About regular expansion of a two-phase ball

Abstract

The work is devoted to the research of an expansion into a vacuum of a ball, which is filled with a two-phase fluid. In assumptions that the dynamics passes in a regular mode, the velocities of the phases are linear functions by space coordinate and the first phase spreads into the void faster than the second phase there is obtained a solution of equations of two-phase fluid dynamics, which describes an expansion of a ball into a vacuum. This solution generalizes the known Sedov solution, which determines an expansion of a gas cloud into a vacuum, to the case of a ball filled with a gas suspension. In the last part of the work there are derived asymptotic formulas determining a relationship between the velocities of the phases and the radii of two balls.