How does the surrounding gas cause an impacting drop to splash?
In plain words
A drop hitting a smooth dry surface in air throws off a thin sheet that breaks into droplets, but in thin enough air the same impact does not splash at all. How the air produces the splash is not agreed.
Precise statement
A low-viscosity drop of radius $R \sim 0.1\,\mathrm{cm}$ hitting a smooth dry solid at speed $V$ of a few hundred cm/s splashes at 1 atm but not below a threshold gas pressure $P_{T}$ (Xu, Zhang, Nagel, PRL 2005). Identify the gas-mediated force that lifts the thin liquid sheet ejected near the contact line, and derive P_T(V, R, liquid viscosity, gas mean free path) together with the time and position of sheet ejection.
What would settle it
Simultaneous measurement of gas-film thickness, sheet ejection time and $P_{T}$ across gases and liquid viscosities, matched by a theory without fitted parameters.
Status in the literature
Competing models invoke aerodynamic lift on the advancing sheet (Riboux and Gordillo 2014) and Kelvin-Helmholtz instability of a thin air film (arXiv:1509.01230); none is confirmed over the full parameter range.
Related problems
- More general than Scaling of the splash-threshold gas pressure with viscosity and gas