Numerical study of evaporation and condensation phenomena by molecular dynamics and kinetic theory of gases

液体或固体表面的蒸发和冷凝一直是流体物理基础研究的重要课题。分子气体动力学(稀薄气体动力学)可以准确地描述蒸汽在其凝聚(液体或固体)相附近的行为。这实际上是通过在蒸汽和其凝聚相之间的界面上求解带有动力学边界条件的Boltzmann方程来实现的。然而，动力学边界条件的物理适用性从未得到验证，在分子气体动力学的框架下也不能确定凝聚系数。在这项研究中，我们通过分子动力学(MD)的数值方法、对Gauss-BGK-Boltzmann方程初边值问题的数值分析以及激波管实验来检验它的物理有效性。结果表明，在汽液界面上，Boltzmann方程的边界条件是汽相分子三个速度分量的一维麦克斯韦方程与一个凝结系数因子的乘积。与传统的模型边界条件一样，垂直于界面的速度分量的麦克斯韦量由液体温度来表征，而切向分量的麦克斯韦量则由不同的温度来描述，温度是界面能量通量的线性函数。凝结系数是恒定的，等于仅由液体温度决定的蒸发系数。

The evaporation from and condensation on a liquid or solid surface have long been an important subject of fundamental researches in physics of fluids. Molecular gas dynamics (rarefied gas dynamics) can give an accurate description of the behavior of vapor adjacent to its condensed (liquid or solid) phase. This has actually been accomplished by solving the Boltzmann equation with a kinetic boundary condition at an interface between vapor and its condensed phase. However, the physical appropriateness of the kinetic boundary condition has never been verified, and the parameter called condensation coefficient cannot be determined in the framework of the molecular gas dynamics. In this research, we examined its physical validity by the numerical method of molecular dynamics (MD), numerical analysis of the initial and boundary value problem of Gaussian-BGK-Boltzmann equation, and experiments using a shock tube. As a result, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellians for the three velocity components of vapor molecules and a factor including well-defined condensation coefficient. The Maxwellian for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.