The role of viscosity on drop impact forces on non-wetting surfaces (2311.03012v6)

Abstract: 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 kinetic energy) and the Ohnesorge number $Oh$ (dimensionless viscosity). The first peak amplitude $F_1$ and the time $t_1$ to reach it depend on inertial timescales 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: $F_1/F_\rho \sim \sqrt{Oh}$ and $t_1/\tau_\rho \sim 1/\sqrt{Oh}$, 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.

• The paper shows that the first force peak scales with inertial forces at low viscosities and transitions to a viscosity-influenced regime beyond 100 times water’s viscosity.
• The paper identifies a second force peak during drop retraction, where capillary resonance and the emergence of a Worthington jet amplify the impact force under low-Oh conditions.
• The paper employs experimental techniques, numerical simulations, and scaling analyses to provide insights that can optimize applications such as inkjet printing and erosion prevention.

The Influence of Viscosity on Drop Impact Forces on Non-Wetting Surfaces

The interplay of diverse forces when a liquid drop impacts a solid surface has always intrigued researchers, given its fundamental and applied significance. The paper by Sanjay et al. explores the nuanced role of viscosity in such scenarios, specifically focusing on non-wetting substrates and deciphering the surprising dynamics that arise due to varying viscosities.

Overview

The paper meticulously examines the forces that develop when a liquid drop makes contact with a solid non-wetting surface: a topic that extends implications across industries from inkjet printing to materials science. The authors employ a combination of experimental techniques, direct numerical simulations, and scaling arguments to articulate a comprehensive understanding of the phenomenon that has largely been characterized by the Weber number ($We$) reflecting impact kinetic energy and the Ohnesorge number ($Oh$) representing viscosity.

Key Findings

Using a systematic approach, the research portrays the emergence of two distinct peaks in the temporal evolution of the impact force. The first peak aligns with the immediate impact, governed by the interplay of inertial forces and surface tension. The second peak, more intriguingly, is linked with the drop's retraction and take-off—where a Worthington jet is often initiated if conditions permit.

• First Force Peak ($F_1$): At low viscosities, $F_1$ scales with the inertial force ($F_\rho = \rho V^2 D_0^2$). This relation holds up to viscosities 100 times that of water, after which new scaling laws take precedence: $F_1 \sim F_\rho\sqrt{Oh}$, portraying the influence of viscous dissipation. Here, the time to reach the first peak ($t_1$) also changes, scaling inversely with $\sqrt{Oh}$, consistent with dissipation-driven dynamics.
• Second Force Peak ($F_2$): The paper further illuminates the second peak characterized by inertio-capillary timescales. Independent of viscosity, the magnitude of this peak showcases dependencies on both viscosity and impact velocity. Remarkably, under specific low-Oh conditions, capillary resonance amplifies this second peak beyond the first—correlated with a high-speed Worthington jet formation which dissipates at higher viscosities.

Practical and Theoretical Implications

The breadth and depth of results underscore the critical role of viscosity in dictating impact dynamics beyond initial assumptions of inertial or capillary dominance. This has practical ramifications in designing systems to mitigate surface erosion or optimize inkjet printing technologies. It highlights a potential crossover effect that could be controlled or harnessed—modulating surface properties or environmental parameters to achieve desirable outcomes, such as enhanced adherence or reduced splashing.

From a theoretical standpoint, the findings encourage a reevaluation of existing models and scaling laws to incorporate nuanced viscous dynamics, potentially influencing future research on complex fluid dynamics, including non-Newtonian fluids or impact on compliant surfaces. The paper signifies a step towards a more unified framework that integrates interdisciplinary insights into the fluid mechanics of impact phenomena.

Future Outlook

This paper lays the groundwork for several exploration avenues. Extending the findings to broader fluid classes, including yield-stress and viscoelastic fluids, can offer insights into a wider spectrum of impact behaviors. Furthermore, investigating the interaction of multiple droplets or more intricate surface geometries can unearth emergent behaviors critical for advanced manufacturing processes.

In conclusion, Sanjay et al.'s work provides an exhaustive investigation into viscosity's impact on drop dynamics, uncovering complex interdependencies that define the interaction of fluid and surface. Their blend of experimental and computational rigor sets a benchmark for future studies in the fluid dynamics community.