A Monodisperse Population Balance Model for Nanoparticle Agglomeration in the Transition Regime

Nanoparticle agglomeration in the transition regime (e.g. at high pressures or low temperatures) is commonly simulated by population balance models for volume-equivalent spheres or agglomerates with a constant fractal-like structure. However, neglecting the fractal-like morphology of agglomerates or their evolving structure during coagulation results in an underestimation or overestimation of the mean mobility diameter, dm, by up to 93 or 49%, repectively. Here, a monodisperse population balance model (MPBM) is interfaced with robust relations derived by mesoscale discrete element modeling (DEM) that account for the realistic agglomerate structure and size distribution during coagulation in the transition regime. For example, the DEM-derived collision frequency, β, for polydisperse agglomerates is 82 ± 35% larger than that of monodisperse ones and in excellent agreement with measurements of flame-made TiO₂ nanoparticles. Therefore, the number density, NAg, mean, dm, and volume-equivalent diameter, dv, estimated here by coupling the MPBM with this β and power laws for the evolving agglomerate morphology are on par with those obtained by DEM during the coagulation of monodisperse and polydisperse primary particles at pressures between 1 and 5 bar. Most importantly, the MPBM-derived NAg, dm, and dv are in excellent agreement with the data for soot coagulation during low temperature sampling. As a result, the computationally affordable MPBM derived here accounting for the realistic nanoparticle agglomerate structure can be readily interfaced with computational fluid dynamics in order to accurately simulate nanoparticle agglomeration at high pressures or low temperatures that are present in engines or during sampling and atmospheric aging.