Splash crown formation from a falling drop

Partly settled. Some of it is understood, some is still argued about.

Kapitza's problem #65 in the 1966 collection asks students to explain how a splash forms and how splash height scales with impact velocity and stone/drop size, in the spirit of Worthington's 1877 photographic studies of splashes. High-speed imaging (Edgerton's famous 'milk-drop coronet' photos) made the crown-and-spike geometry iconic well before it was theoretically understood. Since the 1990s-2000s, groups led by Zaleski, Thoroddsen, Deegan and others identified air-film entrapment and Rayleigh-Taylor-type rim instabilities as key mechanisms, but a fully predictive theory linking impact parameters to spike number and crown height is still incomplete, especially for thin films and low-viscosity regimes.

A puddle splash looks chaotic yet organizes itself into an almost perfectly periodic crown of spikes, and nobody has a complete first-principles formula for how many spikes appear.

Explanations that circulated

• The splash is caused simply by the drop pushing liquid outward like a solid piston (ignores the trapped-air / thin-film instability mechanisms now known to matter)
• Crown finger number is set only by the Weber number (shown insufficient; film thickness and viscosity also matter)

References

• Experimental investigation of splash and crown formation during single drop impact on wetted surfaces, C. Josserand, S. Zaleski et al. (various groups), Experiments in Fluids, 2003
• Crown-forming instability phenomena in the drop splash problem, Krechetnikov & Homsy (and related groups), Journal of Colloid and Interface Science, 2009