Drop splashing after impact onto immiscible pools of different viscosities

Droplet impact onto liquid pools is a canonical scenario relevant to numerous natural phenomena and industrial processes. However, despite their ubiquity, multi-fluid systems with the drop and pool consisting of different liquids are far less well understood. Our hypothesis is that the post-impact dynamics greatly depends on the pool-to-droplet viscosity ratioμ_p/μ_d, which we explore over a range of six orders of magnitude using a combination of experiments and theoretical approaches (mathematical modelling and direct numerical simulation). Our findings indicate that in this scenario the splashing threshold and the composition of the ejecta sheet are controlled by the viscosity ratio. We uncover that increasing the pool viscosity decreases the splashing threshold for high viscosity pools (μ_p/μ_d≳35) when the splash comes from the droplet. By contrast, for low viscosity pools, the splash sheet comes from the pool and increasing the pool viscosity increases the splashing threshold. Surprisingly, there are conditions for which no splashing is observed under the conditions attainable in our laboratory. Furthermore, considering the interface velocity together with asymptotic arguments underlying the generation of the ejecta has allowed us to understand meaningful variations in the pressure during impact and rationalise the observed changes in the splashing threshold.