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

A discrete population balance model is formulated in order to analyze the precipitation process of barium sulfate nanoparticles taking place in the droplets of a water-in-oil microemulsion. The model accounts for the distribution of reactants over the droplet population in terms of discrete numbers of the reacting ionic species (Ba2+, SO42−), as well as for the nucleation and growth of solid particles in terms of discrete BaSO4-molecular units. The introduction of physically motivated assumptions leads to a considerable reduction of complexity of the population balance model. The kinetic parameters for nucleation and growth are estimated by fitting of simulated particle size distributions to recently published experimental data by Niemann et al. [B. Niemann, P. Veit, K. Sundmacher, Nanoparticle precipitation in reverse microemulsions: particle formation dynamics and tailoring of particle size distributions, Langmuir 24 (1), 2008, 4320–4328] and Adityawarman et al. [D. Adityawarman, A. Voigt, P. Veit, K. Sundmacher, Precipitation of BaSO4 nanoparticles in a non-ionic microemulsion: identification of suitable control parameters, Chem. Eng. Sci. 60 (12), 2005, 3373–3381]. The obtained parameter values support the conclusion that particle nucleation follows a heterogeneous mechanism and that the nanostructure of the microemulsion has a significant effect on the particle growth mechanism. The considered microemulsion-assisted precipitation process allows the generation of nanoparticle morphologies which are not attainable by classical bulk phase precipitation processes.