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Zbl 1173.35527
Boyer, Franck; Lapuerta, Céline
Study of a three component Cahn-Hilliard flow model. (English)
[J] ESAIM, Math. Model. Numer. Anal. 40, No. 4, 653-687 (2006). ISSN 0764-583X; ISSN 1290-3841/e

Summary: In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency properties with the two-component models. Notice that our model is also able to cope with some total spreading situations. We propose to take into account the hydrodynamics of the mixture by coupling our ternary Cahn-Hilliard system and the Navier-Stokes equation supplemented by capillary force terms accounting for surface tension effects between the components. Finally, we present some numerical results which illustrate our analysis and which confirm that our model has a better behavior than other possible similar models.

MSC 2000:: *35K55 Nonlinear parabolic equations
76T30 Three or more component flows
82C24 Interface problems (dynamic and non-equilibrium)
35B35 Stability of solutions of PDE
35Q35 Other equations arising in fluid mechanics
76D05 Navier-Stokes equations (fluid dynamics)

Keywords: multicomponent flows; Cahn-Hilliard equations; stability

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