Impact of initial charge distributions on the kinetics of charged particle coagulation

We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation, we examine how different charge distributions and net system charge affect cluster growth dynamics. Electrostatic interactions are incorporated directly into the classical Brownian collision kernel, yielding charge-dependent modifications of the collision rates that may either enhance or suppress aggregation depending on the signs and magnitudes of the interacting charges. Our simulations reveal distinct regimes of growth: at intermediate times, charge heterogeneity accelerates or delays aggregation depending on the initial underlying charge distribution, while at long times the system tends toward quasi--stationary states whose properties depend on the net charge. Comparisons between Gaussian and Cauchy--Lorentz initial charge statistics highlight the role of heavy-tailed distributions in promoting faster cluster growth. These findings contribute to a unified understanding of coagulation kinetics in charged particulate systems, with potential implications for aerosol and astrophysical coagulation processes, volcanic ash aggregation, and clustering in industrial fluidized granular beds.