Continuous species transport and population balance models for first drying stage of nanosuspension droplets

The present contribution reports on comparison and verification of two different modelling approaches to intra-droplet mass transfer for nanosuspension droplet drying in the constant-rate period. The first approach is continuous species transport (CST) modelling coupling external gas-droplet heat and mass transfer to a species transport equation of intra-droplet diffusion of nanoparticles. The second approach is a population balance (PB) model with similar description of external heat and mass transfer from gas to droplet. In contrast to the CST model, the PB approach deals with dispersed particles as a population and accounts for the change of nanoparticle distribution by possible aggregation. Both CST and PB models have been successively validated using published and new experimental drying data on single silica nanosuspension droplet. A parametric study revealed insignificant differences in the predicted temporal evolutions of solid volume fraction profiles and values of locking point between the two models when aggregation was “turned off” in the PB model. These small differences can be explained by different mathematical formulations and numerical implementations of the two modelling approaches. A larger contrast between the CST and PB models is the predicted duration of the first drying stage, which has been found to be longer in the case of CST approach. Such divergence is explained by the absence of a shell shrinkage period in the current PB formulation. When applied with aggregation, the PB model can predict the experimentally observed decrease in the diffusion coefficient after the gelation point.

► Two modelling approaches for nanosuspension droplet drying are compared. ► Continuous species transport approach uses diffusion equation for nanoparticles. ► Alternatively, population balance model deals with nanoparticles as a population. ► Both models were successively validated using published and new experimental data. ► Without aggregation, differences in the two model parametric predictions are minor.