A theoretical explanation for possible temperature discontinuities across a macroscopically-sharp plane solidification front

This work aims to theoretically investigate the possible situations of temperature discontinuities prevailing across propagating plane front solidification interfaces. A generalization of interfacial conditions is proposed, which can accommodate finite macroscopic jumps in the interfacial temperature. This is achieved by implicitly accounting for two disparate and unresolved time-scales, which are respectively associated with the interfacial heat conduction and the molecular rearrangements that are necessary for phase transformation. Through the present theoretical estimates, possibilities of extending continuum-based formulations towards accommodating deterministic rates of plane front propagation in case of directional solidification of pure materials can be explored.