Modeling of aggregation of fractal dust clusters in a laminar protoplanetary disk

The evolutionary hydrodynamic model for the formation and growth of loose dust aggregates in the aerodisperse medium of a laminar disk, which was originally comprised of the gas and solid (sub)micrometer particles, is considered as applied to the problem of the formation of planetesimals in the Solar protoplanetary cloud. The model takes into account the fractal properties of dust clusters. It is shown that the clusters partly merge in the process of cluster-cluster coagulation, giving rise to the formation of large fractal aggregates that are the basic structure-forming elements of loose protoplanetesimals arising as a result of physicochemical and hydrodynamic processes similar to the processes of growth of the fractal clusters. Earlier, the modeling was conventionally performed in an “ordinary” continuous medium without considering the multifractional structure of the dust component of the protoplanetary cloud and the fractal nature of the dust clusters being formed during its evolution. Instead, we propose to consider a complex of loose dust aggregates as a special type of continuous medium, namely, the fractal medium for which there exist points and regions that are not filled with its particles. We suggest performing the hydrodynamic modeling of this medium, which has a noninteger mass dimensionality, in a fractional integral model (its differential form) that takes the fractality into account using fractional integrals whose order is determined by a fractal dimensionality of the disk medium.