Drifting mass accommodation coefficients: in situ measurements from a steady state molecular dynamics setup

ABSTRACT

A fundamental understanding of the evaporation/condensation phenomena is vital to many fields of science and engineering, yet there is many discrepancies in the usage of phase-change models and associated coefficients. First, a brief review of the kinetic theory of phase change is provided, and the mass accommodation coefficient (MAC, $\alpha$) and its inconsistent definitions are discussed. The discussion focuses on the departure from equilibrium; represented as a macroscopic “drift” velocity. Then, a continuous flow, phase change driven molecular-dynamics setup is used to investigate steady-state condensation at a flat liquid-vapor interface of argon at various phase-change rates and temperatures to elucidate the effect of equilibrium departure. MAC is computed directly from the kinetic theory-based Hertz–Knudsen (H-K) and Schrage (exact and approximate) expressions without the need for a priori physical definitions, ad-hoc particle injection/removal, or particle counting. MAC values determined from the approximate and exact Schrage expressions (${\alpha }_{app}^{Schrage}$ and ${\alpha }_{exact}^{Schrage}$) are between 0.8 and 0.9, while MAC values from the H-K expression (${\alpha }^{H-K}$) are above unity for all cases tested. ${\alpha }_{exact}^{Schrage}$ yield value closest to the results from transition state theory [J Chem Phys, 118, 1392–1399 (2003)]. The departure from equilibrium does not affect the value of ${\alpha }_{exact}^{Schrage}$ but causes ${\alpha }^{H-K}$ to vary drastically emphasizing the importance of a drift velocity correction. Additionally, equilibrium departure causes a nonuniform distribution in vapor properties. At the condensing interface, a local rise in vapor temperature and a drop in vapor density is observed when compared with the corresponding bulk values. When the deviation from bulk values are taken into account, all values of MAC including ${\alpha }_{exact}^{Schrage}$ show a small yet noticeable difference that is both temperature and phase-change rate dependent.

Graphical abstract

KEYWORDS:

• Mass accommodation coefficient
• kinetic theory of phase change
• Hertz-Knudsen equation
• Schrage relationships
• molecular dynamics

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Declaration of interests

The authors have no conflicts of interest to report.

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Notes

1. A majority of papers erroneously refer to Equation (1.8)(1.8) $\dot{m}{ }^{\mathrm{\prime }\mathrm{\prime }}=\frac{2\alpha }{2-\alpha }\sqrt{\frac{k_b}{2\pi m}}\left({\rho }_{sat}{|}_{T_i^L}\sqrt{T_i^L}-{\rho }^V\sqrt{T^V}\right)$(1.8) as the original Schrage expression. Although it is derived from the original equation developed by Schrage [7], there are two inherent assumptions: (i) the drift velocity of the vapor molecules is small in comparison to the mean thermal velocity, and, (ii) ideal gas equation is used to evaluate vapor density.