On ideal and real two-fluid mixtures of dispersed type: bubbly and droplet flow.

ORAL

Abstract

Starting from Hamilton's principle, we derive an ideal two-phase fluid model in Lagrangian form. With this description, insight toward understanding the ill-posedness of such two-phase flow models is obtained. Issues related to non-hyperbolicity, stability, and existence of strong solutions are also revisited. Adding the effect of viscosity to each fluid, we study the behavior of (linear) sound waves in this type of media (real multi-fluid). This classical physics question is a continuation of the wave studies of Kirchhoff (1868) and Stokes (1845) in a (mono)fluid. We give attenuation and dispersion formulae due to viscous effect in real two-fluid mixtures of dispersed type.

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Publication:
[1] Morrison, PJ, Andreussi, T & Pegoraro, F 2020 Lagrangian and dirac constraints for the
ideal incompressible fluid and magnetohydrodynamics. Journal of Plasma Physics 86 (3).
[2] Morrison, Philip J 1998 Hamiltonian description of the ideal fluid. Reviews of Modern Physics
70 (2), 467.
[3] Stewart, H. & Wendroff, B. 1984 Two-phase flow: Models and methods. Journal of
Computational Physics (56), 363–409.
[4] Kirchhoff, G. 1868 Ueber den einfluss der w ̈armeleitung in einem gase auf die schallbewegung.
Ann. Phys. (210), 177–193.
[5] Stokes, G.G. 1845 On the theories of the internal friction in fluids in motion, and of the equilibrium and motion of elastic solids. Transactions of the Cambridge Philosophical Society 8 (22), 287–342.

Presenters

  • Azeddine ZAIDNI

    Mohammed VI Polytechnic University, College of Computing, Benguuerir,Morocco

Authors

  • Azeddine ZAIDNI

    Mohammed VI Polytechnic University, College of Computing, Benguuerir,Morocco

  • Philip J Morrison

    Department of Physics and Institute for Fusion Studies, University of Texas at Austin, 78712 USA, Physcis Department, University of Texas at Austin, Austin, TX, University of Texas at Austin

  • Saad Benjelloun

    Makhbar Mathematical Sciences Research Institute, Casablanca, Morocco