Phase field modelling in phase transition problems

在德法合作的框架下，我们计划开发和研究一个相场模型，该模型能够描述临界点的离散通道（在连续体方法的极限下）-从单相超临界状态到临界点附近的两相亚临界状态-以及法拉第不稳定性，从连续不混相到混相的二元流体在地面和微重力环境中。这两个问题在大规模工业应用中都没有找到合适的理论描述。我们计划使用相场方法来解决这两个问题。德国团队在不同情况下的相场建模（超过10年）方面有丰富的经验，如倾斜固体表面上初始薄膜的接触线问题（液滴的形成），液滴的合并或马兰戈尼流的发生。法国团队在非混相/混相流体系统的物理和稳定性（超过10年）以及近临界流动的物理（近20年）方面拥有专业知识。这两个团队正计划合作，以分享他们的知识，解决两个复杂而未解决的问题。

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.