2020/09/09 by Marina A. Ferreira, Ferreira, Marina A. · 2 citations
Earth and Planetary Sciences · Environmental Science · #Coagulation and Flocculation Studies #FOS: Physical sciences #Mathematical Physics (math-ph) #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.2009.04436
openalex publication_date 2020/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Binary coagulation is an important process in aerosol dynamics by which two particles merge to form a larger one. The distribution of particle sizes over time may be described by the so-called Smoluchowski's coagulation equation. This integrodifferential equation exhibits complex non-local behaviour that strongly depends on the coagulation rate considered. We first discuss well-posedness results for the Smoluchowski's equation for a large class of coagulation kernels as well as the existence and nonexistence of stationary solutions in the presence of a source of small particles. The existence result uses Schauder fixed point theorem, and the nonexistence result relies on a flux formulation of the problem and on power law estimates for the decay of stationary solutions with a constant flux. We then consider a more general setting. We consider that particles may be constituted by different chemicals, which leads to multi-component equations describing the distribution of particle compositions. We obtain explicit solutions in the simplest case where the coagulation kernel is constant by using a generating function. Using an approximation of the solution we observe that the mass localizes along a straight line in the size space for large times and large sizes.