Here, the growth and detailed structure of particles undergoing agglomeration are investigated from the free molecular to the continuum regime by discrete element modelling (DEM). Particles coagulating in the free molecular regime follow ballistic trajectories described by an event-driven method, whereas in the near-continuum (gas-slip) and continuum regimes, Langevin dynamics describe their diffusive motion. Agglomerates containing about 10â30 primary particles, on the average, attain their asymptotic fractal dimension, Df, of 1.91 or 1.78 by ballistic or diffusion-limited clusterâcluster agglomeration, corresponding to coagulation in the free molecular or continuum regimes, respectively. A correlation is proposed for the asymptotic evolution of agglomerate Df as a function of the average number of constituent primary particles, np that can be readily used in process design for synthesis of nanomaterials or in environmental models for ambient aerosols (e.g. air pollution and climate forcing).
Agglomerates exhibit considerably broader self-preserving size distribution (SPSD) by coagulation than spherical particles: the number-based geometric standard deviations of the SPSD agglomerate radius of gyration in the free molecular and continuum regimes are 2.27 and 1.95, respectively, compared to â¼1.45 for spheres. In the transition regime, agglomerates exhibit a quasi-SPSD whose geometric standard deviation passes through a minimum at Knudsen number Kn â 0.2. In contrast, the asymptotic Df shifts linearly from 1.91 in the free molecular regime to 1.78 in the continuum regime. Population balance models using the radius of gyration as collision radius underestimate (up to about 80%) the small tail of the SPSD and slightly overpredict the overall agglomerate coagulation rate, as they do not account for cluster interpenetration during coagulation. In the continuum regime, when a recently developed agglomeration rate is used in population balance equations, the resulting SPSD is in excellent agreement with that obtained by DEM.