A conceptual and mathematical framework for the singularity-free modeling of non-equilibrium solidification/melting and non-isothermal dynamic wetting is developed where both processes are embedded into a broader class of physical phenomena as particular cases. This allows one to consider problems describing fluid flows with phase transitions and dynamic wetting occurring independently or interactively in a regular conceptually consistent way without ad hoc assumptions. The simplest model formulated on the basis of this approach explains, at this stage qualitatively, the arrest of the moving contact line observed experimentally in the impact and spreading of a molten drop on a cold substrate. The classical Stefan problem and the model of isothermal dynamic wetting as an interface formation process are recovered as limiting cases.

中文翻译：

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凝固和动态润湿：统一的建模框架

开发了一种用于非平衡凝固/熔化和非等温动态润湿的无奇点建模的概念和数学框架，其中这两个过程都作为特殊情况嵌入到更广泛的物理现象类别中。这允许人们考虑描述具有相变和动态润湿的流体流动的问题，这些问题以规则的概念一致的方式独立或交互发生，无需临时假设。在此方法的基础上制定的最简单的模型在此阶段定性地解释了在熔滴在冷基板上的撞击和扩散中通过实验观察到的移动接触线的停滞。经典的 Stefan 问题和作为界面形成过程的等温动态润湿模型被恢复为极限情况。