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The thermo-wetting instability driving Leidenfrost film collapse

Significance The insulating vapor film formed during film boiling dramatically reduces the heat flux from the surface. This can be highly detrimental in the quenching of metal alloys, the cooling of nuclear fuel rods, and the thermal control of electronic and photonic devices. On the other hand, the vapor film can also be harnessed to reduce liquid–solid drag as well as design levitating, self-rotating rotors and self-propelled droplets for lab-on-a-chip applications. Control of vapor film collapse in different systems and operating conditions is therefore highly desirable. Surface wettability is known to influence this collapse. However, a comprehensive thermo-wetting instability theory that predicts observed data has been elusive. This work proposes such a theory. 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 semiempirical models that account for the Rayleigh–Taylor instability, nucleation rates, and superheat limits. However, formulating 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 investigate 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-driven transport of vapor mass and the 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 wetting instability governing the LFP.