  Above a critical temperature known as the Leidenfrost point (LFP), a heated
surface can suspend a liquid droplet above a film of its own vapor. The
insulating vapor film can be highly detrimental in metallurgical quenching and
thermal control of electronic devices, but may also be harnessed to reduce drag
and generate power. Manipulation of the LFP has occurred mostly through
experiment, giving rise to a variety of semi-empirical models that account for
the Rayleigh-Taylor instability, nucleation rates, and superheat limits.
However, a truly comprehensive model has been difficult given that the LFP
varies dramatically for different fluids and is affected by system pressure,
surface roughness and liquid wettability. Here, we identify the vapor film
instability for small length scales that ultimately sets the collapse condition
at the Leidenfrost point. From a linear stability analysis, it is shown that
the main film stabilizing mechanisms are the liquid-vapor surface tension,
viscous transport of vapor mass, and evaporation at the liquid-vapor interface.
Meanwhile, van der Waals interaction between the bulk liquid and the solid
substrate across the vapor phase drives film collapse. This physical insight
into vapor film dynamics allows us to derive an ab-initio, mathematical
expression for the Leidenfrost point of a fluid. The expression captures the
experimental data on the LFP for different fluids under various surface
wettabilities and ambient pressures. For fluids that wet the surface (small
intrinsic contact angle), the expression can be simplified to a single,
dimensionless number that encapsulates the thermo-wetting instability governing
the LFP.
