The asymptotic solution of particle growth in the convective undercooled melt driven by a biaxial straining flow

A dynamical system of particle growth in the convective undercooled melt driven by a biaxial straining flow is modeled. A uniformly valid asymptotic solution for the interface evolution in particle growth is obtained by means of the multiple variable expansion method. The analytical solution as a function of both azimuth angle and polar angle shows that the interface shape of particle growth in the biaxial straining flow is significantly deformed by the biaxial straining flow. The biaxial straining flow results in higher local growth rate near the surface where the flow comes in and leads to lower local growth rate near the surface where the flow goes out. Due to the difference in local growth rate, an initially spherical particle will evolve into a prolate barrel-like shape in the biaxial straining flow.