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.

Keywords: multicomponent flows, Cahn-Hilliard equations, stability

@article{M2AN_2006__40_4_653_0, author = {Boyer, Franck and Lapuerta, C\'eline}, title = {Study of a three component {Cahn-Hilliard} flow model}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {653--687}, publisher = {EDP-Sciences}, volume = {40}, number = {4}, year = {2006}, doi = {10.1051/m2an:2006028}, mrnumber = {2274773}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2006028/} }

TY - JOUR AU - Boyer, Franck AU - Lapuerta, Céline TI - Study of a three component Cahn-Hilliard flow model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 653 EP - 687 VL - 40 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2006028/ DO - 10.1051/m2an:2006028 LA - en ID - M2AN_2006__40_4_653_0 ER -

%0 Journal Article %A Boyer, Franck %A Lapuerta, Céline %T Study of a three component Cahn-Hilliard flow model %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 653-687 %V 40 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2006028/ %R 10.1051/m2an:2006028 %G en %F M2AN_2006__40_4_653_0

Boyer, Franck; Lapuerta, Céline. Study of a three component Cahn-Hilliard flow model. ESAIM: Modélisation mathématique et analyse numérique, Volume 40 (2006) no. 4, pp. 653-687. doi : 10.1051/m2an:2006028. http://archive.numdam.org/articles/10.1051/m2an:2006028/

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