Maximum Diameter of Impacting Liquid Droplets

The maximum diameter a droplet that impacts on a surface will attain is the subject of controversy, notably for high-velocity impacts of low-viscosity liquids such as water or blood. We study the impact of droplets of simple liquids of different viscosities, and a shear-thinning complex fluid (blood), for a wide range of surfaces, impact speeds, and impact angles. We show that the spreading behavior cannot simply be predicted by equating the inertial to either capillary or viscous forces, since, for most situations of practical interest, all three forces are important. We determine the correct scaling behaviors for the viscous and capillary regimes and, by interpolating between the two, allow for a universal rescaling. The results for different impact angles can be rescaled on this universal curve also, by doing a simple geometrical correction for the impact angle. For blood, we show that the shear-thinning properties do not affect the maximum diameter and only the high-shear rate viscosity is relevant. With our study, we solve a long-standing problem within the fluid-dynamics community: We attest that the spreading behavior of droplets is governed by the conversion of kinetic energy into surface energy or dissipated heat. Energy transfer into internal flows marginally hinders droplet spreading upon impact.