Large impact velocities suppress the splashing of micron-sized droplets

Abstract

Here we investigate 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. Experiments show that the smaller R is, the larger the impact velocity V for the drop to splash needs to be but also that splash is inhibited if Weλ=ρV2λ/σ≳0.5, with σ, ρ, and λ indicating the interfacial tension coefficient, the liquid density, and the mean free path of gas molecules. This result has been validated for two different values of the Ohnesorge number Ohλ=μ/ρλσ, with μ indicating the liquid viscosity, defined using only the material properties of the liquid and of the surrounding gaseous atmosphere. The underlying reason for this a priori unexpected finding results from the fact that the thin liquid film ejected after the drop touches the substrate is, under many practical conditions, Ht≃σ/(ρV2) Riboux and Gordillo [Phys. Rev. Lett. 113, 024507 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.024507]. Then, for sufficiently large values of V, the thickness of the lamella becomes similar to the mean free path of gas molecules, i.e., Ht≈λ, and, under these conditions, the splash of the drop is inhibited because the lift force causing the liquid to dewet the partially wetting solid is negligible. The spreading to splashing and the splashing to spreading transitions observed experimentally as the impact velocity is increased and the radii of the droplets is above a certain threshold value are very well predicted by the theory in G. Riboux and J. M. Gordillo [Phys. Rev. Lett. 113, 024507 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.024507] and J. M. Gordillo and G. Riboux [J. Fluid Mech. 871, R3 (2019)JFLSA70022-112010.1017/jfm.2019.396] once the aerodynamic lift force is set to zero for Ht/λ≲2, i.e., when Weλ≳0.5.