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

Abstract

For the accurate description of heat and mass transfer through a vapor-liquid interface, the appropriate modeling of the interface during nonequilibrium phase change (net evaporation/condensation) is a crucial issue. The aim of this study is to propose a microscopic interfacial model which should be imposed at the interface as the kinetic boundary condition for the Boltzmann equation. In this study, we constructed the kinetic boundary condition for monoatomic molecules over a wide range of liquid temperature based on mean field kinetic theory, and we validated the accuracy of the constructed kinetic boundary condition by solving the boundary value problem of the Boltzmann equation. These results showed that we can impose the kinetic boundary condition at the interface by simply specifying liquid temperature and simulate the complex vapor-liquid two-phase flow induced by net evaporation/condensation. Furthermore, we applied the constructed kinetic boundary condition to the boundary condition for the fluid-dynamic-type equations. This application enables us to deal with a large spatio-temporal scale of the interfacial dynamics in the vapor-liquid two-phase system with net evaporation/condensation.

Kinetic boundary condition in vapor–liquid two-phase system during unsteady net evaporation/condensation

“…In our recent studies [24,27], we confirmed that ρv z is well described as a linear function of σ/ρ * and furthermore that β ne and β nc depend only on liquid temperature. When J coll = 0 in Eq.…”

“…In this section, we explain the KBC that is established in the vapor-liquid two-phase system with steady net evaporation/condensation [24,27]. As the starting point, we examine a conventional KBC that is expressed as the linear combination of the diffuse reflection and complete condensation conditions [30,31],…”

“…In contrast, with the development of high-performance computing from the late 1990s to the present, numerous studies have performed a molecular simulation of the full vapor-liquid two-phase system including the nonequilibrium transition layer in terms of constructing the KBC [11,12,13,14,19,20,21,22,23,24,25,26,27]. Although it is clear that liquid temperature changes with time according to the heat and mass transfer caused by net evaporation/condensation, most of the studies mentioned above assume a steady or quasi-steady net evaporation/condensation because of the high computational cost of molecular simulation.…”

“…The aim of this study is to investigate the KBC in the vapor-liquid two-phase system with unsteady net evaporation/condensation by a molecular simulation based on mean-field kinetic theory. This type of molecular simulation allows us to reduce the computational cost compared with the typically used molecular dynamics simulation [15,24,25,26,27,28,29]. In this study, we examine whether the KBC can be imposed by simply specifying liquid temperature even in unsteady net evaporation/condensation in order to extend the previous results that the KBC, which is established in the vapor-liquid two-phase system with steady net evaporation/condensation [24,27], depends only on liquid temperature (a detailed explanation of this KBC is given in Section 2.1).…”

Mass and heat transfer between evaporation and condensation surfaces: Atomistic simulation and solution of Boltzmann kinetic equation

“…Moreover, even the small differences between the experimental conditions (such as chemical impurities on the interface and variation of surface temperatures of liquids being investigated) may have a dramatic effect on the measurement results. The dependence of evaporation and condensation coefficients from the surface temperature is also reported in simulation works (27,28). It was found that those coefficients, which are close to unity at low temperatures, begin to decrease if the surface temperature is increased well above the triple point.…”