Splashing of drops impacting rough substrates

Here, we present experimental results of drops of low viscosity fluids of radii R, density ρ and interfacial tension coefficient σ, impacting with a velocity V over different types of sandpapers characterized by their grit size, ε. It is shown that the transition from spreading to splashing at normal atmospheric conditions can be classified depending on the value of the parameter ε/H_t = We_ε = We(ε/R), with We = ρV²R/σ the Weber number and H_t the initial thickness of the thin film which is ejected along the substrate once the drop touches the solid. When We_ε ≤ 1 and the liquid wets the substrate, the critical value of the Weber number above which the drop splashes, We_c, can be predicted using the results in Gordillo & Riboux (J. Fluid Mech., vol. 871, 2019, R3). Moreover, if the liquid does not wet the substrate, it is also shown that the splash velocity can be predicted using the theory for superhydrophobic substrates in Quintero, Riboux & Gordillo (J. Fluid Mech., vol. 870, 2019, 175−188). For those cases in which We_ε ≥ 1 and the liquid wets the substrate, we demonstrate that the critical Weber number for splashing decreases with ε as We_c ∝ (R cosθ₀ / ε)^3/5, with θ₀ the value of the Young contact angle.