Fricke, Mathis ; Ouro-Koura, El Assad ; Raju, Suraj ; von Klitzing, Regine ; De Coninck, Joël ; Bothe, Dieter (2023)
An analytical study of capillary rise dynamics: Critical conditions and hidden oscillations.
In: Physica D: Nonlinear Phenomena, 455
doi: 10.1016/j.physd.2023.133895
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
The rise of a liquid column inside a thin capillary against the action of gravity is a prototypical example of a dynamic wetting process and plays an important role for applications but also for fundamental research in the area of multiphase fluid dynamics. Since the pioneering work by Lucas and Washburn, many research articles have been published which aim at a simplified description of the capillary rise dynamics using complexity-reduced models formulated as ordinary differential equations. Despite the fact that these models are based on profound simplifications, they may still be able to describe the essential physical mechanisms and their interplay. In this study, we focus on the phenomenon of oscillations of the liquid column. The latter has been observed experimentally for liquids with sufficiently small viscosity leading to comparably small viscous dissipation. Back in 1999, Quéré et al. formulated a condition for the appearance of rise height oscillations for an ODE model introduced by Bosanquet in 1923. This model has later been extended to include further dissipative mechanisms. In this work, we extend the mathematical analysis to a larger class of models including additional channels of dissipation. We show that Quéré’s critical condition is generalized to Ω+β<2, where Ω was introduced earlier and β is an additional non-dimensional parameter describing, e.g., contact line friction. A quantitative prediction of the oscillation dynamics is achieved from a linearization of the governing equations. We apply the theory to experimental data by Quéré et al. and, in particular, reveal the oscillatory behavior of dynamics for the nearly critically damped case of ethanol.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Fricke, Mathis ; Ouro-Koura, El Assad ; Raju, Suraj ; von Klitzing, Regine ; De Coninck, Joël ; Bothe, Dieter |
| Art des Eintrags: | Bibliographie |
| Titel: | An analytical study of capillary rise dynamics: Critical conditions and hidden oscillations |
| Sprache: | Englisch |
| Publikationsjahr: | 2023 |
| Ort: | Amsterdam |
| Verlag: | Elsevier |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Physica D: Nonlinear Phenomena |
| Jahrgang/Volume einer Zeitschrift: | 455 |
| DOI: | 10.1016/j.physd.2023.133895 |
| URL / URN: | https://www.sciencedirect.com/science/article/abs/pii/S01672... |
| Kurzbeschreibung (Abstract): | The rise of a liquid column inside a thin capillary against the action of gravity is a prototypical example of a dynamic wetting process and plays an important role for applications but also for fundamental research in the area of multiphase fluid dynamics. Since the pioneering work by Lucas and Washburn, many research articles have been published which aim at a simplified description of the capillary rise dynamics using complexity-reduced models formulated as ordinary differential equations. Despite the fact that these models are based on profound simplifications, they may still be able to describe the essential physical mechanisms and their interplay. In this study, we focus on the phenomenon of oscillations of the liquid column. The latter has been observed experimentally for liquids with sufficiently small viscosity leading to comparably small viscous dissipation. Back in 1999, Quéré et al. formulated a condition for the appearance of rise height oscillations for an ODE model introduced by Bosanquet in 1923. This model has later been extended to include further dissipative mechanisms. In this work, we extend the mathematical analysis to a larger class of models including additional channels of dissipation. We show that Quéré’s critical condition is generalized to Ω+β<2, where Ω was introduced earlier and β is an additional non-dimensional parameter describing, e.g., contact line friction. A quantitative prediction of the oscillation dynamics is achieved from a linearization of the governing equations. We apply the theory to experimental data by Quéré et al. and, in particular, reveal the oscillatory behavior of dynamics for the nearly critically damped case of ethanol. |
| Freie Schlagworte: | SFB1194_A09 |
| Zusätzliche Informationen: | Artikel-ID: 133895 |
| 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 DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1194: Wechselseitige Beeinflussung von Transport- und Benetzungsvorgängen > Projektbereich B: Modellierung und Simulation > B02: Direkte Numerische Simulation lokal gekoppelter Grenzflächentransportprozesse an Kontaktlinien bei dynamischen Benetzungsprozessen |
| Hinterlegungsdatum: | 07 Dez 2023 14:07 |
| Letzte Änderung: | 07 Dez 2023 14:07 |
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