The exact mechanism with which a fluid interface interacts dynamically with a solid surface during wetting is still open to research. Among the many subjects addressed in this field in the literature, the "moving contact line problem" is one that has been ubiquitous since at least the 1970s, where a paradox in the description of the contact line was found to exist. The paradox in a few words is the next: macroscopic hydrodynamic models using the no-slip boundary condition will predict infinite shear stress close to the contact line. The most promising studies to tackle the problem come from information provided by molecular dynamics simulations. They have confirmed that close to the contact line, the no-slip boundary condition is relaxed to some form of slip. Unfortunately, molecular simulations are still limited to very small scales in space and time, so hydrodynamic models and numerical simulations based on Navier-Stokes equations are still needed. In these simulations, the Continuum Surface Force model CSF for the calculation of the capillary contribution introduces a grid dependent contact line velocity and shear at the wall, which is a problem we proposed to solve here. In this work, we analyze the flow close to the moving contact line in the context of corner stokes-flow and explore the effects of the boundary conditions at the wall. One of these conditions offered in the literature, provides relief to the shear divergence and also opens the possibility to observe Moffatt vortices in the vicinity of the contact line, not yet seen in experiments or numerical simulations. We explore this possibility analytically and then numerically using the code JADIM. The latter task is constrained by the contamination of the velocity field by the so-called spurious velocities if the VOF method is used. To solved this inconvenient, a very promising version of the front-tracking method with lagrangian markers is implemented and enhanced to handle non-uniform distribution of markers without losing its spurious velocities elimination features. Numerical tests are conducted to validate the implementation, spurious velocities are reduce close to machine precision and comparison to benchmark data is performed obtaining good agreement. Tests including contact lines are then compared with exact solutions for shape analyzing the effect of the Bond number, showing remarkable results. Numerical experiments with this implementation close to a contact line show the existence of vortical patterns during of spreading. Finally, and based on the theoretical background developed in this work, a new sub-grid model method is proposed for macroscopic numerical simulations and implemented in the new front-tracking method of JADIM. Quantitative data is obtained and compared to numerical and experimental spreading cases revealing improvement of grid convergence and excellent agreement.
| Identifer | oai:union.ndltd.org:univ-toulouse.fr/oai:oatao.univ-toulouse.fr:19481 |
| Date | 29 November 2017 |
| Creators | Febres Soria, Mijail |
| Source Sets | Université de Toulouse |
| Detected Language | English |
| Type | PhD Thesis, PeerReviewed, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | http://oatao.univ-toulouse.fr/19481/ |
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