# Boundary conditions for dynamic wetting — A mathematical analysis

## 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.

Item Type: Report 2019 Fricke, Mathis ; Bothe, Dieter Boundary conditions for dynamic wetting — A mathematical analysis English 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. DFG-Collaborative Research Centres (incl. Transregio)DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research CentresDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting ProcessesDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and SimulationDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and Simulation > B01: Modelling and VOF based Simulation of the Multiphysics of Irreversible Thermodynamic Transfer Processes at Dynamic Contact Lines 11 Dec 2019 12:33 http://arxiv.org/pdf/1911.02310 ASCII CitationDublin CoreBibTeXMODSSimple MetadataEP3 XMLIBW_RDAEndNoteT2T_XMLAtomJSONHTML CitationRDF+XMLMultiline CSVReference Manager TUfind oder in Google
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