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M. Michaud et al.
B Sec
Secondary nucleation rate [1/(m
3 *s)]
B Het
Heterogeneous nucleation rate [1/(m
3 *s)]
c i
Concentration of species i [mol/l]
c
∞
L
Bulk concentration [mol/l]
D p
Diffusion coefficient of phase p [m
2 /s]
E
Engulfment factor [1/s]
f
Particle size distribution density [1/m]
f A,i
Shape factor of phase i [–]
g
Residual describing the complex equilibria [–]
G i
Diffusion limited growth rate in direction i [m/s]
H A
Hamaker constant [J]
He
Adsorption constant [–]
h i,m
Net particle formation rate of solid phase i in zone m [1/(m*s)]
J
Jacobian of the residual describing the complex equilibra [–]
I
Ion activity product of all solid phases [mol
x /l
x ]
k
Order of moment [–]
k B
Boltzmann constant [J/K]
l
Oder of mixed moment [–]
k i
Equilibrium constant of reaction i [mol
x /l
x ]
K SP,P
Solubility product of phase p [mol
x /l
x ]
M
Mixing matrix [–]
M i
Molar mass of species i [kg/mol]
N
Total number of nodes for DQMOM [–]
N s
Size of the property vector for node positions [–]
n i,m
Particle number density of phase i in zone m [1/(m*s)]
n 0
Particle number at the beginning of the simulation [–]
o j
Logarithmic concentration of species j [–]
R
Ripening rate [m/s]
R s
Reaction stoichiometry matrix [–]
R i
Radius of interacting particle [m]
S p
Supersaturation of solid phase p [–]
S ξ
Source term for moment transformation [1/(m*s)]
Sh
Sherwood number [–]
T
Temperature [K]
U
Molar balance stoichiometry matrix [–]
u i
Mean velocity of internal variable [m/s]
V M
Molecular volume [m
3 /mol]
V Growth Volume growth during time step t [m
3 ]
w i
Weighting factor for the Nelder-Mead optimization [–]
W ij
Fuchs stability ratio [–]
W tot
Total interaction potential [J]
x
Particle diameter [m]
x crit
Critical particle diameter [m]
Y
Normalized center-to-center distance of interacting particles [–]
z i
Ion charge of species i [–]
M. Michaud et al.
B Sec
Secondary nucleation rate [1/(m
3 *s)]
B Het
Heterogeneous nucleation rate [1/(m
3 *s)]
c i
Concentration of species i [mol/l]
c
∞
L
Bulk concentration [mol/l]
D p
Diffusion coefficient of phase p [m
2 /s]
E
Engulfment factor [1/s]
f
Particle size distribution density [1/m]
f A,i
Shape factor of phase i [–]
g
Residual describing the complex equilibria [–]
G i
Diffusion limited growth rate in direction i [m/s]
H A
Hamaker constant [J]
He
Adsorption constant [–]
h i,m
Net particle formation rate of solid phase i in zone m [1/(m*s)]
J
Jacobian of the residual describing the complex equilibra [–]
I
Ion activity product of all solid phases [mol
x /l
x ]
k
Order of moment [–]
k B
Boltzmann constant [J/K]
l
Oder of mixed moment [–]
k i
Equilibrium constant of reaction i [mol
x /l
x ]
K SP,P
Solubility product of phase p [mol
x /l
x ]
M
Mixing matrix [–]
M i
Molar mass of species i [kg/mol]
N
Total number of nodes for DQMOM [–]
N s
Size of the property vector for node positions [–]
n i,m
Particle number density of phase i in zone m [1/(m*s)]
n 0
Particle number at the beginning of the simulation [–]
o j
Logarithmic concentration of species j [–]
R
Ripening rate [m/s]
R s
Reaction stoichiometry matrix [–]
R i
Radius of interacting particle [m]
S p
Supersaturation of solid phase p [–]
S ξ
Source term for moment transformation [1/(m*s)]
Sh
Sherwood number [–]
T
Temperature [K]
U
Molar balance stoichiometry matrix [–]
u i
Mean velocity of internal variable [m/s]
V M
Molecular volume [m
3 /mol]
V Growth Volume growth during time step t [m
3 ]
w i
Weighting factor for the Nelder-Mead optimization [–]
W ij
Fuchs stability ratio [–]
W tot
Total interaction potential [J]
x
Particle diameter [m]
x crit
Critical particle diameter [m]
Y
Normalized center-to-center distance of interacting particles [–]
z i
Ion charge of species i [–]