Brownian coagulation of a bi-modal distribution of both spherical and fractal aerosols

In this article, we describe the development of the microphysical equations to treat the interaction of two populations of aerosols, with different geometrical structures, written with moment of distributions, interacting through Brownian coagulation. This problem was solved specifically for the case of Titan, the larger satellite of Saturn, where small aerosols have a spherical shape, large aerosols have a fractal aggregated structure and where aerosols bear an electric charge. The two populations interact in the mesosphere. The fractal structure of the large aerosols also has a consequence on the shape of the size distribution and on the laws of the microphysics that must be accounted a priori in the method. The case of Titan is probably one of the most complex and, in this work, we have written the set of equations in the most general way so they can be used for any other cases. Once developed, we finally compare the results yielded by our new model with the results obtained with the classical model based on a description in bins.