Significance Statement
Misaki Kon and colleagues proposed a microscopic interfacial model which should be imposed at the vapor-liquid interface with the mass flux in the normal direction (net evaporation and condensation) as the kinetic boundary condition, KBC, over a wide range of liquid temperature. The research is now published in peer-reviewed journal, International Journal of Heat and Mass Transfer.
The KBC is the boundary condition for the Boltzmann equation which governs the spatiotemporal development of the molecular velocity distribution function. The boundary condition for the macroscopic equation, e.g., fluid-dynamic type equations, at the vapor-liquid interface can only be derived by the microscopic approach like the analysis of the Boltzmann equation with the accurate KBC. Although it is necessary to track the molecular motions, such as evaporation, reflection, and condensation, in order to construct the accurate KBC, these molecular motions cannot be uniquely distinguished especially in the case of high liquid temperature.
The research team proposed a novel method of constructing the KBC without explicitly distinguishing these molecular motions. This novel method can reduce the computational cost by employing the molecular simulation based on mean-field kinetic theory (EV-DSMC simulation), and thereby it is possible to construct the KBC over a wide range of liquid temperature. In this method, the relation between the mass flux passing through the vapor-liquid interface due to evaporation/condensation and the density of molecules entering the interface from the vapor phase is formulated by the EV-DSMC simulation. They found that this relation is well described as a linear function even in the case of high liquid temperature. This result indicated that the KBC depends only on liquid temperature regardless of the degree of net evaporation and condensation.
The research term also validated the accuracy of the constructed KBC by applying the numerical simulation of the Boltzmann equation. They compared the macroscopic variables in vapor, e.g., density, temperature, and velocity, obtained from the numerical simulation of the Boltzmann equation with the constructed KBC and the EV-DSMC simulation. The KBC is validated if and only if the macroscopic variables in vapor calculated these two simulations agree with the high degree of accuracy because the macroscopic variables in vapor strongly depend on the KBC. As a result, the macroscopic variables calculated by these two simulations are in excellent agreement with each other. They concluded that that the constructed KBC can be guaranteed to be accurate.
This study applied the constructed KBC to the macroscopic boundary condition for the fluid-dynamic type equations. This application makes it possible to accurately deal with the interfacial dynamics in the vapor-liquid two-phase system with net evaporation and condensation.
Journal Reference
Misaki Kon, Kazumichi Kobayashi, Masao Watanabe, Liquid Temperature Dependence of Kinetic Boundary Condition at Vapor–Liquid Interface, International Journal of Heat and Mass Transfer 99 (2016) 317–326.
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japa
Go To International Journal of Heat and Mass Transfer