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.…
Author: | Philipp Werner |
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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): | ![]() |