Population Balance Modelling and CFD analysis in a Multi-scale Approach for Flash Nano-precipitation*

Polymer nanoparticles (NP) formation is investigated by a multi-scale modelling approach focusing on poly-$\varepsilon$-caprolactone (PCL) self-assembly in acetone-water mixtures via flash nano-precipitation (FNP). The control of the final NP size at the outlet of the mixer and the evolution of the particle size distribution, cluster mass distribution (CMD), are guaranteed by a suitable population balance model (PBM) closed with the quadrature method of moments (QMOM). The CMD moments are transported and coupled with computational fluid dynamics (CFD). NP size is characterised in terms of mean radius of gyration, expressed through Flory theory. Molecules are treated as “building blocks” undergoing aggregation once the solubility limit is exceeded. The rate at which two NP collide and aggregate is expressed by the aggregation kernels, built upon molecular dynamics simulations. Turbulent fluctuations on NP formation are taken into account thanks to the direct quadrature method of moments coupled with the interaction-and-exchange-with-the-mean (DQMOM-IEM) method. Favre-averaged continuity and Navier-Stokes equations are implemented, in order to consider the density fluctuations of the system. The model is validated against experiments, showing an excellent agreement.