a erros acentuados na avaliacao da tensao e do campo de velocidade proximo ao canto reentrante do estrangulamento. Introduzimos uma tecnica numerica baseada em diferencas finitas, permitindo-nos analisar o comportamento de fluido Oldroyd-B com altos numeros de Weissenberg no problema da contracao planar.

https://tema.sbmac.org.br/tema/article/download/431/367

Técnicas Numéricas para Simulação da Contração Planar de Fluidos Oldroyd-B

Este trabalho objetiva apresentar um panorama dos Grupos de Pesquisa (GP) do Paraná que possuem linhas de pesquisa sobre Tecnologias Digitais em Educação Matemática. É uma pesquisa documental, exploratória, de abordagem mista. A busca foi realizada no Diretório de Grupos de Pesquisa, onde foram identificados 19 Grupos, dos quais foram selecionados 124 pesquisadores e coletados 91 artigos segundo os critérios adotados. Duas universidades comportam 57% dos GP, três destes concentram mais da metade dos artigos selecionados. Dos 91, 42 são teóricos e 49 resultam de aplicações em sala, sendo 20 na formação docente. O uso de softwares e/ou aplicativos aparece em 41 trabalhos, com destaque ao Geogebra e Scratch, 19 e 10 respectivamente. As temáticas Objetos de Aprendizagem e Lousa Digital aparecem em 17 e cinco trabalhos. A Modelagem Matemática é abordada em cinco trabalhos, uso de jogos e gamificação em quatro, e a Geometria é o conteúdo mais trabalhado.

Luciane Grossi

Papers

Die-swell, splashing drop and a numerical technique for solving the Oldroyd B model for axisymmetric free surface flows

Técnicas Numéricas para Simulação da Contração Planar de Fluidos Oldroyd-B

Tecnologias Digitais em Educação Matemática: panorama dos Grupos de Pesquisa do Paraná