Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing

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 μ=3×10(-4) to μ=10(-2)  Pa s, and interfacial tension coefficients varying between σ=17 and σ=72  mN m(-1). Our predictions are also in fair agreement with the measured critical speed of drops impacting in different gases at reduced pressures given by Xu et al. [Phys. Rev. Lett. 94, 184505 (2005).