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Well-posedness of a two-phase flow with soluble surfactant

Bothe, D. and Prüss, J. and Simonett, G. Chipot, M. and Escher, J. (eds.) (2005):
Well-posedness of a two-phase flow with soluble surfactant.
In: Nonlinear Elliptic and Parabolic Problems, Birkhäuser, pp. 37-61, [Conference or Workshop Item]

Item Type: Conference or Workshop Item
Erschienen: 2005
Editors: Chipot, M. and Escher, J.
Creators: Bothe, D. and Prüss, J. and Simonett, G.
Title: Well-posedness of a two-phase flow with soluble surfactant
Language: English
Title of Book: Nonlinear Elliptic and Parabolic Problems
Publisher: Birkhäuser
Uncontrolled Keywords: Navier-Stokes equations, surface tension, Marangoni forces, maximal regularity, surface transport theorem
Divisions: 04 Department of Mathematics > Mathematical Modelling and Analysis
UNSPECIFIED
Zentrale Einrichtungen
04 Department of Mathematics
Date Deposited: 12 Apr 2011 12:55
Identification Number: doi:10.1007/3-7643-7385-7_3
Alternative Abstract:
Alternative abstract Language
The presence of surfactants, ubiquitous at most °uid/liquid interfaces, has a pronounced e®ect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momen- tum along the interface { so-called Marangoni e®ects. The mathematical model gov- erning the dynamics of such systems is studied for the case in which the surfactant is soluble in one of the adjacent bulk phases. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phase. Within the model, the motions of the surfactant and of the adjacent bulk °uids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing Lp-maximal regularity we ob- tain well-posedness of this model for a certain initial con¯guration. The proof is based on recent Lp-theory for two-phase °ows without surfactant.English
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