中文摘要：

研究了均匀形核的金属液滴凝固过程,应用渐近分析法求得金属液滴内晶核生长数学模型的渐近解,分析了表面张力、界面动力学参数、初始晶核尺寸和过冷度对晶核界面生长速度、晶核半径以及液滴凝固时间的影响.在一定的过冷条件下,表面张力和界面动力学参数显著减缓了晶核界面生长速度.在凝固开始的很短时间内晶核界面生长速度迅速上升,当速度上升到最大值后,随着晶核半径的增大,界面生长速度逐渐减慢,表面张力和界面动力学参数对晶核生长速度的作用也逐渐减小.过冷度越大,液滴凝固时间越短.经过在开始的瞬变凝固阶段之后,温度场从设定的初始分布迅速地调整为由过冷度、表面张力、界面动力学参数等所确定的特定温度分布.

英文摘要：

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.