Role of Jakob number in Leidenfrost phenomena unveiled by theoretical modeling

The Leidenfrost phenomenon in its most common form is encountered when a droplet is levitated and driven by its own vapor. The recently discovered "cold Leidenfrost phenomenon" expands this phenomenon into low-temperature regimes. Although various theoretical models have been proposed, analytical exploration on generalized dimensionless laws is still absent. In this work, we elucidated the role of the dimensionless Jakob number in the Leidenfrost phenomenon through theoretical modeling. The model was verified by examining the cold Leidenfrost phenomenon of both a dry ice nub on the surface of water and a liquid nitrogen droplet on a smooth silicon surface. Regardless of the specific configuration, the dimensionless temperature distribution in the vapor film only depends on the Jakob number of the vapor and presents linear dependence when the Jakob number is below 0.25. This theoretical model would facilitate the exploration of physics for Leidenfrost events and, therefore, guide prediction as well as the design of applications in the future.