An investigation of spherical micro/nanoparticle melting using asymptotic matchings in a weak formulation

In this paper, we investigate the speed of moving boundaries for melting micro/nanoparticles in the initial and final stages using asymptotic matchings in a weak formulation of the problem. We find that such a speed is initially proportional to the flux across the moving boundary, however a blowup occurs in a finite time when the surface tension is considered, both numerically and theoretically, by assuming linear relations between thermal conductivities and diffusivities, which paves the way to tackle the related two and higher phase change problems. Last but not least, we verify our theoretical outcomes using a quasi-stationary approximation approach.