Inertial phase separation in rotating self-gravitating media

Abstract

The centrifugal separation of foreign inclusions (particles) in a rotating spherical volume of a self-gravitating medium is considered in the hydrodynamic approximation. Using the full Lagrangian approach, the particle trajectories and radial concentration profiles are studied for a rigid-body velocity distribution in the carrier phase. The regimes of continuum and free-molecular flow around the particles are considered. The cases of a “heavy” (with density greater than that of the carrier phase and traveling toward the center) and a “light-weight” (traveling toward the periphery) admixture are investigated. Analytical and numerical solutions corresponding to steady-state spherically symmetric boundary conditions for the dispersed phase are found. It is shown that the presence of rotation may result in a significant angular anisotropy of the radial particle concentration distributions and, in particular, in the formation of ring-shaped accumulation zones of “heavy” inclusions in the equatorial plane. The solutions obtained can be used to explain the mechanisms of onset of density nonuniformities in planet cores, the formation of planetary systems from gas-particle clouds, and the behavior of aerosol particles in atmospheric vortices.