Maximum spreading of impacting shear-thinning and shear-thickening drops

The maximum spreading of an impacting liquid drop is a key metric for characterizing the fundamental fluid process of drop impact. While extensively studied for Newtonian liquids, how far a non-Newtonian drop can spread upon impacting a solid substrate remains an open question. Here, by combining simulations, experiments, and scaling analyses, we establish a general framework for predicting the maximum spreading of drops of generalized Newtonian liquids, encompassing both shear-thinning and shear-thickening behaviors. Through an analysis of the energy budget at maximum spreading, we identify a characteristic shear rate that governs the viscous dissipation during drop impact. The finding allows us to map the spreading of non-Newtonian drops onto that of Newtonian drops, revealing the quantitative dependence of the maximum spreading diameter on various impact parameters and rheological properties of liquids. Our study addresses the long-standing challenge of understanding the impact dynamics of non-Newtonian drops, and provides valuable guidance for designing non-Newtonian liquids to achieve desired impact outcomes.