15 Compartmental Population Balances by Means of Monte Carlo Methods
531
Table 2 Material constants
for Ag at a temperature of
1300 K
Symbol
Description
Value
Source
m 1
Atomic mass
1.792 × 10 −25 kg
[37]
v M
Atomic volume
1.922 × 10 −29 m 3
[37]
p s
Vapor pressure
1.324 pa
[37]
σ
Surface tension
0.9024 J/m 2
[38]
with S =
N G k B T
p s
(13)
R
(gir)
N (N G ) = R
(cou)
N
· exp
⎛
⎝ (36 · π )
1
3 ·
σ · v
2
3
1
k B · T
⎞
⎠ ; R
(cls)
N (N G ) = R
(cou)
N
· S (14)
The influence of these different nucleation theories has been discussed for atmospheric simulation scenarios [27] and are briefly sketched for a metallic system
describing the nucleation of Ag vapor in the following. The material parameters in
Eqs. (10–14) assume values summarized in Table 2 at a temperature of T = 1300 K.
The simulation of a isothermal nucleation induced due to an initial supersaturation
of S 0 = 100 of Ag vapor and the presence of an initial (background) PSD with a mean
geometric diameter of 2 nm and a geometric standard deviation of 1.2 rendering a total
number-concentration of 10
16 m
−3 is used as an initial condition. The temperature
is kept constant to 1300 K during the course of the simulation.
The monomer concentration exhibits the fastest depletion rate for the Girshickbased nucleation rate, as is shown in Fig. 5a. This is due the highest nucleation rate
which is plotted in comparison with other nucleation theories in Fig. 5b. This leads in
turn to the highest particle concentrations for the Girshick-based nucleation theory
(see figure Fig. 5c). The nucleation theories show the most striking differences at the
early stages of the simulation, for longer simulation times, (i.e. t > 0.01 s), similar
Fig. 5 Isothermal Ag particle synthesis with initial PSD and supersaturation S 0 = 100. The
saturation surplus S − 1 (a), the corresponding nucleation rates (b) and the total particle numberconcentrations (c) are shown. The nucleation rates R
(cou)
N
(Courtney) R
(gir)
N
(Girshick) and R
(cls)
N
(Classic) are defined in Eqs. (13) and (14)
531
Table 2 Material constants
for Ag at a temperature of
1300 K
Symbol
Description
Value
Source
m 1
Atomic mass
1.792 × 10 −25 kg
[37]
v M
Atomic volume
1.922 × 10 −29 m 3
[37]
p s
Vapor pressure
1.324 pa
[37]
σ
Surface tension
0.9024 J/m 2
[38]
with S =
N G k B T
p s
(13)
R
(gir)
N (N G ) = R
(cou)
N
· exp
⎛
⎝ (36 · π )
1
3 ·
σ · v
2
3
1
k B · T
⎞
⎠ ; R
(cls)
N (N G ) = R
(cou)
N
· S (14)
The influence of these different nucleation theories has been discussed for atmospheric simulation scenarios [27] and are briefly sketched for a metallic system
describing the nucleation of Ag vapor in the following. The material parameters in
Eqs. (10–14) assume values summarized in Table 2 at a temperature of T = 1300 K.
The simulation of a isothermal nucleation induced due to an initial supersaturation
of S 0 = 100 of Ag vapor and the presence of an initial (background) PSD with a mean
geometric diameter of 2 nm and a geometric standard deviation of 1.2 rendering a total
number-concentration of 10
16 m
−3 is used as an initial condition. The temperature
is kept constant to 1300 K during the course of the simulation.
The monomer concentration exhibits the fastest depletion rate for the Girshickbased nucleation rate, as is shown in Fig. 5a. This is due the highest nucleation rate
which is plotted in comparison with other nucleation theories in Fig. 5b. This leads in
turn to the highest particle concentrations for the Girshick-based nucleation theory
(see figure Fig. 5c). The nucleation theories show the most striking differences at the
early stages of the simulation, for longer simulation times, (i.e. t > 0.01 s), similar
Fig. 5 Isothermal Ag particle synthesis with initial PSD and supersaturation S 0 = 100. The
saturation surplus S − 1 (a), the corresponding nucleation rates (b) and the total particle numberconcentrations (c) are shown. The nucleation rates R
(cou)
N
(Courtney) R
(gir)
N
(Girshick) and R
(cls)
N
(Classic) are defined in Eqs. (13) and (14)