Rapid solidification of subcooled small metallic drops

Accurate rapidly and slowly varying analytical solutions are obtained for the problem of the rapid solidification by convection of subcooled small metallic drops. These solutions, which were suggested by the approximate results obtained by using a quasi-moving-boundary approach, are useful in estimating metallurgical parameters in rapid rate solidification technology. The rapidly varying regular perturbation solution describes recalescence during which the liquid core increases very quickly from the nucleation temperature to the melting point. Enormous internal heat transfer rates dominate the process, and the solid-liquid interface is morphologically unstable, during recalescence. External convective heat transfer dominates after recalescence, and the slowly varying solution shows that this period begins when the dimensionless thickness of the solidified region is approximately equal to 1 -(1 — S)^1/3. The position of the interface after recalescense is given by (I — S — 3 Hθ)^1/3. Complete freezing of the droplets occurs at time t -(R²/α₁)(1— S)/3H. The time required for recalescence is on the order of microseconds and is usually only a small fraction of the total freezing time.