Nonequilibrium velocity distribution of evaporating water molecules: Molecular beam measurement and its impact on the fluid dynamics boundary conditions at a liquid-vapor interface

The Hertz-Knudsen equation is one of the widely-used boundary conditions for mass flux at a liquid-vapor interface. The derivation of this equation assumes that molecules evaporate from the liquid surface following the Maxwell-Boltzmann velocity distribution. However, the validity of this assumption is questionable for a nonequilibrium condition with a non-zero mass flux of phase change.

Recently, we developed an experimental setup to measure the velocity distribution of evaporating water molecules from a liquid-vapor interface, which is kept in a vacuum using a nanoporous membrane. This setup enabled measuring the nonequilibrium velocity distribution by suppressing molecular collisions after evaporation and showed that the velocity distribution slightly deviates from the Maxwell-Boltzmann distribution. The velocity distribution of evaporating molecules contains a smaller amount of slow molecules and a larger amount of fast molecules than the Maxwell-Boltzmann distribution. This result is consistent with the previously reported molecular dynamics simulations.

In this presentation, we discuss how the deviation from the Maxwell-Boltzmann distribution impacts the boundary conditions applied for a liquid-vapor interface in macroscopic flow analyses in light of our recent experimental results.