The role of viscosity on drop impact forces on non-wetting surfaces

A liquid drop impacting a rigid substrate undergoes deformation and spreading due to normal reaction forces, which are counteracted by surface tension. On a non-wetting substrate, the drop subsequently retracts and takes off. Our recent work (Zhang et al., Phys. Rev. Lett., vol. 129, 2022, 104501) revealed two peaks in the temporal evolution of the normal force - one at impact and another at jump-off. The second peak coincides with a Worthington jet formation, which vanishes at high viscosities due to increased viscous dissipation affecting flow focusing. In this article, using experiments, direct numerical simulations and scaling arguments, we characterize both the peak amplitude F₁ at impact and the one at takeoff (F₂) and elucidate their dependency on the control parameters: the Weber number (dimensionless impact kinetic energy) and the Ohnesorge number (dimensionless viscosity). The first peak amplitude F₁ and the time t₁ to reach it depend on inertial time scales for low viscosity liquids, remaining nearly constant for viscosities up to 100 times that of water. For high viscosity liquids, we balance the rate of change in kinetic energy with viscous dissipation to obtain new scaling laws: F₁/F_ρ ∼ √Oh and, t₁/τ_ρ where F_ρ and τ_ρ are the inertial force and time scales, respectively, which are consistent with our data. The time t₂ at which the amplitude F₂ appears is set by the inertiocapillary time scale, τ_γindependent of both the viscosity and the impact velocity of the drop. However, these properties dictate the magnitude of this amplitude.