Hydrodynamic Aspects of Modeling of the Mass Transfer and Coagulation Processes in Turbulent Accretion Disks

This paper considers, in the context of modeling the evolution of a protoplanetary cloud, the hydrodynamic aspects of the theory of concurrent processes of mass transfer and coagulation in a two-phase medium in the presence of shear turbulence in a differentially rotating gas–dust disk and of polydisperse solid particles suspended in a carrying flow of solid particles. The defining relations are derived for diffuse fluxes of particles of different sizes in the equations of turbulent diffusion in the gravitational field, which describe the convective transfer, turbulent mixing, and sedimentation of disperse dust grains onto the central plane of the disk, as well as their coagulation growth. A semiempirical method is developed for calculating the coefficients of turbulent viscosity and turbulent diffusion for particles of different kinds. This method takes into account the inverse effects of dust transfer on the turbulence evolution in the disk and the inertial differences between disperse solid particles. To solve rigorously the problem of the mutual influence of the turbulent mixing and coagulation kinetics in forming the gas–dust subdisk, the possible mechanisms of gravitational, turbulent, and electric coagulation in a protoplanetary disk are explored and the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particles' size distribution function is considered. This method takes into account the fact that this distribution belongs to a definite parametric class of distributions.