Impact forces of water drops falling on superhydrophobic surfaces (2202.02437v3)

Abstract: A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show here, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. We characterize both peaks and elucidate how they relate to the different stages of the drop impact process. The time at which the second peak appears coincides with the formation of a Worthington jet, emerging through flow-focusing, and it is independent of the impact velocity. However, the magnitude of this peak is dictated by the drop's inertia and surface tension. We show that even low-velocity impacts can lead to a surprisingly high peak in the normal force, namely when a more pronounced singular Worthington jet occurs due to the collapse of an air cavity in the drop.

• The paper reveals that droplet impacts exhibit two distinct force peaks, with a novel second peak linked to the formation of a Worthington jet.
• The paper employs synchronized high-speed photography and direct numerical simulations to accurately quantify the dynamic impact forces.
• The paper discusses practical implications, highlighting potential risks in applications like inkjet printing and spray coatings due to force surges.

Impact Forces of Water Drops on Superhydrophobic Surfaces

The paper titled "Impact forces of water drops falling on superhydrophobic surfaces" investigates the complex dynamics of droplet impacts on surfaces engineered to be almost perfectly non-wetting. The paper presents detailed analysis of the impact forces, elucidating the distinct stages of droplet behavior during and after the impact, particularly highlighting the emergence of previously unknown phenomena.

Key Findings

In contrast to earlier studies that mostly focused on wetting surfaces, this research aims to fill the knowledge gap by exploring the dynamics and forces involved when drops impact superhydrophobic substrates. The authors identify two distinct peaks in the normal reaction force during the impact of water drops — the first related to the initial impact and the second coinciding with the formation of the Worthington jet.

1. First Force Peak: Consistent with previous studies on wetting surfaces, an inertial force peak occurs just after the droplet contacts the surface. This peak is associated with the rapid deceleration of the drop and the impulse force exerted by it.
2. Second Force Peak: The novel contribution of this paper is the identification of a second peak in the normal force, which arises due to the formation of a Worthington jet. This phenomenon occurs during the retraction phase when the droplet attains its maximum diameter and begins to recoil. The second peak force can even surpass the first, particularly under conditions facilitating the formation of a singular jet.
3. Role of Worthington Jet: The second force peak is more pronounced when a Worthington jet forms through flow focusing, arising either from capillary wave convergence or collapse of an air cavity within the droplet.

Numerical and Experimental Methodology

Both experiments and direct numerical simulations (DNS) were employed to meticulously measure the impact forces. High-speed photography synchronized with force sensing provided empirical data, while DNS facilitated a comprehensive understanding of the internal flow dynamics and forces. The quantitative congruence between experimental and simulation results establishes the robustness of the findings.

Theoretical and Practical Implications

The second force peak, particularly in the low Weber number regime, is of significant interest because it presents potential risks of damage through high magnitudes of force surges. This has practical ramifications for applications where drop impacts are integral, such as in inkjet printing and spray coatings where superhydrophobic surfaces are employed to minimize liquid-solid contact.

From a theoretical viewpoint, the results introduce new insights into droplet dynamics, particularly the singular behavior induced by the non-wetting properties of the substrate. The paper provides critical estimations for characteristic times and scales that govern the dynamics of such impacts.

Prospective Research Directions

Future research can extend these findings by exploring broader parameter spaces, including varying drop viscosity and substrate motion. Additionally, the impact of environmental factors such as temperature and pressure on force dynamics could broaden the understanding of such systems. Understanding the mechanistic basis under a variety of conditions will further assist in optimizing designs for superhydrophobic surfaces in technology and materials science.

In conclusion, this paper substantially enriches the understanding of droplet impact forces on superhydrophobic surfaces, offering essential insights with significant implications for both theory and application.