524
G. Kotalczyk and F. E. Kruis
Fig. 2 The concept of ‘stochastic resolution’ can be used to describe the coagulation-scheme
developed Zhao et al. [22]. Only the choice for s f = W min leads to the correct description of the
general rule presented in the ‘simulation entries’ line
The coagulation rate β
(w) for this coagulation-scheme can be derived from the
population balance equation:
dn(v)
dt
=
1
2
v
∫
0
β
v − v
, v
n
v − v
n
v
dv
− n(v)
∞
∫
0
β
v, v
n
v
dv
(4)
Instead of the ‘original’ concentrations n(v), the concentrations of the MCsystems n
(MC)
(v) =
n(v)
s f
are being considered. The multiplication of the PBE with
the factor
1
s f
=
1
W min
leads to the following modified coagulation rate of the MCparticles: β
(MC)
= W min · β. Hence there is one MC-particle of the W min -species and
W max
W min
MC-particles of the W max -species, the overall rate for the coagulation between
one W min -MC-particle and one of the W max -MC-particles is:
β
(w)
=
W max
W min
· β
(MC)
= W max · β
(5)
G. Kotalczyk and F. E. Kruis
Fig. 2 The concept of ‘stochastic resolution’ can be used to describe the coagulation-scheme
developed Zhao et al. [22]. Only the choice for s f = W min leads to the correct description of the
general rule presented in the ‘simulation entries’ line
The coagulation rate β
(w) for this coagulation-scheme can be derived from the
population balance equation:
dn(v)
dt
=
1
2
v
∫
0
β
v − v
, v
n
v − v
n
v
dv
− n(v)
∞
∫
0
β
v, v
n
v
dv
(4)
Instead of the ‘original’ concentrations n(v), the concentrations of the MCsystems n
(MC)
(v) =
n(v)
s f
are being considered. The multiplication of the PBE with
the factor
1
s f
=
1
W min
leads to the following modified coagulation rate of the MCparticles: β
(MC)
= W min · β. Hence there is one MC-particle of the W min -species and
W max
W min
MC-particles of the W max -species, the overall rate for the coagulation between
one W min -MC-particle and one of the W max -MC-particles is:
β
(w)
=
W max
W min
· β
(MC)
= W max · β
(5)