Peculiarities of fully Lagrangian approach for modeling dilute two‐phase mixtures with close phase densities

The methods of calculating dilute two‐phase flows with a collisionless dispersed phase (particles, drops, or bubbles) fall essentially in two categories: Eulerian and Lagrangian. A limitation of the Eulerian approach is the exclusion of flows with crossing particle trajectories. An effective Lagrangian method for calculating flows with the formation of caustics in particle‐trajectory patterns was proposed earlier (see, for example [1]) for the case when the interphase force contains only “local” interaction terms (aerodynamic drag, Saffman force, etc.). In this paper, the fully Lagrangian approach is generalized to the case of similar phase densities, when in the interphase momentum exchange, in addition to the Stokes drag, the differential terms (virtual‐mass and Archemedes forces) and the integral term (Basset force) should be taken into account. The use of the method is illustrated by the calculation of redistributing particles or bubbles in a rotating spherical volume of a self‐gravitating viscous fluid (a model of development of density nonuniformities in the Earth core). A substantial anisotropy in radial particle concentration distributions and the possibility of forming local particle accumulation zones in the equatorial plane is indicated in the calculations.