The Permeable Particle Model to Describe the Collisional Evolution of Dust Clusters in Protoplanetary Gas–Dust Disks

The development of the permeable particle method for the dust cluster evolution problems is proposed. The key element that describes the rheological properties of porous dust clusters and affects the results of their collisional evolution is the coefficient of restitution. The continuous and discontinuous formulations of the relation for the coefficient of restitution during collisions are given. A parametric study of the dependence of the coefficient of restitution on the cluster characteristics and the relative collision energy has been carried out. Clusters with a high fractal dimension are shown to have a distinct bounce threshold during collisions. The evolution of a system of 20 000 clusters with various electric charges has been simulated numerically. It is shown that in the absence of other factors, electrostatic interactions can lead to a rapid growth of cluster agglomerates. However, the weakness of individual mechanical bonds between clusters makes such agglomerates unstable to destruction not only due to the collisions, but also due to the increasing repulsive force of similarly charged clusters in the agglomerate. It is shown that when the external influence of the gaseous medium is taken into account, spatially extended structures are formed in the cluster system. The velocity field of a turbulent vortex is considered as an external influence on a system of electrically charged clusters. It is shown that in this case, a filamentary structure is formed on the vortex axis, with its central part being occupied by clusters with a low fractal dimension and the densest clusters with a high fractal dimension being concentrated near its surface.