[Paper Review] The Leidenfrost effect: from quasi-spherical droplets to puddles

Yves Pomeau, M. Le Berre+2 more|arXiv (Cornell University)|Aug 13, 2012

Fluid Dynamics and Heat Transfer7 references3 citations

TL;DR

This paper develops a lubrication-based model to describe the Leidenfrost effect across droplets and puddles, deriving coupled equations for the vapor film thickness and pressure. It predicts scaling laws for the concave vapor bubble shape, showing excellent agreement with experiments for droplets (R < Rc) and large puddles (R ≫ Rc), with evaporation primarily occurring through the vapor layer rather than the droplet top or neck regions.

ABSTRACT

In the framework of the lubrication approximation, we derive a set of equations describing the steady bottom profile of Leidenfrost drops coupled with the vapor pressure. This allows to derive scaling laws for the geometry of the concave bubble encapsulated between the drop and the hot plate under it. The results agree with experimental observations in the case of droplets with radii smaller than the capillary length Rc as well as in the case of puddles with radii larger than Rc.

Motivation & Objective

• To develop a theoretical framework for the Leidenfrost effect that spans from small droplets to large puddles.
• To understand the geometry and pressure distribution in the vapor film beneath a Leidenfrost droplet or puddle.
• To identify the dominant evaporation pathways and their dependence on droplet size and physical parameters.
• To validate the lubrication approximation across multiple length scales, from R ≪ Rc to R ≫ Rc.
• To explain experimental observations of droplet lift-off and vapor bubble morphology using a unified scaling approach.

Proposed method

• Formulates a set of coupled equations for the bottom surface height h(r) and local vapor pressure p(r) in the lubrication approximation.
• Applies the lubrication approximation to the thermal and viscous flow fields in the vapor gap between the droplet and hot plate.
• Derives scaling laws for the vapor bubble shape by analyzing the balance between viscous flow, evaporation, and pressure gradients.
• Uses asymptotic analysis to identify distinct regimes based on droplet radius relative to Rl, Ri, and Rc.
• Matches the continuum fluid dynamics model with kinetic theory limits (e.g., Knudsen effects) in thin vapor films.
• Compares theoretical predictions with experimental data on droplet and puddle profiles and evaporation rates.

Experimental results

Research questions

• RQ1 How does the shape of the vapor film beneath a Leidenfrost droplet evolve with droplet size?
• RQ2 What are the dominant mechanisms of mass loss in Leidenfrost systems across different size regimes?
• RQ3 How do the scaling laws for the vapor bubble thickness and pressure depend on physical parameters like viscosity, thermal conductivity, and surface tension?
• RQ4 In what size range does the lubrication approximation remain valid for the vapor flow and heat transfer?
• RQ5 Why is evaporation predominantly localized in the vapor layer rather than at the droplet top or neck?

Key findings

• The model successfully predicts the concave shape of the vapor bubble beneath Leidenfrost droplets and puddles, matching experimental observations across R < Rc and R ≫ Rc.
• For droplets with R ≪ Rc, the vapor film thickness h increases as the droplet radius R decreases, explaining the lift-off behavior observed at small sizes.
• In the regime Ri < R < Rc, the pressure in the vapor gap is much smaller than Laplace pressure, justifying the use of a uniform pressure approximation and spherical shape near the droplet bottom.
• For large puddles (R ≫ Rc), the vapor gap splits into a trapped bubble and a narrow neck, with distinct scaling laws applying to each region.
• Evaporation is found to be dominated by mass loss through the vapor layer, with Jtop/Jfilm ∼ (Rl / √(R Rc))^{3/5} and Jneck/Jfilm ∼ (Rl R²c / R³)^{1/10}, both much less than unity, indicating minimal evaporation at the top or neck.
• The approach breaks down for R ≲ Rl due to loss of lubrication approximation, consistent with observed droplet lift-off and instability.