Fricke, Mathis ; Bothe, Dieter (2019)
Boundary conditions for dynamic wetting — A mathematical analysis.
Report, Bibliographie
Kurzbeschreibung (Abstract)
The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in (Lukyanov, Pryer, Langmuir 2017) aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model by Lukyanov and Pryer. It is found that the solution may still be singular for the latter model.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2019 |
| Autor(en): | Fricke, Mathis ; Bothe, Dieter |
| Art des Eintrags: | Bibliographie |
| Titel: | Boundary conditions for dynamic wetting — A mathematical analysis |
| Sprache: | Englisch |
| Publikationsjahr: | 11 Dezember 2019 |
| URL / URN: | http://arxiv.org/pdf/1911.02310 |
| Kurzbeschreibung (Abstract): | The moving contact line paradox discussed in the famous paper by Huh and Scriven has lead to an extensive scientific discussion about singularities in continuum mechanical models of dynamic wetting in the framework of the two-phase Navier Stokes equations. Since the no-slip condition introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in (Lukyanov, Pryer, Langmuir 2017) aims for regular solutions through modified boundary conditions. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the boundary conditions have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model by Lukyanov and Pryer. It is found that the solution may still be singular for the latter model. |
| Fachbereich(e)/-gebiet(e): | DFG-Sonderforschungsbereiche (inkl. Transregio) DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen > Projektbereich B: Modellierung und Simulation DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen > Projektbereich B: Modellierung und Simulation > B01: Modellierung und VOF-basierte Simulation der Multiphysik irreversibler thermodynamischer Transferprozesse an dynamischen Kontaktlinien |
| Hinterlegungsdatum: | 11 Dez 2019 12:33 |
| Letzte Änderung: | 05 Jun 2023 12:57 |
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