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Méthodes Level Set pour des problèmes d'interface en microfluidique

Abstract : This dissertation is dedicated to the numerical simulation of immiscible bifluid flows and its application to Microfluidics. To this end, we use a Level Set approach coupled to the resolution of Stokes or Navier-Stokes equations with surface tension.
The first part describes some numerical methods developed to follow evolving interfaces and then puts a special emphasis on the tools of the Level Set method. In particular, we detail ENO and WENO discretizations of Hamilton-Jacobi equations and existing methods for reinitialisation.
In the second part, we focus on the numerical analysis and resolution of surface tension - driven immiscible bifluid flows. We begin by the presentation of mathematical models, discretisations and solvers of the flow. We then derive theoretically a new stability condition induced by surface tension, for low and medium Reynolds numbers where stabilized interfaces can occur. We further introduce a splitting method which allows to decrease simulation time.
Finally, in the third part, we gather all tools presented previously and numerically simulate droplets hydrodynamics in microchannels. We present numerical results of two codes we entirely developed : a two-dimensional cartesian code and a three-dimensional axisymetric code. We compare our results with physical experiments conducted by the LOF laboratory (Rhodia - CNRS) and observe a good agreement. Particularly, we numerically bring to the fore new mixing dynamics inside microdroplets.
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https://tel.archives-ouvertes.fr/tel-00189409
Contributor : Paul Vigneaux <>
Submitted on : Wednesday, June 25, 2008 - 10:55:08 AM
Last modification on : Friday, November 6, 2020 - 3:25:57 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 5:04:15 PM

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  • HAL Id : tel-00189409, version 2

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Paul Vigneaux. Méthodes Level Set pour des problèmes d'interface en microfluidique. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2007. Français. ⟨tel-00189409v2⟩

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