The asymptotic solution for the particle growth in the undercooled melt driven by a straining flow

Abstract

The moving boundary problem of particle growth in the convective undercooled melt driven by a straining flow is studied by means of the multiple variable expansion method. The resulting uniformly valid asymptotic solution shows the growth behavior of a spherical particle in the straining flow. The straining flow enhances the energy transfer rate and results in higher local growth velocity of the particle near the interface where the flow is incoming, whereas near the interface where the flow is outgoing, the straining flow decreases the energy transfer rate and results in lower local growth velocity of the particle. Because of the difference in local interface growth velocities of the particle, the interface of the particle opposite to the incoming straining flow protrudes outward more significantly than that facing the outgoing straining flow, an initially spherical particle in the undercooled melt with the straining flow evolves to be gravely distorted into different shapes.