Analytical Consideration for the Maximum Spreading Factor of Liquid Droplet Impact on a Smooth Solid Surface

Experimental investigation on the bouncing dynamics of a liquid marble during the impact on a hydrophilic surface

Liquid marbles are droplets coated by hydrophobic particles. At low Weber numbers (We), when impacting a hydrophilic surface, the marble may bounce on the substrate repeatedly without any rupturing until the quiescence condition is achieved. The marble bouncing has gained far less attention, although its rich underlying physics is due to the interaction between liquid core, hydrophobic grain, and surrounding air. Accordingly, this research experimentally scrutinizes the marble impact and subsequent bouncing on a hydrophilic surface for the first time. Additionally, the conversion of kinetic, gravitational potential, inertial, and surface energies occurring regularly during the impact is exhaustively surveyed. Moreover, the effect of Weber and gravitational Bond numbers (Bo) on the bouncing time, maximum spreading time, maximum spreading ratio, maximum elongation ratio, and maximum restitution are investigated, which characterize the marble impact and bouncing dynamics. This study is one of the limited investigations exploring the effects of the gravitational Bond number on the results. Dimensionless correlations are proposed for the mentioned parameters based on the experimental data. Furthermore, utilizing the simplifying theoretical presumptions, correlations are suggested based on the scale analysis for the spreading time and maximum spreading ratio. The results imply that the mentioned parameters behave differently at low and moderate Weber numbers, though the distinction is more pronounced in the case of the bouncing time, maximum spreading time and maximum spreading ratio. Although increasing with the Weber number when WeWecr. In addition, the maximum elongation ratio linearly grows with the Weber number.

Coalescence-Induced Self-Propelled Particle Transport with Asymmetry Arrangement

We experimentally investigated the coalescence-induced droplet-particle jumping phenomenon on a submillimeter scale in symmetric and asymmetric particle arrangements with poly(methyl methacrylate) (PMMA) particles and stainless steel (SS) particles. Coalescence-induced droplet-particle jumping exhibited excellent capability and interesting behavior for both droplet jumping enhancement and particle transport. The particle increased the normalized droplet jumping velocity from 0.250 for no particle case to 0.315 and 0.320 for symmetric and asymmetric particle cases. Compared with similar-sized macrostructures fixed between droplets, better jumping performance with particles may be attributed to avoiding the work of adhesion during droplet-macrostructure separation. Besides, all particles always sunk at the bottom in the symmetric cases, while the stick mode for PMMA particles and sink, wander, and jet modes for SS particles appeared in the asymmetry cases. We revealed that the asymmetric particle arrangement induces an unbalanced surface tension force, which may provide a driving force in the vertical direction. Additionally, a small enough resistive force caused by hydrophobic particles is another necessary condition for the wonder and jet mode. Finally, we realized a significantly superior particle transport in the asymmetric SS particle cases with maximum particle height reaching ∼2.1 mm, ∼12.4 times the particle radius, the most significant vertical self-propelled transport distance currently.

Understanding and Utilizing Droplet Impact on Superhydrophobic Surfaces: Phenomena, Mechanisms, Regulations, Applications, and Beyond

Droplet impact is a ubiquitous liquid behavior that closely tied to human life and production, making indispensable impacts on the big world. Nature-inspired superhydrophobic surfaces provide a powerful platform for regulating droplet impact dynamics. The collision between classic phenomena of droplet impact and the advanced manufacture of superhydrophobic surfaces is lighting up the future. Accurately understanding, predicting, and tailoring droplet dynamic behaviors on superhydrophobic surfaces are progressive steps to integrate the droplet impact into versatile applications and further improve the efficiency. In this review, the progress on phenomena, mechanisms, regulations, and applications of droplet impact on superhydrophobic surfaces, bridging the gap between droplet impact, superhydrophobic surfaces, and engineering applications are comprehensively summarized. It is highlighted that droplet contact and rebound are two focal points, and their fundamentals and dynamic regulations on elaborately designed superhydrophobic surfaces are discussed in detail. For the first time, diverse applications are classified into four categories according to the requirements for droplet contact and rebound. The remaining challenges are also pointed out and future directions to trigger subsequent research on droplet impact from both scientific and applied perspectives are outlined. The review is expected to provide a general framework for understanding and utilizing droplet impact.

