Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

Abstract

We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers ($\mathit{Re}$). At high $\mathit{Re}$, when inertia dominates the impact processes, we show that the early time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high $\mathit{Re}$. When viscous forces gradually set in with decreasing $\mathit{Re}$, we analyse the early time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing $\mathit{Re}$. Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high $\mathit{Re}$ following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high $\mathit{Re}$. The limit of the self-similar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop-impact processes.