Sharp and diffuse interface models for the evolution of surfaces that are immersed in fluids and coupled through surfactants

Scharfe und diffuse Grenzflächenmodelle zur Erfassung der zeitlichen Entwicklung von Oberflächen, welche von Fluiden umschlossen und durch Surfactants gekoppelt sind

Please always quote using this URN: urn:nbn:de:bvb:29-opus4-167752
  • In this thesis a framework for modelling two coupled hypersurfaces evolving in a three-dimensional domain that is filled with a fluid is developed in terms of partial differential equations that can be classified as free boundary problems. In particular, the coupling of both hypersurfaces depends on particles of a species that evolve on one of the surfaces. Since they influence the surface tension, they can be understood as surfactants. We use two common approaches for modelling free boundary problems, namely sharp and diffuse interfaces by using similar physical arguments for their derivation as well as a formal asymptotic analysis. From the modelling framework, we specify particularIn this thesis a framework for modelling two coupled hypersurfaces evolving in a three-dimensional domain that is filled with a fluid is developed in terms of partial differential equations that can be classified as free boundary problems. In particular, the coupling of both hypersurfaces depends on particles of a species that evolve on one of the surfaces. Since they influence the surface tension, they can be understood as surfactants. We use two common approaches for modelling free boundary problems, namely sharp and diffuse interfaces by using similar physical arguments for their derivation as well as a formal asymptotic analysis. From the modelling framework, we specify particular models for the evolution of biomembranes, and, even more specific, for studying the biological phenomenon of cell blebbing. Properties of these models are investigated by means of rigorous mathematical analysis showing existence of solutions, existence and stability of stationary solutions where possible, as well a singular limits. We also present numerical algorithms for simulative studies of cell blebbing models and report and interpret results obtained from their computations. Thus we can validate that our models qualitatively reproduce phenomena that have been reported in the biological literature.show moreshow less

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Metadaten
Author:Philipp Werner
Persistent identifiers - URN:urn:nbn:de:bvb:29-opus4-167752
Referee:Martin Burger, Harald Garcke, Matthias Röger
Advisor:Martin Burger, Harald Garcke
Document Type:Doctoral Thesis
Language:English
Year of publication:2021
Date of online publication (Embargo Date):2021/07/05
Publishing Institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Granting institution:Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Naturwissenschaftliche Fakultät
Acceptance date of the thesis:2021/05/21
Release Date:2021/07/12
Tag:Free Boundary Problems, Level Set Methods, Phase Field Methods, Fluid Mechanics, Coupled Surfaces, Cell Blebbing
Institutes:Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
5 Naturwissenschaften und Mathematik / 53 Physik / 532 Mechanik der Fluide; Mechanik der Flüssigkeiten
5 Naturwissenschaften und Mathematik / 57 Biowissenschaften; Biologie / 570 Biowissenschaften; Biologie
open_access (DINI-Set):open_access
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International
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