A mathematical model of the Leidenfrost effect on an axisymmetric droplet

A simple mathematical model is developed for the Leidenfrost effect on an axisymmetric droplet. We first examine the practice of describing large droplets as cylindrical and small droplets as almost spherical, by solving the Young-Laplace equation. Best fit formulas are presented relating the droplet surface area to volume. The full model for Leidenfrost is then discussed. This shows that the calculation may be reduced to the solution of three first order ordinary differential equations involving the volume, evaporation rate, and vapor film thickness. Comparison with experimental results shows good agreement provided the model incorporates two components neglected in previous theoretical studies. First, a finite heat transfer coefficient between the vapor and substrate is required. Second evaporation from the upper surface of the droplet must be included, even for large droplets.