The critical impact speed for the splash of a drop

TL;DR

This paper derives and experimentally validates a criterion for the critical impact speed at which a drop either spreads or disintegrates upon hitting a dry surface, considering material and atmospheric properties.

Contribution

It introduces a new equation for splash threshold velocity based on fluid properties, drop size, and atmospheric mean free path, validated with multiple liquids.

Findings

Derived a formula for splash threshold velocity.

Validated the formula with eight different liquids.

Showed the influence of fluid and atmospheric properties on splash behavior.

Abstract

Making use of experimental and theoretical considerations, in this Letter we deduce a criterion to determine the critical velocity for which a drop impacting a smooth dry surface either spreads over the substrate or disintegrates into smaller droplets. The derived equation, which expresses the splash threshold velocity as a function of the material properties of the two fluids involved, the drop radius and the mean free path of the molecules composing the surrounding gaseous atmosphere, has been thoroughly validated experimentally at normal atmospheric conditions using eight different liquids, with viscosities ranging from $3\times 10^{-4}$ to $10^{-2}$ Pa$\cdot$s and interfacial tension coefficients which vary between $17$ and $72$ mN$\cdot$m$^{-1}$.