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On the Interface Formation Model for Dynamic Triple Lines

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Mathematical Fluid Dynamics, Present and Future

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 183))

Abstract

This paper revisits the theory of Y. Shikhmurzaev on forming interfaces as a continuum thermodynamical model for dynamic triple lines. We start with the derivation of the balances for mass, momentum, energy and entropy in a three-phase fluid system with full interfacial physics, including a brief review of the relevant transport theorems on interfaces and triple lines. Employing the entropy principle in the form given in (Bothe and Dreyer (2015) Continuum thermodynamics of chemically reacting fluid mixtures. Acta Mech. 226, 1757–1805, [1]), but extended to this more general case, we arrive at the entropy production and perform a linear closure, except for a nonlinear closure for the sorption processes. Specialized to the isothermal case, we obtain a thermodynamically consistent mathematical model for dynamic triple lines and show that the total available energy is a strict Lyapunov function for this system.

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Acknowledgements

The first author (D.B.) is grateful for support by the DFG within the cluster of excellence “Center of Smart Interfaces”, TU Darmstadt. The second author (J.P.) thanks the DFG for continuous support in the framework of individual research projects.

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Authors and Affiliations

  1. Center of Smart Interfaces & Fachbereich Mathematik, Technische Universität Darmstadt, Alarich-Weiss-Str. 10, 64287, Darmstadt, Germany

    Dieter Bothe

  2. Institut Für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Str. 5, 06120, Halle (saale), Germany

    Jan Prüss

Authors
  1. Dieter Bothe
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  2. Jan Prüss
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Correspondence to Dieter Bothe .

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Editors and Affiliations

  1. Department of Mathematics, Waseda University, Tokyo, Japan

    Yoshihiro Shibata

  2. Department of Mathematics, Waseda University, Tokyo, Japan

    Yukihito Suzuki

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Bothe, D., Prüss, J. (2016). On the Interface Formation Model for Dynamic Triple Lines. In: Shibata, Y., Suzuki, Y. (eds) Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics & Statistics, vol 183. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56457-7_2

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