Leidenfrost Effect: Why Water Drops Dance on a Hot Pan

What you see. A steel skillet on a hob with water drops on it. Below 100 °C a drop just evaporates slowly; from about 105 °C it boils violently and is gone in a second or two; far above the Leidenfrost point (about 200–300 °C for water) the drop floats on a cushion of its own vapour, barely touching the metal, and survives for tens of seconds. Click the pan to add drops, tilt the pan to make a levitating drop slide, and magnify the gap to see it (the real gap is only 50–200 µm).

Film boiling. Heat crosses the vapour gap of thickness e by conduction, q = kv ΔT / e, and evaporates liquid at mdot = q π rc² / L* (L* = latent heat plus half the vapour sensible heat). The vapour has to leave sideways through the gap: lubrication theory for a disc of radius r_c gives the pressure p(r) = 3 μv u (rc² − r²) / e³ with injection speed u = q/(ρ_vL*). Integrating, the supporting force is 3π μv u rc⁴ / (2 e³); setting it equal to the weight m g gives e = [3π μv kv ΔT rc⁴ / (2 ρv L* m g)]1/4. The contact disc is r_c = R²/l_c for a small near-spherical drop and the pancake radius for a drop larger than the capillary length l_c = √(σ/ρg) = 2.5 mm. For a puddle e ∝ m^1/4 and mdot ∝ m^3/4.

The Leidenfrost point is taken from Berenson's minimum film-boiling temperature, ΔT = 0.127 (ρv L / kv) [gΔρ/(ρl+ρv)]2/3 [σ/(gΔρ)]1/2 [μv/Δρ]1/3, about 220 °C for water; his minimum flux (about 20 kW/m²) is used only as a cross-check. Below it the drop touches the metal: nucleate boiling follows a Rohsenow-type q ∝ ΔT³ up to Zuber's critical heat flux (about 1.1 MW/m² at ΔT = 30 K), and transition boiling is a straight line in log–log from the critical flux down to the film flux at the Leidenfrost point. Below 100 °C the drop evaporates by vapour diffusion, mdot = 2π D R ρvs(1 − RH). On a tilted pan the weight component along the pan equals the viscous drag in the gap, m g sinα = μv v π rc² / e, so a levitating drop slides at a steady speed.

Honest simplifications. Steam properties are linear fits at the mean film temperature; the vapour pressure under the drop is not allowed to change the vapour density; the Leidenfrost point does not depend on drop size here (it does slightly in experiments); the contact disc radius uses order-one scaling (Biance et al.) instead of solving the drop shape; radiation uses an assumed effective emissivity 0.5 and is added to the evaporation but not to the gap; wetted drops are modelled as flat pancakes with a 90° contact angle; the boiling-curve numbers are textbook correlations, not measurements on your pan. Real Leidenfrost points depend strongly on surface roughness and cleanliness (roughly 200–300 °C), and the cushion in a real drop oscillates (star-shaped modes) which is not modelled. Drops are drawn at true size; the vapour gap and the 'wobble' of boiling drops are exaggerated for visibility.

Checks. (1) the Simpson integral of the pressure over the disc equals the weight; (2) closed-form puddle lifetime (m^1/4 linear in time) against numerical integration; (3) critical and minimum fluxes against textbook values; (4) the Berenson Leidenfrost point lies in the measured range, the drop film flux there is the same order as Berenson's q_min, and the heat entering the gap equals the latent heat used.