.2020 May 18;10(1):8143.

doi: 10.1038/s41598-020-64905-5.

Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions

Kotaro Ohashi¹, Kazumichi Kobayashi², Hiroyuki Fujii¹, Masao Watanabe¹

Affiliations

PMID:32424295
PMCID: PMC7235219
DOI: 10.1038/s41598-020-64905-5

Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions

Kotaro Ohashi et al. Sci Rep.2020.

.2020 May 18;10(1):8143.

doi: 10.1038/s41598-020-64905-5.

Authors

Kotaro Ohashi¹, Kazumichi Kobayashi², Hiroyuki Fujii¹, Masao Watanabe¹

Affiliations

¹ Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628, Japan.
² Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Sapporo, 060-8628, Japan. kobakazu@eng.hokudai.ac.jp.

PMID:32424295
PMCID: PMC7235219
DOI: 10.1038/s41598-020-64905-5

Erratum in

Author Correction: Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions.
Ohashi K, Kobayashi K, Fujii H, Watanabe M.Ohashi K, et al.Sci Rep. 2020 Jul 1;10(1):11094. doi: 10.1038/s41598-020-68283-w.Sci Rep. 2020.PMID:32606333Free PMC article.

Abstract

We investigated the evaporation and condensation coefficients of vapor, which represent evaporation and condensation rates of vapor molecules, under high gas pressure (high gas density) conditions in a system of a vapor/gas-liquid equilibrium state. The mixture gas is composed of condensable gas (vapor) and non-condensable gas (NC gas) molecules. We performed numerical simulations of vapor/gas-liquid equilibrium systems with the Enskog-Vlasov direct simulation Monte Carlo (EVDSMC) method. As a result of the simulations, we found that the evaporation and condensation fluxes decrease with increasing NC gas pressure, which leads to a decrease in the evaporation and condensation coefficients of vapor molecules. Especially, under extremely high gas pressure conditions, the values of these coefficients are close to zero, which means the vapor molecules cannot evaporate and condensate at the interface. Moreover, we found that the vapor molecules behave as NC gas molecules under high gas pressure conditions. We also discussed the reason why NC gas molecules interfere with evaporation and condensation of vapor molecules at the vapor/gas-liquid interface.

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Conflict of interest statement

The authors declare no competing interests.

Figures

**Figure 1**
Molecular mass fluxes at a vapor/gas–liquid interface. $J_{call}^{ω}$ denotes the colliding molecular mass flux, $J_{out}^{ω}$ is the outgoing molecular mass flux, $J_{evap}^{ω}$ is the evaporating molecular mass flux, $J_{cond}^{ω}$ is the condensing molecular mass flux, and $J_{ref}^{ω}$ is the reflecting molecular mass flux. $ω = V$ denotes the molecular mass fluxes for vapor molecules at the interface, and $ω = G$ those for NC gas molecules.

**Figure 2**
(a) Schematic of the present simulation condition (steady vapor/gas–liquid equilibrium). At the center of the system, there is a thin liquid film; (b) Schematic of the molecular fluxes in the vicinity of vapor/gas–liquid interface. We can count the number of molecules using mixture gas and liquid boundaries; $J_{evap}^{ω}$ denotes the evaporating molecular mass flux for $ω$ component molecules, $J_{ref}^{ω}$ the reflecting molecular mass flux, and $J_{cond}^{ω}$ the condensing molecular mass flux.

**Figure 3**
Number density profiles of each simulation case: (a) vapor component, $n^{V} σ^{3}$ ; (b) NC gas component, $n^{G} σ^{3}$ ; (c) non-dimensional NC gas pressure ${\hat{p}}^{G} = p^{G} σ^{3} / k T_{0}$ as a function of molar fraction of dissolved NC gas moleculesμ. Each number near the symbols denotes each case number. The dotted line shows the eye guide (linear relation of the Henry’s law). Macroscopic quantities of Case 8: (d) number density, velocity, and temperature fields; (e) mean-field forces of vapor and NC gas molecules.

**Figure 4**
Molecular mass fluxes, evaporation coefficient, and condensation coefficient of vapor and NC gas molecules as a function ofμ: (a) outgoing, evaporating, and reflecting vapor molecules; (b) colliding, condensing, and reflecting vapor molecules; (c) outgoing, evaporating, and reflecting NC gas molecules; (d) colliding, condensing, and reflecting NC gas molecules; (e) evaporation and condensation coefficients of vapor molecules; (f) evaporation and condensation coefficients of NC gas molecules; (g) evaporating and condensing molecular mass fluxes as the function of $N_{l - g}^{NC}$ ; and (h) schematic of $J_{evap}^{V}$ and $J_{cond}^{V}$ . Due to the collision of molecules between the liquid and mixture gas boundaries, the backscattering for $J_{evap}^{V}$ and $J_{cond}^{V}$ increases.

**Figure 5**
Molecular velocity distribution function (VDF) normalized to unity at the mixture gas boundary (the position to impose KBC): (a) vapor of Case 1; (b) NC gas of Case 1; (c) vapor of Case 8; and (d) NC gas of Case 8.

**Figure 6**
Non-dimensional number of reflecting molecules at the interface: (a) definition of reflect position of reflecting molecules between mixture gas and liquid boundaries; (b) non-dimensional number of reflecting molecules in Case 1; (c) non-dimensional number of reflecting molecules in Case 8; (d) non-dimensional stall time of reflecting for vapor and NC gas molecules in Case 1; (e) non-dimensional stall time of reflecting vapor and NC gas molecules in Case 8.

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Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions

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Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions

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