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Well-posedness of a Two-phase Flow with Soluble Surfactant

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Nonlinear Elliptic and Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 64))

Abstract

The presence of surfactants, ubiquitous at most fluid/liquid interfaces, has a pronounced effect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momentum along the interface — so-called Marangoni effects. The mathematical model governing 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 fluids are coupled by means of an interfacial momentum source term that represents Marangoni stresses. Employing L p -maximal regularity we obtain well-posedness of this model for a certain initial configuration. The proof is based on recent L p -theory for two-phase flows without surfactant.

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Authors and Affiliations

  1. Institut für Mathematik & Department Chemie, Technische Chemie und Chemische Verfahrenstechnik, Universität Paderborn, Warburger Str. 100, D-33098, Paderborn, Germany

    D. Bothe

  2. Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-60120, Halle, Germany

    J. Prüss

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    G. Simonett

Authors
  1. D. Bothe
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  2. J. Prüss
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  3. G. Simonett
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Editor information

Editors and Affiliations

  1. Universitá Pierre et Marie Curie, Paris

    Haim Brezis

  2. Rutgers University, New Brunswick, N.J.

    Haim Brezis

  3. Angewandte Mathematik, Universität Zurich, Winterthurerstr. 190, 8057, Zürich, Switzerland

    Michel Chipot

  4. Institute of Applied Mathematics, University of Hannover, Welfengarten 1, 30167, Hannover, Germany

    Joachim Escher

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Bothe, D., Prüss, J., Simonett, G. (2005). Well-posedness of a Two-phase Flow with Soluble Surfactant. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_3

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