Expressions for the evaporation and condensation
coefficients in the Hertz-Knudsen relation:
Supporting information — List of symbols
Aaron H. Persad and Charles A. Ward∗
University of Toronto, Department of Mechanical and Industrial Engineering,
Thermodynamics and Kinetics Laboratory, 5 King’s College Road, Toronto, Canada, M5S
3G8
1
Table S1: Nomenclature: list of acronyms. Continued in Table S2.
Acronym
CCN
CKT
DIPPR
DOF
HK
HKS
LJ
M-B
MD
MFP
NIST
PMMA
PVC
SPC/E
SRT
TED
TED-SRT
Definition
cloud condensation nuclei
classical kinetic theory
Design Institute of Physical Properties Research
vibrational degrees of freedom
Hertz-Knudsen
Hertz-Knudsen-Schrage
Lennard-Jones
Maxwell-Boltzmann
molecular dynamics
mean free path
National Institute of Standards and Technology
polymethyl methacrylate
polyvinyl chloride
extended simple point charge model
statistical rate theory
thermal energy dominant
thermal-energy-dominant limit of statistical rate theory
2
Table S2: Continued from Table S1. Nomenclature: list of symbols. Continued in Table S3.
Latin symbol
Atst
cz
cLp
cVp
C
C0
C1
C2
Ea
Err(z)
Err(Ps )
h̄
hf g
hV
j LV
j0LV
jeL
jeV
∗
jev
LV
jHKS
kB
Ke
KLV
Definition
effective area of transition state
particle velocity normal to the interface (and relative to its velocity)
constant-pressure-specific heat of the liquid phase
constant-pressure-specific heat of the vapor phase
proportionality constant
curvature of a spherical interface
primary axis of curvature
secondary axis of curvature
activation energy for evaporation
error associated with the determination of parameter z
average fitting error of Ps (T ) expression
reduced Planck constant
evaporative latent heat
specific enthalpy of the vapor phase
net flux from the liquid phase to the vapor phase
local net evaporation flux
equilibrium unidirectional evaporation flux
equilibrium unidirectional condensation flux
local evaporation flux in the TED-SRT relation
net evaporation flux determined from the HKS relation
Boltzmann constant
equilibrium molecular exchange rate across the liquid-vapor interface
exchange rate of molecules across the liquid-vapor interface
3
Table S3: Continued from Table S2. Nomenclature: list of symbols. Continued in Table S4.
Latin symbol
m
n
Ps
Ps∗
Ps†
PV
V
V
P1 , P2 , P3V
V
Pcalc
PmV
Pw
qvib
r
R
T
Tc
Te
Tw
TI
TIL
TIV
T0
L
T (t)
TnL
vf
vL
vV
VLJ
|Vve |
Z
Definition
molecular mass
number of atoms, or number of carbon atoms
saturation-vapor pressure
saturation-vapor pressure determined from the TED-SRT relation
saturation-vapor pressure determined from the SRT relation
vapor-phase pressure
calculated vapor-phase pressures assuming equality between σe and σc
calculated vapor-phase pressure
measured vapor-phase pressure
probability of emission
vibrational partition function
total number of data points
universal gas costant
temperature
critical temperature
equilibrium temperature
surface temperature of emitted molecule
thermally equilibrated interfacial temperature
interfacial liquid temperature
interfacial vapor temperature
plate temperature
measured time-dependent-liquid-phase temperature
interfacial liquid temperature data point
specific volume of liquid at saturation
specific volume of liquid
specific volume of vapor
Lennard-Jones potential
quantum state transition matrix
compressibility factor
4
Table S4: Continued from Table S3. Nomenclature: list of symbols.
Greek symbol
αm
αs
αt
γ
LV
γ
Γ
δLJ
∆T
∆TILV
∆TILV ∗
∆sLV
∆sLV
ct
∆sLV
ph
∆sLV
∆T
∆sLV
ω`
εw
ζ
η
θ`
θw
µL
µV
σ
σ1 , σ2 , σ3
σc
σc∗
σc
σe
σe∗
T L (t)
ω
ω`
Definition
(mass) accommodation coefficient
sticking coefficient
thermal accommodation coefficient
scaling factor for the condensation coefficient
liquid-vapor surface tension
distance between molecules
molecular diameter
difference between plate temperatures
interfacial temperature discontinuity
interfacial temperature discontinuity from the TED-SRT relation
entropy change from an evaporating molecule
continuum contributions to entropy change
phonon contributions to entropy change
temperature discontinuity contributions to entropy change
vibrational frequency contributions to entropy change
depth of potential well
energy of emitted molecule
quantum state energy density
term in the SRT mass flux expression
characteristic temperature
angle of emission normal to the interface
chemical potential of the liquid phase
chemical potential of the vapor phase
coefficient assuming equality between σe and σc
calculated coefficients assuming equality between σe and σc
condensation coefficient
condensation coefficient in the TED-SRT relation
average condensation coefficient
evaporation coefficient
evaporation coefficient in the TED-SRT relation
calculated time-dependent-liquid-phase temperature
scaling factor for the condensation coefficient
internal molecular vibration frequency
5