Presets and playback
Presets
Plate and drop
Layers
Model checks
The science
The vapour cushion
On a plate far above the boiling point the bottom of a drop evaporates so fast that a thin vapour layer lifts it. Heat flows through the layer by conduction, so the evaporated mass flux per area is ρvw = kvΔT / (h'δ) with the modified latent heat h' = hfg + ½ cp,vΔT and gap thickness δ. The vapour leaves radially through the gap in lubrication (Poiseuille) flow, which gives a pressure p(r) = 3μv w (R2 − r2) / δ3.
Floating condition
Integrating the pressure over the footprint and equating it with the weight gives M g = 3π μv kv ΔT R4 / (2 ρv h' δ4), so δ = [3π μv kv ΔT R4 / (2 ρv h' M g)]1/4: for water on a 400 C plate a few tens of micrometres. A hotter plate makes the gap thicker only as ΔT1/4. The drop is modelled as a flat disc of the same volume with height min(2a, 2√(γ/ρlg)) (a puddle thickness of two capillary lengths).
Lifetime and the boiling curve
The film state conducts heat poorly, so the drop lives long. Below the Leidenfrost point TL the liquid touches the plate and boils violently. The page uses a cubic nucleate-boiling law up to a critical heat flux of 1.2 MW/m2 at 30 K superheat for water (scaled by the latent heat for other liquids), log-linear interpolation through the transition regime down to the film-boiling flux at TL, and the film formula above. Lifetime follows from integrating dM/dt = −qπR2/h'; the longest lifetime sits just above TL.
Honest simplifications
Vapour properties are constants evaluated near the film temperature; radiation, convection above the drop, vapour-layer instabilities, drop oscillations and the real surface dependence of TL are ignored, so TL is a slider rather than a prediction. The cylinder-equivalent footprint overestimates the contact area of very small near-spherical drops. Liquid nitrogen on a room-temperature table is modelled with the same equations and constant properties.
What to try
Run Water drop on a 400 C plate and watch the drop shrink and the gap thicken slightly. Compare Water at 150 C (contact boiling: short life) and Just above the Leidenfrost point, the longest-lived state. Look at graph 1 to see lifetime versus plate temperature and try Liquid nitrogen on a 20 C table.