Phase field modelling in phase transition problems

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In the frame of a German-French collaboration, we plan to develop and investigate numerically a phase field model able to describe the discrete passage (in the limit of continuum approach) of the critical point - from monophasic supercritical state to two-phase subcritical state nearby the critical point - as well as the Faraday instability from the continuous immiscible to miscible states of binary fluids in both ground-based and microgravity environments. Both problems with large industrial applications cannot find a suitable theoretical description until now. We plan to use the phase-field approach in order to solve these two subjects. The German team has a great experience on the phase-field modelling (for over 10 years) of different cases like the contact-line problems from an initial thin film on an inclined solid surface (formation of liquid drops), the coalescence of drops or the occurrence of Marangoni flows. The French team has the expertise on the physics and the stability of the immiscible/miscible fluid system (for more than 10 years) and the physics of near-critical flows (for almost 20 years). The two teams are planning to collaborate in order to share their knowledge and solve two complex and unsolved problems.