Bird Eric, Liang Zhi
Department of Mechanical Engineering, California State University, Fresno, California 93740, USA.
Phys Rev E. 2020 Oct;102(4-1):043102. doi: 10.1103/PhysRevE.102.043102.
In this work, we use the kinetic theory of gases (KTG) to develop a theoretical model to understand the role of internal motions of molecules on the maximum evaporation flux from a planar liquid surface. The kinetic theory is applied to study the evaporation of molecular fluids into a vacuum and predict the dimensionless maximum evaporation flux (J_{R,max}, i.e., the ratio of the maximum evaporation flux to the molar flux emitted from a liquid surface). The key assumptions regarding the velocity distribution function (VDF) of polyatomic molecules in the highly nonequilibrium vapor near the evaporating surface are validated by the VDF obtained directly from molecular dynamics (MD) simulations. Our KTG-based analysis shows that J_{R,max} is affected by the specific heat (c_{V,int}) associated with internal degrees of freedom of fluid molecules. When the maximum evaporation flux is reached, the isotropic evaporating vapor far from the liquid surface moves at its speed of sound regardless of whether it is a monatomic vapor or polyatomic vapor. To fundamentally understand the evaporation of a molecular fluid into a vacuum, we solve the Boltzmann transport equation (BTE) to obtain the temperature, density, and flow speed distributions in the highly nonequilibrium evaporating vapor flow. Our BTE solutions indicate that there are several universal features of the evaporating vapor when the maximum evaporation flux occurs. In particular, we find that the evaporating vapor flow speed reaches the maximum value of sqrt[1.5] times the most probable thermal speed in the vapor flow direction at the vacuum boundary, and this maximum value is independent of fluid properties. All theoretical predictions in this work are verified by the MD simulation results of the evaporation of the model liquid Ar and the model liquid n-dodecane into a vacuum, and existing experimental data.
在这项工作中，我们运用气体动力学理论（KTG）建立了一个理论模型，以理解分子内部运动对平面液体表面最大蒸发通量的作用。应用气体动力学理论研究分子流体向真空中的蒸发，并预测无量纲最大蒸发通量（(J_{R,max})，即最大蒸发通量与从液体表面发射的摩尔通量之比）。关于蒸发表面附近高度非平衡蒸汽中多原子分子速度分布函数（VDF）的关键假设，通过直接从分子动力学（MD）模拟获得的VDF进行了验证。我们基于KTG的分析表明，(J_{R,max})受与流体分子内部自由度相关的比热（(c_{V,int})）影响。当达到最大蒸发通量时，远离液体表面的各向同性蒸发蒸汽以其声速移动，无论它是单原子蒸汽还是多原子蒸汽。为了从根本上理解分子流体向真空中的蒸发，我们求解玻尔兹曼输运方程（BTE），以获得高度非平衡蒸发蒸汽流中的温度、密度和流速分布。我们的BTE解表明，当出现最大蒸发通量时，蒸发蒸汽有几个普遍特征。特别是，我们发现蒸发蒸汽流速在真空边界处沿蒸汽流动方向达到最概然热速度的(\sqrt{1.5})倍的最大值，并且这个最大值与流体性质无关。这项工作中的所有理论预测都通过模型液体氩和模型液体正十二烷向真空中蒸发的MD模拟结果以及现有的实验数据得到了验证。
