Study of a three component Cahn-Hilliard flow model

Franck Boyer; Céline Lapuerta

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 4, page 653-687
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Boyer, Franck, and Lapuerta, Céline. "Study of a three component Cahn-Hilliard flow model." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 653-687. <http://eudml.org/doc/249713>.

@article{Boyer2006,
abstract = { 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. },
author = {Boyer, Franck, Lapuerta, Céline},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Multicomponent flows; Cahn-Hilliard equations; stability.; multicomponent flows; stability},
language = {eng},
month = {11},
number = {4},
pages = {653-687},
publisher = {EDP Sciences},
title = {Study of a three component Cahn-Hilliard flow model},
url = {http://eudml.org/doc/249713},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Boyer, Franck
AU - Lapuerta, Céline
TI - Study of a three component Cahn-Hilliard flow model
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 4
SP - 653
EP - 687
AB - 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.
LA - eng
KW - Multicomponent flows; Cahn-Hilliard equations; stability.; multicomponent flows; stability
UR - http://eudml.org/doc/249713
ER -

References

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