288
M. Michaud et al.
already gives a reasonable estimate on the precipitation kinetics. As expected for
a mixing-controlled system, in the beginning of the formation process, the mean
particle size differs in the two mixing zones. Growth in the iron-rich zone is faster
than in the alkaline zone. In both zones, a rapid increase in nucleation after a short
time causes an intermediate decrease of the mean particle sizes. However, the final
sizes in both zones are equal for each solubility product as both zones exchange
particles and therefore converge after a sufficiently long enough mixing time. The
calculated mean final particle size is situated in the low μm range and lies in a similar
regime as reported in literature [3].
In both of the discussed cases, mixing strongly influences the transient particle
formation dynamics and thus the final particle properties. Accordingly, mixing must
be carefully considered in particular with respect to up-scaling. Recently, we found
self-similar profiles of supersaturation and of the resulting PSDs for the case of
precipitation of drug molecules in a T-mixer [7]. These promising results provide
strong hints that unifying scale-up principles can be derived, at least during flow
synthesis of nanoparticles.
7.2 Systems with Complex Phase Composition: gerhardtite
(Cu 2 NO 3 (OH) 3 )
As the next example, we consider the simulation of a multicomponent system. Literature data for solubility products are available and are in very good agreement to the
simulated values [25–28]. The alkaline precipitation of copper salts leads to multiple solids of different chemical composition. The addition of zinc sources leads to
copper-zinc salts, which are important precursors for Cu/ZnO catalysts for methanol
synthesis [5]. The solids that form during this precipitation include copper hydroxide (Cu(OH) 2 ), zinc hydroxide (Zn(OH) 2 ), malachite (Cu 2 CO 3 (OH) 2 ), gerhardtite
(Cu 2 NO 3 (OH) 3 ) and the mixed phase rosasite (Cu 1.4 Zn 0.6 CO 3 (OH) 2 ). The complex
chemical network for precipitating the desired compound rosasite (see Table 2) is
implemented into the hydrochemistry model as a stoichiometric matrix α (Eq. 61)
listing all of the reactive species of the system.
The resulting stoichiometry matrix implemented into the hydrochemistry model
can be written as:
M. Michaud et al.
already gives a reasonable estimate on the precipitation kinetics. As expected for
a mixing-controlled system, in the beginning of the formation process, the mean
particle size differs in the two mixing zones. Growth in the iron-rich zone is faster
than in the alkaline zone. In both zones, a rapid increase in nucleation after a short
time causes an intermediate decrease of the mean particle sizes. However, the final
sizes in both zones are equal for each solubility product as both zones exchange
particles and therefore converge after a sufficiently long enough mixing time. The
calculated mean final particle size is situated in the low μm range and lies in a similar
regime as reported in literature [3].
In both of the discussed cases, mixing strongly influences the transient particle
formation dynamics and thus the final particle properties. Accordingly, mixing must
be carefully considered in particular with respect to up-scaling. Recently, we found
self-similar profiles of supersaturation and of the resulting PSDs for the case of
precipitation of drug molecules in a T-mixer [7]. These promising results provide
strong hints that unifying scale-up principles can be derived, at least during flow
synthesis of nanoparticles.
7.2 Systems with Complex Phase Composition: gerhardtite
(Cu 2 NO 3 (OH) 3 )
As the next example, we consider the simulation of a multicomponent system. Literature data for solubility products are available and are in very good agreement to the
simulated values [25–28]. The alkaline precipitation of copper salts leads to multiple solids of different chemical composition. The addition of zinc sources leads to
copper-zinc salts, which are important precursors for Cu/ZnO catalysts for methanol
synthesis [5]. The solids that form during this precipitation include copper hydroxide (Cu(OH) 2 ), zinc hydroxide (Zn(OH) 2 ), malachite (Cu 2 CO 3 (OH) 2 ), gerhardtite
(Cu 2 NO 3 (OH) 3 ) and the mixed phase rosasite (Cu 1.4 Zn 0.6 CO 3 (OH) 2 ). The complex
chemical network for precipitating the desired compound rosasite (see Table 2) is
implemented into the hydrochemistry model as a stoichiometric matrix α (Eq. 61)
listing all of the reactive species of the system.
The resulting stoichiometry matrix implemented into the hydrochemistry model
can be written as: