The evaporation and condensation at an interface of vapor and its condensed phase is considered. The validity of kinetic boundary condition for the Boltzmann equation, which prescribes the velocity distribution function of molecules outgoing from the interface, is investigated by the numerical method of molecular dynamics for argon. From the simulations of evaporation into vacuum, the spontaneous-evaporation flux determined by the temperature of condensed phase is discovered. Condensation coefficient in equilibrium states can then be determined without any ambiguity. It is found that the condensation coefficient is close to unity below the triple-point temperature and decreases gradually as the temperature rises. The velocity distribution of spontaneously evaporating molecules is found to be nearly a half-Maxwellian at a low temperature. This fact supports the kinetic boundary condition widely used so far. At high temperatures, on the other hand, the velocity distribution deviates from the half-Maxwellian.
REFERENCES
1.
C. Cercignani, Rarefied Gas Dynamics (Cambridge University Press, New York, 2000).
2.
Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston, 2002).
3.
The parameter α in the first term in Eq. (1) is sometimes called the evaporation coefficient and distinguished from the condensation coefficient. See Eq. (8), and also,
R.
Meland
and T.
Ytrehus
, “Evaporation and condensation Knudsen layers for nonunity condensation coefficient
,” Phys. Fluids
15
, 1348
(2003
).4.
M.
Matsumoto
and Y.
Kataoka
, “Dynamic processes at a liquid surface of methanol
,” Phys. Rev. Lett.
69
, 3782
(1992
).5.
K.
Yasuoka
and M.
Matsumoto
, “Evaporation and condensation at a liquid surface. I. Argon
,” J. Chem. Phys.
101
, 7904
(1994
).6.
T.
Tsuruta
, H.
Tanaka
, and T.
Masuoka
, “Condensation/evaporation coefficient and velocity distributions at liquid–vapor interface
,” Int. J. Heat Mass Transfer
42
, 4107
(1999
).7.
G.
Nagayama
and T.
Tsuruta
, “A general expression for the condensation coefficient based on transition state theory and molecular dynamics simulation
,” J. Chem. Phys.
118
, 1392
(2003
).8.
R.
Meland
and T.
Ytrehus
, “Boundary condition at a gas–liquid interphase,” in Rarefied Gas Dynamics
, edited by T. J.
Bartel
and , M. A.
Gallis
, AIP Conf. Proc.
No. 585
(AIP
, Melville
, 2001
), p. 583
.9.
R.
Meland
, “Molecular exchange and its influence on the condensation coefficient
,” J. Chem. Phys.
117
, 7254
(2002
).10.
A.
Frezzotti
and L.
Gibelli
, “A kinetic model for equilibrium and non-equilibrium structure of the vapor–liquid interface,” in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics
, edited by A. D.
Ketsdever
and , E. P.
Muntz
, AIP Conf. Proc.
No. 663
(AIP
, New York
, 2003
), p. 980
.11.
M.
Mecke
, J.
Winkelmann
, and J.
Fischer
, “Molecular dynamics simulation of the liquid–vapor interface: The Lennard-Jones fluid
,” J. Chem. Phys.
107
, 9264
(1997
).12.
A.
Trokhymchuk
and J.
Alejandre
, “Computer simulations of liquid/vapor interface in Lennard-Jones fluids: Some questions and answers
,” J. Chem. Phys.
111
, 8510
(1999
).13.
J.-P.
Hansen
and L.
Verlet
, “Phase transitions of the Lennard-Jones system
,” Phys. Rev.
184
, 151
(1969
).14.
J. H.
Dymond
and B. J.
Alder
, “Pair potential for argon
,” J. Chem. Phys.
51
, 309
(1969
).15.
J. J.
Burton
, “Calculation of properties of solid argon from the Dymond–Alder potential
,” Chem. Phys. Lett.
15
, 312
(1970
).16.
Ch.
Tegeler
, R.
Span
, and W.
Wagner
, “A new equation of state for argon covering the fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MPa
,” J. Phys. Chem. Ref. Data
28
, 779
(1999
).17.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1988).
18.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
19.
S. I.
Anisimov
, D. O.
Dunikov
, S. P.
Malyshenko
, and V. V.
Zhakhovskii
, “Properties of a liquid–gas interface at high-rate evaporation
,” J. Chem. Phys.
110
, 8722
(1999
).20.
T.
Tsuruta
and G.
Nagayama
, “Molecular dynamics study on condensation coefficients of water
,” Trans. Jpn. Soc. Mech. Eng., Ser. A
68
, 1898
(2002
) (in Japanese).21.
M.
Matsumoto
, “Molecular dynamics of fluid phase change
,” Fluid Phase Equilib.
144
, 307
(1998
).22.
A.
Thran
, M.
Kiene
, V.
Zaporojtchenko
, and F.
Faupel
, “Condensation coefficients of Ag on polymers
,” Phys. Rev. Lett.
82
, 1903
(1999
).23.
K. J.
Kossacki
, W. J.
Markiewicz
, Y.
Skorov
, and N. I.
Kömle
, “Sublimation coefficient of water ice under simulated cometary-like conditions
,” Planet. Space Sci.
47
, 1521
(1999
).24.
S.
Fujikawa
, M.
Kotani
, H.
Sato
, and M.
Matsumoto
, “Molecular study of evaporation and condensation of an associating liquid
,” Heat Transfer-Jpn. Res.
23
, 595
(1994
).25.
H. K.
Cammenga
, “Evaporation mechanisms of liquids
,” Curr. Top. Mater. Sci.
5
, 335
(1980
).26.
The volume element in the vacuum simulation is fixed on the moving coordinate defined by Eq. (14).
27.
As a check of a necessary condition for statistical independence, we have confirmed that the correlation coefficients are small compared with unity.
28.
Exactly speaking, the condensed phase has a in the moving coordinate. However, it is too small to be seen in Figs. 9(a) and 9(d).
29.
V. V.
Zhakhovskii
and S. I.
Anisimov
, “Molecular-dynamics simulation of evaporation of a liquid
,” JETP
84
, 734
(1997
).
This content is only available via PDF.
© 2004 American Institute of Physics.
2004
American Institute of Physics
You do not currently have access to this content.
