High speeds micron-sized droplets impact onto smooth substrate*

The spreading-splashing transition of millimetric drops impacting over a smooth solid substrate received abundant consideration in the last decades. It is known that this transition takes place, for given material properties of both the liquid and the surrounding gaseous atmosphere, when the impact velocity V is above the critical velocity for splashing of a few meters per second. Here the transition from spreading to splashing of drops with radii R varying from millimeters to tens of microns impacting onto a smooth and dry partially wetting substrate at normal atmospheric conditions is investigated. Experiments show that the smaller R is, the larger the impact velocity V for the drop to splash needs to be but also that, unexpectedly, splash is inhibited if We_λ = ρ V² λ / σ ≧ 0.5, with σ, ρ, and λ indicating the interfacial tension coefficient, the liquid density, and the mean free path of gas molecules. The reason of this behaviour results from the fact that the thickness H_t of the thin liquid film ejected after the drop touches the substrate, under many practical conditions is H_t ≅ σ / (ρ V²) whose values becomes similar to the mean free path of gas molecules, i.e., H_t ∼ λ for sufficiently large values of the impacting velocity V.