What happens between surface tension and gravity.

• The tear-drop myth.

  Standing drops are spheres — surface tension minimises area. Falling raindrops are oblate spheroids with a flattened underside (Beard & Chuang 1987). The iconic teardrop shape does not exist in nature.

• Plateau's laws.

  In soap foams three films always meet along an edge at 120°, and four edges at a vertex at the tetrahedral angle 109.47°. Jean Taylor proved the rules rigorously in 1976 — they follow purely from energy minimisation.

• Tears of Wine.

  James Thomson 1855: ethanol evaporates faster than water, so local surface tension rises. The gradient pulls liquid upwards — the Marangoni effect creates the tears at the edge of a wine glass.

• Coffee ring.

  Evaporation at a pinned contact line drives a capillary flow outward that carries nearly all suspended particles with it. Deegan et al. (Nature 1997) showed the power law is universal across substrate and particle type.

• Coalescence.

  When two drops touch, their surfaces connect through an ever-thinning bridge — the "neckdown". Jens Eggers 1995 showed the moment the bridge reaches zero thickness follows a universal scaling law.

• Terminal velocity.

  A raindrop quickly reaches its speed limit because drag grows with v². Gunn & Kinzer 1949: 1 mm → 4 m/s, 2 mm → 6.5 m/s, 5.8 mm → 9.2 m/s. Beyond that, Plateau-Rayleigh breaks the drop up.

From a spark photograph to a quantum theory of splash.

1. Worthington 1908.

   Arthur Mason Worthington spent fourteen years at Royal Naval College Devonport recording the geometry of impact splashes with spark stroboscopy. The result: the crown is not random — its spikes are regularly spaced, their number scales with the fourth root of the Weber number. Harold "Doc" Edgerton turned this into the iconic Milk Drop Coronet (1936) with microsecond flashes. Krechetnikov & Homsy (2009) finally showed the spikes arise from a rim instability analogous to Rayleigh-Taylor and Richtmyer-Meshkov mechanics.

2. Plateau-Rayleigh breakup.

   Joseph Plateau observed in 1873 that a water jet becomes unstable once its length exceeds its circumference. Lord Rayleigh computed the fastest-growing wavelength in 1879: λ ≈ 9.01·R. Consequence: raindrops never exceed about 5.8 mm (Gunn & Kinzer 1949) — beyond that limit they break up in free fall by exactly this mechanism. Jens Eggers (1997) supplied the non-linear theory of the pinch-off singularity.

3. Three impact regimes.

   What happens on impact does not depend on drop size or velocity separately, but on two dimensionless ratios: the Weber number (inertia versus surface tension) and the Reynolds number (inertia versus viscosity). Yarin (2006) consolidated the diagram. Below We ≈ 30 the drop spreads as a thin disk; from 30 to 80 it forms a smooth crown; above 80 the rim breaks into secondary droplets — true splashing. The exact secondary-droplet threshold follows the Mundo constant K = We·Oh^(-0.4) ≈ 657.

4. Lotus and Leidenfrost.

   Two very different escapes from impact. On super-hydrophobic structures like the lotus leaf (contact angle > 150°, hierarchical wax nano-roughness) air stays trapped between drop and substrate in the Cassie-Baxter state — the drop bounces (Richard & Quéré 2000). On a plate above 193 °C a 10-100 µm vapour layer forms that thermally decouples the drop — it floats for minutes (Leidenfrost 1756). Same underlying physics: a gas layer between drop and substrate. Different energy source.