标题： 一种热力学一致的自由边界模型，用于演化域中具有移动接触线、可变接触角和体-界面相互作用的两相流动 显示英文标题

标题： A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Moving Contact Lines, Variable Contact Angles and Bulk-Surface Interaction

摘要： 我们推导出一个热力学一致的模型，该模型描述了在演化域中的两相流的时间演化。 域的自由边界运动由体相中的混合物速度场驱动，该速度场由纳维-斯托克斯方程确定。 为了考虑体相和边界之间的相互作用，我们进一步考虑边界上的两种材料，这些材料可能与体相中的材料相同或不同。 体相和表面材料分别由各自的相场表示，其时间演化由体相-表面对流的Cahn-Hilliard方程描述。 这种方法允许物质在体相和表面之间转移，以及体相中的扩散界面与域边界之间的可变接触角。 为了更准确地描述相应的接触线运动，我们在速度场中包含了一个广义的Navier滑移边界条件。 我们通过考虑局部质量平衡和能量耗散定律从头开始推导我们的模型。 最后，通过拉格朗日乘数方法完成推导。 我们进一步表明，我们的模型推广了文献中的先前模型，这些模型可以通过删除动态边界条件或假设域的静态边界从我们的系统中恢复得到。 显示英文摘要

摘要： We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which is determined by a Navier--Stokes equation. In order to take interactions between bulk and boundary into account, we further consider two materials on the boundary, which may be the same or different materials as those in the bulk. The bulk and the surface materials are represented by respective phase-fields, whose time evolution is described by a bulk-surface convective Cahn--Hilliard equation. This approach allows for a transfer of material between bulk and surface as well as variable contact angles between the diffuse interface in the bulk and the boundary of the domain. To provide a more accurate description of the corresponding contact line motion, we include a generalized Navier slip boundary condition on the velocity field. We derive our model from scratch by considering local mass balance and energy dissipation laws. Finally, the derivation is completed via the Langrange multiplier approach. We further show that our model generalizes previous models from the literature, which can be recovered from our system by either dropping the dynamic boundary conditions or assuming a static boundary of the domain.