Compound Droplet Impact on a Thin Hydrophobic Cylinder

The impact of compound droplets on solid surfaces is a ubiquitous phenomenon that pervades both the natural and technological fields. A comprehensive understanding of the dynamics of the droplet impact on solid surfaces is therefore of paramount importance for a broad range of applications. In this study, we investigate the impact of a water-in-oil compound droplet on a thin hydrophobic cylindrical surface, with regard to the Weber number and cylinder dimensions. Owing to the prewetting effect of the oil, the droplet completely engulfs the cylinder during impact. The ensuing breakups of oil and water engender various unique impact outcomes, which are depicted via a phase map. The phase boundaries are described by analyzing the gravitational and drag forces exerted by the cylinder. A threshold value of the Weber number is found beyond which its effect on the azimuthal spreading process becomes less obvious. The distinctive axial spreading processes of oil and water are illustrated through high-speed imaging from both front and side perspectives, revealing that droplet oscillation is critically influenced by the Weber number. Our work elucidates the impact dynamics of compound droplets on curved surfaces, providing pivotal insights into related thermal management, droplet printing, and coating fabrication applications.

Jet or wet? Droplet post-impact regimes on concave contours

Droplet collision and subsequent spreading or wetting interactions with the solid substrate exhibit rich and interesting physics and are also important for various utilities. The fluid dynamics becomes more interesting and insightful when the wettability and geometry of the surface are tuned and altered. This study investigates the post-impact regimes of droplet impact on hydrophilic and superhydrophobic concave profile grooves (having dimensions comparable to that of the droplet). The post-collision hydrodynamics for such substrate-droplet system is three-dimensional, as in addition to droplet dynamics in the azimuthal direction, liquid jets may also be generated in the axial direction of the groove. Thereby the system may either lead to wetting or jetting, depending on the impact conditions. The effect of the impact Weber number (We) on the jet velocity, non-dimensional spreading width (γ) and non-dimensional south-pole film thickness (h*) has been probed and quantified. The observations reveal that the role of the wettability of the substrate is more profound in the recoiling stage than in the spreading stage, because inertial forces dominate in the latter. It is also noted that the spreading width increases and south-pole height decreases with increasing the impact Weber number. The opposite trend is noted upon increasing the groove concavity by altering just one dimension of the groove. The jet velocity is found to be the highest immediately after the impact and eventually decreases in a nonlinear fashion. Further, it has been found that the jet velocity increases with increasing the impact Weber number and that this effect is more prominent for superhydrophobic surfaces. A semi-analytical framework has been proposed to predict the jet velocity evolution in terms of governing Weber (We) and capillary (Ca) numbers. The predictions of the proposed model are in good agreement with the experimental observations.

A Machine Learning Approach for Predicting the Maximum Spreading Factor of Droplets upon Impact on Surfaces with Various Wettabilities

Drop impact on a dry substrate is ubiquitous in nature and industrial processes, including aircraft de-icing, ink-jet printing, microfluidics, and additive manufacturing. While the maximum spreading factor is crucial for controlling the efficiency of the majority of these processes, there is currently no comprehensive approach for predicting its value. In contrast to the traditional approach based on scaling laws and/or analytical models, this paper proposes a data-driven approach for estimating the maximum spreading factor using supervised machine learning (ML) algorithms such as linear regression, decision tree, random forest, and gradient boosting. For this purpose, a dataset of hundreds of experimental results from the literature and our own—spanning the last thirty years—is collected and analyzed. The dataset was divided into training and testing sets, each representing 70% and 30% of the input data, respectively. Subsequently, machine learning techniques were applied to relate the maximum spreading factor to relevant features such as flow controlling dimensionless numbers and substrate wettability. In the current study, the gradient boosting regression model, capable of handling structured high-dimensional data, is found to be the best-performing model, with an R2-score of more than 95%. Finally, the ML predictions agree well with the experimental data and are valid across a wide range of impact conditions. This work could pave the way for the development of a universal model for controlling droplet impact, enabling the optimization of a wide variety of industrial applications.

How an Oxide Layer Influences the Impact Dynamics of Galinstan Droplets on a Superhydrophobic Surface

When exposed to air, gallium-based alloys rapidly form a thin oxide layer with viscoelasticity and high adhesion. Although previous work demonstrated that an oxide layer inhibits liquid metal droplet rebound, there is still a lack of a quantitative study to elaborate how an oxide layer affects the impact dynamics. To address this issue, we experimentally investigate Galinstan droplet impingement on a superhydrophobic CuO nanoblade surface and physically explain the difference in the dynamic characteristics of oxidized and unoxidized droplets. Experimental results show that the effect of an oxide layer becomes prominent during the retraction phase. The high adhesion significantly suppresses retraction and rebound, while the elastic response prevents a droplet from sufficiently stretching and maintains the stability of the morphology. More importantly, we systematically and quantitatively explore the influence of an oxide layer on several critical impact parameters, which contributes to a comprehensive understanding of the impact dynamics of liquid metal droplets. It is indicated that an oxide layer has little effect on the maximum spreading factor and spreading time, whereas it causes a 45% reduction of the restitution coefficient and a 36% increase in contact time. Notably, the scaling laws that describe the critical impact parameters of unoxidized droplets show good agreement with the ones known from ordinary Newtonian fluids.