On the motion of a spherical cavity in a melt

Abstract

Gas inclusions significantly influence the quality of solidifying melts. Dissolved gases in liquid metals, due to diffusion and chemical reactions, contribute to the formation and growth of new inclusions. The mathematical problem of the dynamic behavior of a spherical cavity is solved using the Navier‑Stokes equation, treating the melt as a viscous incompressible fluid. An expression for the change in radius of a spherical cavity under Newtonian behavior of the melts is obtained.