Verification of size-resolved population balance modeling for engineered nanoparticles under high concentration

Concerns have increased regarding the efficacy of population balance modeling (PBM) for determining the size-resolved behavior of engineered nanoparticles (ENPs) in chemical reactors, flames and workplaces. For the first time, we used a well-designed experiment to verify the feasibility of PBM and crucial factors affecting the accuracy of this method when size-resolved behavior was primarily concerned. The dynamic processes were designed to maximally represent high concentration involving aggregate production, deposition, coagulation, and transport. A population balance equation corresponding to the physical changes in an experiment was established and was further solved using the highly accurate moving sectional method. We verified four representative aggregate collision rate functions, namely the modified Fuchs collision rate function, Dahneke's collision function, harmonic mean collision function, and aggregate function newly developed by Thajudeen et al. (Aerosol Sci. Technol. 46 (2012) 1174-1186). The PBM implemented using the Thajudeen et al.'s aggregate function revealed highest agreement between the simulation and measurement. We observed both fractal dimension and primary particle diameter have apparent effects on the accuracy of PBM, indicating that both are key parameters in the implementation of PBM, whereas the pre-exponential factor only slightly affects the accuracy of PBM. The PBM with constant primary particle size, fractal dimension, and pre-exponential factor was finally verified as a reliable method for studying size-resolved evolution of ENPs over time.