# The thermo-wetting instability driving Leidenfrost film collapse

## TL;DR

This paper develops a physics-based model for the Leidenfrost point, identifying vapor film instability mechanisms and deriving an expression that matches experimental data across various fluids and conditions.

## Contribution

It introduces a linear stability analysis revealing the vapor film collapse mechanism and provides an ab-initio formula for the Leidenfrost point applicable to different fluids and surfaces.

## Key findings

- The vapor film instability is driven by van der Waals forces.
- The derived formula accurately predicts the Leidenfrost point.
- A dimensionless number encapsulates the instability for wetting surfaces.

## Abstract

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.