LAUSR

Abstract A mathematical model for the liquid-phase synthesis of spherical nanoparticles in continuous flow micro- and milli-reactors was developed, accounting for residence time distributions (RTD). These distributions were derived for the reactants and the particles involved in the synthesis. The kinetic parameters needed to describe the reactions were calculated from experimental data available in the literature from batch reactors, with the aid of population balance modelling. They were subsequently used, without further modification, to simulate the synthesis in flow reactors via population balance modelling, averaging the nanoparticle properties at the reactor outlet using the reactor RTDs. The model was employed to describe the synthesis of silica nanoparticles as a case study, and validated against flow reactor results from the literature. The results demonstrate direct RTD effects and indirect diffusion-induced effects on the evolution of the particle size distribution during the flow synthesis. The former are created by the inherent widening of the RTDs, due to the different residence time experienced by each fluid element, leading to a broadening of the particle size distribution. The latter are induced by the difference in diffusivity between nanoparticles and liquid reactants, which leads to different dispersion processes in the reactor for the different components of the reaction mixture. These effects appear as the major cause of particle size distribution difference between (single phase) flow and batch syntheses.