Evaporation and Condensation from or onto the Condensed Phase with an Internal Structure

Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard–Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.

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Effects of the Finite Thermal Conductivity of the Condensed Phase on Evaporation and Condensation Flows of Its Vapor: Existence of the Maximum Mass and Energy Flows

ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 3 ◽

10.1115/ht2007-32743 ◽

2007 ◽

Author(s):

Yoshimoto Onishi ◽

Takahiro Fuji ◽

Yuuki Mannari ◽

Takeshi Ooshida

Keyword(s):

Thermal Conductivity ◽

Boltzmann Equation ◽

Condensed Phase ◽

Fluid Dynamic ◽

Temperature Fields ◽

Condensed Phases ◽

Evaporation And Condensation ◽

Energy Flows ◽

Internal Structures ◽

Dynamic Formulation

Transient to steady motions of a vapor due to evaporation and condensation processes between the plane condensed phases with temperature fields as their internal structures have been studied in detail based on the new governing system at the ordinary fluid dynamic level, i.e., fluid dynamic formulation, which consists of the compressible Navier-Stokes equations and the boundary conditions appropriate for evaporation and condensation problems derived earlier from the kinetic theory analysis. The previous studies based on the Boltzmann equation of BGK type have shown that the mass and energy flows may take their maximum values at a certain value of the latent heat parameter when the condensed phases have temperature fields as their internal structures; the internal structure is a reflection of the thermal conductivity of the condensed phase being finite compared to that of its vapor. This is a striking feature in contrast to the case in which no internal structures exist in the condensed phases. Particular attention, therefore, is paid to the quantitative aspect of this behavior of the mass and energy flows. Incidentally, the comparison between the present results and the corresponding ones from the Boltzmann equation of BGK type has been made and found to be quite good, indicating that the fluid dynamic formulation works satisfactorily in the present case with temperature fields as the internal structures of the condensed phases.

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