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E-grāmata: Transport Processes at Fluidic Interfaces

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There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface.

This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”

Part I Numerical Methods for Sharp Interface Models
1 ALE-FEM for Two-Phase and Free Surface Flows with Surfactants
5(28)
Sashikumaar Ganesan
Andreas Hahn
Kristin Simon
Lutz Tobiska
2 High Order Unfitted Finite Element Methods for Interface Problems and PDEs on Surfaces
33(32)
Christoph Lehrenfeld
Arnold Reusken
3 An Extended Discontinuous Galerkin Framework for Multiphase Flows
65(28)
Thomas Utz
Christina Kallendorf
Florian Kummer
Bjorn Muller
Martin Oberlack
4 Building Blocks for a Strictly Conservative Generalized Finite Volume Projection Method for Zero Mach Number Two-Phase Flows
93(28)
Matthias Waidmann
Stephan Gerber
Michael Oevermann
Rupert Klein
5 Time Discretization for Capillary Flow: Beyond Backward Euler
121(24)
Stephan Weller
Eberhard Bansch
6 Upwind Schemes for Scalar Advection-Dominated Problems in the Discrete Exterior Calculus
145(32)
Michael Griebel
Christian Rieger
Alexander Schier
7 Discrete Exterior Calculus (DEC) for the Surface Navier-Stokes Equation
177(26)
Ingo Nitschke
Sebastian Reuther
Axel Voigt
Part II Analysis and Simulation of Diffusive Interface Models
8 Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities
203(28)
Helmut Abels
Harald Garcke
Gunther Grun
Stefan Metzger
9 Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids
231(24)
Helmut Abels
YuNing Liu
Andreas Schottl
10 Two-Phase Flow with Surfactants: Diffuse Interface Models and Their Analysis
255(16)
Helmut Abels
Harald Garcke
Kei Fong Lam
Josef Weber
11 Phase Field Models for Two-Phase Flow with Surfactants and Biomembranes
271(20)
Sebastian Aland
12 Micro-Macro-Models for Two-Phase Flow of Dilute Polymeric Solutions: Macroscopic Limit, Analysis, and Numerics
291(14)
Gunther Grun
Stefan Metzger
13 Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models
305(50)
Michael Hintermuller
Michael Hinze
Christian Kahle
Tobias Keil
14 Dynamical Stability of Diffuse Phase Boundaries in Compressible Fluids
355(40)
Heinrich Freistuhler
Matthias Kotschote
Part III Experimental and Numerical Investigation of Interfacial Phenomena
15 Experimental and Computational Analysis of Fluid Interfaces Influenced by Soluble Surfactant
395(50)
Chiara Pesci
Holger Marschall
Talmira Kairaliyeva
Vamseekrishna Ulaganathan
Reinhard Miller
Dieter Bothe
16 Complex Patterns and Elementary Structures of Solutal Marangoni Convection: Experimental and Numerical Studies
445(44)
Kerstin Eckert
Thomas Kollner
Karin Schwarzenberger
Thomas Boeck
17 Transport at Interfaces in Lipid Membranes and Enantiomer Separation
489(42)
Oleg Boyarkin
Stefan Burger
Thomas Franke
Thomas Fraunholz
Ronald H.W. Hoppe
Simon Kirschler
Kevin Lindner
Make A. Peter
Florian Strobl
Achim Wixforth
18 Structure Formation in Thin Liquid-Liquid Films
531(46)
Sebastian Jachalski
Dirk Peschka
Stefan Bommer
Ralf Seemann
Barbara Wagner
Part IV Taylor Bubbles: Experiments, Simulation and Validation
19 Taylor Bubbles in Small Channels: A Proper Guiding Measure for Validation of Numerical Methods for Interface Resolving Simulations
577(12)
Martin Worner
20 X-Ray Microtomography of Taylor Bubbles with Mass Transfer and Surfactants in Capillary Two-Phase Flow
589(20)
Stephan Boden
Mohammadreza Haghnegahdar
Uwe Hampel
21 Experimental Investigation and Modelling of Local Mass Transfer Rates in Pure and Contaminated Taylor Flows
609(30)
Sven Kastens
Christoph Meyer
Marko Hoffmann
Michael Schluter
22 Comparative Simulations of Taylor Flow with Surfactants Based on Sharp- and Diffuse-Interface Methods
639(24)
Sebastian Aland
Andreas Hahn
Christian Kahle
Robert Nurnberg
23 Direct Numerical Simulations of Taylor Bubbles in a Square Mini-Channel: Detailed Shape and Flow Analysis with Experimental Validation
663
Holger Marschall
Carlos Falconi
Christoph Lehrenfeld
Rufat Abiev
Martin Worner
Arnold Reusken
Dieter Bothe
Dieter Bothe is Professor for Mathematical Modeling and Analysis in the Department of Mathematics and at the Center of Smart Interfaces at Technical University of Darmstadt. His research concerns nonlinear evolution equations, reaction-diffusion systems and transport processes in two-phase flows, combining modeling with mathematical analysis and numerical simulations.Arnold Reusken is Professor of Numerical Analysis at RWTH-Aachen. His research areas concerns analysis and application of multigrid solvers and other fast iterative methods for discretized PDEs, finite element methods and numerical methods for the simulation of two-phase incompressible flow problems.