Maximum spreading of impacting non-Newtonian drops

The maximum spreading diameter of impacting drops is a crucial parameter characterizing the outcomes of a drop-impact event. While the dependence of the maximum spreading diameter on various impact conditions has been extensively studied for Newtonian drops, a quantitative prediction for non-Newtonian drops remains elusive. The difficulty arises from the large spatiotemporal variations of shear rates during impact, which leads to highly non-uniform viscosity distributions within impacting drops. Here, by combining simulations, experiments and scaling analyses, we provide a universal description of the maximum spreading diameter of non-Newtonian drops on a superhydrophobic surface. Particularly, we identify the characteristic shear rate via a detailed analysis of the energy budget over a wide range of impact conditions. The finding allows us to map the maximum spreading of non-Newtonian drops to that of corresponding Newtonian drops. Our study addresses the long-standing challenge of predicting the maximum spreading of non-Newtonian drops and offers valuable guidelines for designing non-Newtonian liquids with desired impact dynamics.