Inertia and viscosity dictate drop impact forces*

A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Indeed, during this process, we observe a maximum in the normal reaction force owing to the inertial shock experienced by the drop. Naturally, the time to reach this maximum is governed by the inertial timescale. Subsequently, if the substrate is non-wetting, the drop retracts and jumps off. We have recently shown that even the jump-off is associated with a maximum in the normal reaction force [Zhang et al. 2022, arXiv preprint arXiv:2202.02437]. The time at which the second peak appears is set by the inertio-capillary timescale, independent of the material and flow properties, such as the drop's viscosity and impact velocity. However, these properties dictate the magnitude of this peak. Furthermore, the second force peak also coincides with the formation of a Worthington jet which disappears at high viscosity owing to an increase in viscous dissipation that enervates internal momentum leading to poor flow focusing during retraction. In this work, we characterize both these peaks in the normal reaction force and elucidate how they relate to the different stages of the drop impact process (impact, spreading, retraction, and take-off).