Liquid temperature dependence of kinetic boundary condition at vapor–liquid interface

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.  

Liquid temperature dependence of kinetic boundary condition at vapor–liquid interface.Advances in Engineering

About the author

Misaki Kon is a Ph.D. candidate in the division of Mechanical and Space Engineering at Hokkaido University, Sapporo, Japan and is also a Research Fellow at Japan Society for the Promotion of Science. She received B.Sc. (Eng.) degree from National Institute of Technology, Tomakomai College, Tomakomai, Hokkaido in 2012. She received M.Sc. (Eng.) degree from Hokkaido University in 2014. Her research interest is non-equilibrium transport phenomena in the two-phase system, especially flows with phase change.  

About the author

Dr. Kazumichi Kobayashi is an associate professor of the Division of Mechanical and Space Engineering at Hokkaido University, Sapporo, Japan. After he received his Ph.D. from Hokkaido University in 2007, he worked for Osaka Prefecture University and Hokkaido University as an assistant professor for 6 years and attained the current position.

His current research is heat and mass transfer at an interface, cavitation bubble dynamics, and droplet dynamics at a molecular level.  

About the author

Dr. Masao Watanabe is a professor of the division of Mechanical and Space Engineering at Hokkaido University, Sapporo, Japan. He received his Ph.D. from The Johns Hopkins University in 1995.

His current research interests include but are not limited to two-phase flow dynamics, bubble dynamics, droplet impact, interfacial phenomena, nano/micro fluids, and molecular gas dynamics.  

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

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