The kinetic boundary condition for the Boltzmann equation at an interface between a polyatomic vapor and its liquid phase is investigated by the numerical method of molecular dynamics, with particular emphasis on the functional form of the evaporation part of the boundary condition, including the evaporation coefficient. The present study is an extension of a previous one for argon [Ishiyama, Yano, and Fujikawa, Phys. Fluids 16, 2899 (2004)] to water and methanol, typical examples of polyatomic molecules. As in the previous study, molecular dynamics simulations of vapor–liquid equilibrium states and those of evaporation from liquid into a virtual vacuum are carried out for water and methanol. In spite of the formation of molecular clusters in the vapor phase and the presence of the preferential orientation of molecules at the interface, essentially the same results as in the previous study are obtained. When the bulk liquid temperature is relatively low, the evaporation part is the product of the half range Maxwellian for the translational velocity of molecules of saturated vapor at the temperature of the bulk liquid phase, the equilibrium distribution of rotational energy of molecules at the temperature, and the evaporation coefficient (or the condensation coefficient in the equilibrium state). The evaporation coefficients of water and methanol are determined without any ambiguity as decreasing functions of the temperature, and are found to approach unity with the decrease of the temperature.

1.
C.
Cercignani
, Rarefied Gas Dynamics (Cambridge University Press, New York,
2000
).
2.
Y.
Sone
, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston,
2002
).
3.
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
).
4.
R.
Meland
and
T.
Ytrehus
, “
Boundary condition at a gas–liquid interface
,” in Rarefied Gas Dynamics: 22nd International Symposium, edited by
T. J.
Bartel
and
M. A.
Gallis
(American Institute of Physics, New York,
2001
), p.
583
.
5.
A.
Frezzotti
and
L.
Gibelli
, “
A kinetic model for equilibrium and non-equilibrium structure of the vapor–liquid interface
,” in Rarefied Gas Dynamics: 23rd International Symposium, edited by
A. D.
Ketsdever
and
E. P.
Muntz
(American Institute of Physics, New York,
2003
), p.
980
.
6.
T.
Ishiyama
,
T.
Yano
, and
S.
Fujikawa
, “
Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase
,”
Phys. Fluids
16
,
2899
(
2004
).
7.
W.B.
Takens
,
W.
Mischke
,
J.
Korving
, and
J.J. M.
Beenakker
, “
A spectroscopic study of free evaporation of sodium
,” in Rarefied Gas Dynamics, edited by
H.
Oguchi
(University of Tokyo Press, Tokyo,
1984
), p.
976
.
8.
C.
Cercignani
,
W.
Fiszdon
, and
A.
Frezzotti
, “
The paradox of the inverted temperature profiles between an evaporating and a condensing surface
,”
Phys. Fluids
28
,
3237
(
1985
).
9.
The collision mass flux 〈Jcoll is defined as 〈Jcoll〉=−∫∫ξz<00 ξzfcolldE dξxyz,where fcoll is the distribution function for molecules incoming to the interface, and Jcnds is evaluated from Eq. (14) and 〈Jref〉=〈Jout〉−〈Jevapsp (see also Fig. 1).
10.
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
).
11.
M.P.
Allen
and
D.J.
Tildesley
, Computer Simulation of Liquids (Clarendon, Oxford,
1987
).
12.
W. L.
Jorgensen
,
J.
Chandrasekhar
,
J. D.
Madura
,
R. W.
Impey
, and
M. L.
Klein
, “
Comparison of simple potential functions for simulating liquid water
,”
J. Phys. Chem.
79
,
926
(
1983
).
13.
W. L.
Jorgensen
, “
Optimized intermolecular potential functions for liquid alcohols
,”
J. Phys. Chem.
90
,
1276
(
1986
).
14.
J. T.
Wescott
,
L. R.
Fisher
, and
S.
Hanna
, “
Use of thermodynamic integration to calculate the hydration free energies of n-alkanes
,”
J. Chem. Phys.
116
,
2361
(
2002
).
15.
M.
Matsumoto
and
Y.
Kataoka
, “
Study on liquid–vapor interface of water. I. Simulational results of thermodynamic properties and orientational structure
,”
J. Chem. Phys.
88
,
3233
(
1988
).
16.
M.
Kettler
,
I.
Nezbeda
,
A. A.
Chialve
, and
P. T.
Cummings
, “
Effect of the range of interactions on the properties of fluids. Phase equilibria in pure carbon dioxide, acetone, methanol, and water
,”
J. Phys. Chem. B
106
,
7537
(
2002
).
17.
M.
Mecke
, and
J.
Winkelmann
, “
Molecular dynamics simulation of the liquid–vapor interface of dipolar fluids under different electrostatic boundary conditions
,”
J. Chem. Phys.
114
,
5842
(
2001
).
18.
M.
Hloucha
,
A. K.
Sum
, and
S. I.
Sandler
, “
Computer simulation of acetonitrile and methanol with ab initio-based pair potentials
,”
J. Chem. Phys.
113
,
5401
(
2000
).
19.
L.
Vega
,
E.
de Miguel
, and
L. F.
Rull
, “
Phase equilibria and critical behavior of square-well fluids of variable width by Gibbs ensemble Monte Carlo simulation
,”
J. Chem. Phys.
96
,
3233
(
1992
).
20.
W.
Wagner
and
A.
Pruss
, “
The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use
,”
J. Phys. Chem. Ref. Data
31
,
387
(
2002
).
21.
R. D.
Goodwin
, “
Methanol thermodynamic properties from 176 to 673 K at pressures to 700 bar
,”
J. Phys. Chem. Ref. Data
16
,
799
(
1987
).
22.
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
).
23.
In high temperature case, the transition layer extends close to z*≅2, and hence we cannot set Lg* at z*≲2.
24.
T.L.
Hill
, Statistical Mechanics: Principles and Selected Applications (McGraw-Hill, New York,
1956
).
25.
M.
Matsumoto
, “
Molecular dynamics of fluid phase change
,”
Fluid Phase Equilib.
144
,
307
(
1998
).
26.
R.
Marek
and
J.
Straub
, “
Analysis of the evaporation coefficient and the condensation coefficient of water
,”
Int. J. Heat Mass Transfer
44
,
39
(
2001
).
27.
S.
Fujikawa
,
T.
Yano
,
K.
Kobayashi
,
K.
Iwanami
, and
M.
Ichijo
, “
Molecular gas dynamics applied to phase change processes at a vapor–liquid interface: Shock-tube experiment and MGD computation for methanol
,”
Exp. Fluids
37
,
80
(
2004
).
28.
R.C.
Reid
,
J.M.
Prausnitz
, and
T.K.
Sherwood
, The Properties of Gases and Liquids (McGraw-Hill, New York,
1977
).
29.
M.
Matsumoto
and
Y.
Kataoka
, “
Molecular orientation near liquid–vapor interface of methanol: Simulational study
,”
J. Chem. Phys.
90
,
2398
(
1989
).
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