Solidification of metallic droplets based on homogeneous nucleation

The solidification of metallic droplets based on homogeneous nucleation is studied by a mathematical model of nucleus growth in metallic droplets. An asymptotic solution to the model is obtained by the asymptotic analysis method. The effects of surface tension, interface kinetic parameter, initial nucleus size, and undercooling on the growth rate, radius, and solidification time of the nucleus are analyzed on the basis of the asymptotic solution. It is found that surface tension and interface kinetics parameter significantly decrease the growth rate of the nucleus under a certain undercooling condition. The growth rate of the nucleus rapidly rises in the initial short period of solidification. After the growth rate of the nucleus reaches its maximum~ it gradually descends with the increase of nucleus radius. In the meantime, the effects of surface tension and interface kinetic parameter on the growth rate of the nucleus decline gradually. With the increase of undercooling, the solidification time of the droplet decreases. After transient solidification within the initial short period, the temperature distribution in the droplet is rapidly modified from some initial distribution to a certain temperature distribution determined by undercooling, surface tension, interface kinetic parameter, etc.