Reduced discrete population balance model for precipitation of barium sulfate nanoparticles in non-ionic microemulsions

Nanoparticle precipitation in microemulsions: Population balance model and identification of bivariate droplet exchange kernel

“…Case I is an approach with a constant value for all mother droplet combinations, where the amount of reactants and the solubility are not taken into account. Such an approach has been used by Niemann and Sundmacher [9] for a low-dimensional 1d model where the reactant distribution was assumed to be in equilibrium (f redist = 1).…”

“…A microemulsion system can be reasonably balanced by a population balance with three internal coordinates, namely the amounts of the two reactants (N A and N B ) and the number of molecules in solid state (N P ) [9]. The reference droplet number distribution is then defined by F ref (N A , N B , N P , t).…”

“…In most works N crit was always chosen as a fixed parameter for each droplet class with no relation to the thermodynamic parameters of the system. In the work of Niemann and Sundmacher [9] the influence of N crit on the precipitation dynamics is analyzed in detail by the application of the following microemulsion-specific modified Gibbs-Thomson relation:…”

“…Typical values for the microemulsion process found in literature are ranging between 2 (Jain and Mehra [35]) and 8 (Kumar et al [36]), but for bulk precipitation values above 10 can be found (Kashchiev and van Rosmalen [37]). A general derivation of N crit from the Gibbs-Thomson relation was done by Niemann and Sundmacher [9] for microemulsion precipitation. In most works N crit was always chosen as a fixed parameter for each droplet class with no relation to the thermodynamic parameters of the system.…”

“…In previous experimental [3][4][5] and theoretical works [6][7][8][9] the authors identified control parameters for a tailored nanoparticle design in microemulsion systems. In literature successful applications of this technology can be found for lab-scale production of metals [10], bimetals [11,12], metal oxides [13,14], borides [15], carbonates [16], halides [17], pharmaceuticals [18], semiconductors [19,20] and sulfates [21,22].…”