8 Flowsheet Simulation of Integrated Precipitation Processes
271
β
Sum of all sources S i [(m/s)
k+l ]
β Brown
Brownian aggregation kernel [m
3 /s]
β Turb
Turbulent aggregation kernel [m
3 /s]
γ
Interfacial energy [N/m]
γ i
Activity coefficient of species i [–]
ε
Specific power input [W/kg]
ε 0
Vacuum permittivity [A*s/(V*m)]
ε r
Relative permittivity [–]
ζ
Target functional of the Nelder-Mead optimization [–]
η
Dynamic viscosity [Pa*s]
θ
Contact angle for heterogeneous nucleation [–]
Heaviside function [–]
κ
Debye length [1/m]
μ ij
Stoichiometric coefficient of component i in species j [–]
ν
Kinematic viscosity [m
2 /s]
ν ij
Stoichiometric coefficient of species j in reaction i [–]
ξ N,α
Node position of property N of node α [m]
π
Archimedes constant [–]
ρ
Solid density [kg/m
3 ]
σ
Standard deviation of particle size distribution [m]
σ i,p
Stoichiometric coefficient of species i in solid phase p [–]
Solution of implicit equation [–]
i
Surface potential of face i [C/m
2 ]
ω N,α
Node weight of property N of node α [–]
1 Introduction
Precipitation from solution leads to a wide range of solid particles of vastly varying
sizes ranging from a few nanometers to hundreds of microns, different shapes such
as spheres, platelets or cylinders and different composition of inorganic or organic
compounds.
Typical examples considered in this report are the binary compounds ZnO quantum dots (QDs) for opto-electronic applications [1, 2]. BaSO 4 used as white pigment,
and the more complex systems Goethite (FeOOH [3, 4]) as yellow pigment and
Gerhardtite (Cu 2 (NO 3 )(OH) 3 ) as a side product for methanol catalyst preparation
(Cu/ZnO [4, 5]). The design of precipitation processes is a highly complex field of
intense research due to the various and complex underlying phenomena. In general,
the sequence of mixing, reaction, nucleation, growth, ripening and agglomeration
must be considered. Any predictive tool for precipitation must be able to describe
the dynamics of the transient solid formation processes. This includes a sufficient
resolution of fluid dynamics in the reactor coupled to population balance equations
(PBE) for the evolution of solid phases. Today, the full resolution of fluid flow by
271
β
Sum of all sources S i [(m/s)
k+l ]
β Brown
Brownian aggregation kernel [m
3 /s]
β Turb
Turbulent aggregation kernel [m
3 /s]
γ
Interfacial energy [N/m]
γ i
Activity coefficient of species i [–]
ε
Specific power input [W/kg]
ε 0
Vacuum permittivity [A*s/(V*m)]
ε r
Relative permittivity [–]
ζ
Target functional of the Nelder-Mead optimization [–]
η
Dynamic viscosity [Pa*s]
θ
Contact angle for heterogeneous nucleation [–]
Heaviside function [–]
κ
Debye length [1/m]
μ ij
Stoichiometric coefficient of component i in species j [–]
ν
Kinematic viscosity [m
2 /s]
ν ij
Stoichiometric coefficient of species j in reaction i [–]
ξ N,α
Node position of property N of node α [m]
π
Archimedes constant [–]
ρ
Solid density [kg/m
3 ]
σ
Standard deviation of particle size distribution [m]
σ i,p
Stoichiometric coefficient of species i in solid phase p [–]
Solution of implicit equation [–]
i
Surface potential of face i [C/m
2 ]
ω N,α
Node weight of property N of node α [–]
1 Introduction
Precipitation from solution leads to a wide range of solid particles of vastly varying
sizes ranging from a few nanometers to hundreds of microns, different shapes such
as spheres, platelets or cylinders and different composition of inorganic or organic
compounds.
Typical examples considered in this report are the binary compounds ZnO quantum dots (QDs) for opto-electronic applications [1, 2]. BaSO 4 used as white pigment,
and the more complex systems Goethite (FeOOH [3, 4]) as yellow pigment and
Gerhardtite (Cu 2 (NO 3 )(OH) 3 ) as a side product for methanol catalyst preparation
(Cu/ZnO [4, 5]). The design of precipitation processes is a highly complex field of
intense research due to the various and complex underlying phenomena. In general,
the sequence of mixing, reaction, nucleation, growth, ripening and agglomeration
must be considered. Any predictive tool for precipitation must be able to describe
the dynamics of the transient solid formation processes. This includes a sufficient
resolution of fluid dynamics in the reactor coupled to population balance equations
(PBE) for the evolution of solid phases. Today, the full resolution of fluid flow by