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

## TL;DR

This study provides a comprehensive experimental and theoretical analysis of drop impact dynamics on solid surfaces, revealing self-similar behaviors in impact force evolution and spreading across different fluid regimes.

## Contribution

It introduces new self-similar solutions for impact force and drop spreading, validated by experiments across inertial, viscous, and viscoelastic regimes.

## Key findings

- Impact force at high Re follows a square-root scaling.
- Self-similar pressure fields exist during initial impact.
- Exact solutions predict spreading height at high Re.

## 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 (Re). At high 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 Re. When viscous forces gradually set in with decreasing 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 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 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 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.