HAL: hal-00274569, version 2

DOI: 10.1016/j.jcp.2008.02.023

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Journal of Computational Physics 227, 12 (2008) 6140-6164

Available versions:

v1 (2008-04-20)

v2 (2008-05-12)

On stability condition for bifluid flows with surface tension : application to microfluidics

Cédric Galusinski 1, Paul Vigneaux 2, 3, 4

(2008-06-01)

Models for incompressible immiscible bifluid flows with surface tension are here considered. Since Brackbill, Kothe and Zemach (J. Comput. Phys. 100, pp 335-354, 1992) introduced the Continuum Surface Force (CSF) method, many methods involved in interface tracking or capturing are based on this reference work. Particularly, the surface tension term is discretized explicitly and therefore, a stability condition is induced on the computational time step. This constraint on the time step allows the containment of the amplification of capillary waves along the interface and puts more emphasis on the terms linked with the density in the Navier-Stokes equation (i. e. unsteady and inertia terms) rather than on the viscous terms. Indeed, the viscosity does not appear, as a parameter, in this stability condition. We propose a new stability condition which takes into account all fluid characteristics (density and viscosity) and for which we present a theoretical estimation. We detail the analysis which is based on a perturbation study - with capillary wave - for which we use energy estimate on the induced perturbed velocity. We validate our analysis and algorithms with numerical simulations of microfluidic flows using a Level Set method, namely the exploration of different mixing dynamics inside microdroplets.

1:	Institut de Mathématiques de Toulon et du Var (IMATH)
	Université Sud Toulon Var : EA2134
2:	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
3:	Laboratoire de Mathématiques (LAMA)
	CNRS : UMR5127 – Université de Savoie
4:	NUMED (ENS Lyon / UCB Lyon / Inria Grenoble Rhône-Alpes)
	Université Claude Bernard - Lyon I – INRIA – École Normale Supérieure - Lyon – CNRS : UMR5669 – Unité de Mathématiques Pures et Appliquées

Subject

:

Mathematics/Numerical Analysis

Keyword(s): surface tension – curvature – stability condition – bifluid flows – incompressible Navier-Stokes – level set – cartesian finite-volumes – microfluidics – droplets

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From: Paul Vigneaux <>

Submitted on: Saturday, 10 May 2008 17:07:06

Updated on: Tuesday, 22 January 2013 16:55:18