Within the framework of the problem of planetesimals formation in the solar preplanetary cloud, a hydrodynamic model of formation and growth of dust fractal aggregates in the aerodisperse medium of the laminar protoplanetary disc is developed. It is shown how in the process of cluster-cluster coagulation the solid dust particles of (sub)micron sizes coalesce with the formation of enlarged fractal aggregates, which are the main structure-forming element of planetesimals in the disc. In contrast to a number of existing studies, when modelling was carried out in the framework of an ‘ordinary’ continuous medium and when the multidispersity of the dust component, as well as the fractality of the formed friable dust clusters, it is proposed to consider the aerodisperse medium of the disk as a special type of fractal medium, in which there exist spatial regions not filled with particles. Since the kinetics of the processes of fractal bodies enlargement essentially depends on a particular type of coagulation nuclei, a rather general method of their approximation is proposed in the paper, which allows us to obtain simplified expressions for them in the case of laminar motion of the disc medium. We propose a qualitative solution of the Smoluchowski integro-differential equation by means of approximate methods for obtaining the central moments of the distribution function for a fractal disc system and the subsequent use of Pearson curves parameters. The obtained results provide a new approach in solving the key problem of stellar-planetary cosmogony related to the explanation of the process of growth of interstellar dust clusters to large planetesimals.

preplanetary discs, hydrodynamics of fractal media, Smoluchowski equation, coagulation processes

Mathematical modelling in actual problems of science and technics