TY - UNPB

T1 - Inertia & viscosity dictate drop impact forces

AU - Sanjay, Vatsal

AU - Zhang, Bin

AU - Lv, Cunjing

AU - Lohse, Detlef

N1 - Corrected a typo. The equation just before Eq. (3.11) must have sq(D_0) instead of D_0. Thanks to Fabian Denner and his class for pointing it out. :)

PY - 2023/11/6

Y1 - 2023/11/6

N2 - 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., \textit{Phys. Rev. Lett.}, vol. 129, 2022, 104501) revealed two peaks in the temporal evolution of the normal force $F(t)$--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 $F_1$ at impact and the one at take off ($F_2$) and elucidate their dependency on the control parameters: the Weber number $We$ (dimensionless impact velocity) and the Ohnesorge number $Oh$ (dimensionless viscosity). For low-viscosity liquids like water, the amplitude $F_1$ and the time $t_1$ to reach it are governed by inertial timescales, insensitive to viscosity variations up to 100-fold. For large viscosities, beyond this viscosity-independent regime, we balance the rate of change in kinetic energy and the rate of viscous dissipation to obtain the scaling laws: $F_1 \sim F_\rho\sqrt{Oh}$ and $t_1 \sim \tau_\rho/\sqrt{Oh}$, where $F_\rho$ and $\tau_\rho$ are the inertial force and time scales, respectively, which are consistent with our data. The time $t_2$ at which the amplitude $F_2$ appears is set by the inertio-capillary timescale $\tau_\gamma$, independent of both the viscosity and the impact velocity of the drop. However, these properties dictate the magnitude of this amplitude.

AB - 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., \textit{Phys. Rev. Lett.}, vol. 129, 2022, 104501) revealed two peaks in the temporal evolution of the normal force $F(t)$--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 $F_1$ at impact and the one at take off ($F_2$) and elucidate their dependency on the control parameters: the Weber number $We$ (dimensionless impact velocity) and the Ohnesorge number $Oh$ (dimensionless viscosity). For low-viscosity liquids like water, the amplitude $F_1$ and the time $t_1$ to reach it are governed by inertial timescales, insensitive to viscosity variations up to 100-fold. For large viscosities, beyond this viscosity-independent regime, we balance the rate of change in kinetic energy and the rate of viscous dissipation to obtain the scaling laws: $F_1 \sim F_\rho\sqrt{Oh}$ and $t_1 \sim \tau_\rho/\sqrt{Oh}$, where $F_\rho$ and $\tau_\rho$ are the inertial force and time scales, respectively, which are consistent with our data. The time $t_2$ at which the amplitude $F_2$ appears is set by the inertio-capillary timescale $\tau_\gamma$, independent of both the viscosity and the impact velocity of the drop. However, these properties dictate the magnitude of this amplitude.

KW - physics.flu-dyn

KW - cond-mat.soft

U2 - 10.48550/arXiv.2311.03012

DO - 10.48550/arXiv.2311.03012

M3 - Preprint

BT - Inertia & viscosity dictate drop impact forces

PB - ArXiv.org

ER -