A simple model for charged particle aggregation and polarization

In this paper we introduce a charged particle diffusion based aggregation model, which exemplifies an aggregation process affected by the particles’ ”charge”. Equal concentrations of two types (positive and negative) of randomly distributed charged particles are allowed to perform random walks and to aggregate with a given sticking probability. This process leads to the formation of a maximal cluster – called ”cloud” – the mass of which, as well as net ”charge” and electric dipole moment, increase with time, over a wide range of parameters. Through this simple field-free model, we find that the net ”charge” of the maximal cluster, of the overall neutral system, increases with the square root of its (the cloud’s) mass, while the electric dipole moment increases quasi-linearly and in fact super-linearly. Furthermore, the dependence of the electric dipole on the mass is determined by the fractal dimension of the formed maximal cluster (cloud). Thus, we show that an internal electric field, with a field-strength that increases with cloud size, can be spontaneously generated by a simple random-walk/sticking process, completely devoid of any kind of external fields. Potential implications on ”real life” clouds are discussed, i.e., the electric dipole moment based possibility of having atmospheric intra-cloud lightning discharges, and the net electric charge based possibility of having extra-cloud lightning discharges (cloud-to-cloud and cloud-to-ground), all in the absence of gravitational or other external fields or forces. Potential applications to other kinds of clouds and to biology are also discussed.