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The dynamics of a droplet impacting a planar solid substrate was captured through a comprehensive three-dimensional computational analysis. The ANSYS Fluent software was employed to implement the dynamic contact angle model in conjunction with the volume of fluid (VOF) technique. The simulation has been carried out for a single drop impact as well as drop-on-drop impact. The drop-on-drop impact study has been carried out in both coaxial and offset impact cases. The effect of offset has also been studied on the droplet evolution after impacting the sessile droplet resting on a solid surface. The evolution of droplet, including spreading, receding and bounce off, is found to be accelerated in the case of single droplet impact as compared to the coaxial drop-on-drop impact. It is observed that for the drop-on-drop impact, the combined droplet bounces off the surface earlier in the coaxial impact case. The spreading diameter reaches its maxima earlier at the higher offset values. The combined droplet gets detached from the surface at the lower offset value while it remains attached to the surface at the higher offset values.

The current study reports the phenomenon of drop impacts on a hydrophobic surface in the substrate deposition regime (non-splashing), focusing on the characterization of each stage upon impact and different non-dimensional parameters involved such as spreading factor, recoil height and the durations of several phases. The results indicate that the drop dynamics is determined by an interplay of drop inertia, viscosity and surface tension. Apart from Reynolds number (Re) and Weber number (We) which are conventionally used to characterize drop impacts, a new non-dimensional impact parameter, ξ (= 〖We〗^(1/4) 〖Re〗^(1/5)) is introduced, and it is found out that the spreading factor and the different non-dimensional phase durations involved in the drop impact dynamics on a hydrophobic surface, scale fairly well with this newly defined impact parameter. Further, systematic studies into the non-dimensional durations of each phase upon impact, spreading factor and recoil factor (i.e. non-dimensional recoil height) with respect to different non-dimensional parameters are reported.

There are various situations of drop impact on solid surfaces widely occurred in natural phenomenon or used in different industrial applications. However, comparing and classifying these drop impact situations is not easy due to different states of the parameters affecting drop impact dynamics. In this article, a unified transformation framework is proposed to study various situations of vertical/oblique drop impact on horizontal/inclined stationary/moving flat surfaces with/without a crossflow. This simple framework consists of a coordinate with normal and tangential axes on a horizontal stationary surface. For each drop impact situation, the drop velocity, gravitational acceleration, possible induced flow due to the moving surface, and possible crossflow are transformed into the framework. Comparing the transformed versions of considered drop impact situations facilitates identification of their physical similarities/differences and determines which situations (and under what conditions) lead to identical results and can be used interchangeably. Although common situations of drop impact on moving surfaces (having tangential component of surface velocity) lead to asymmetric drop spreading, the possibility of symmetric drop spreading on moving surfaces is demonstrated and analyzed using the proposed transformation framework. This interesting possibility means that for related production lines or experimental setups, where symmetrical drop spreading is required, the surface does not need to be stationary. In such applications/setups, the use of moving surfaces (rather than stationary surfaces) can considerably accelerate the symmetric drop impact process. Our simulation results of several of the considered drop impact situations well confirm the facilities/predictions of the proposed transformation framework.

In this paper, drop reliability of various PBA (printed board assembly) mounting structures is investigated and compared. Then, we built SAC305 (Sn3.0Ag0.5Cu) interconnects for BGA (ball grid array) package failure model to evaluate the drop impact reliability of handheld devices. In order to simulate actual behavior of the solder joint under the drop impact load of handheld devices, we perform explicit full FEA (finite element analysis) modeling. However, this takes a lot of computing time because of the large aspect ratio of element size between solder joints and other structures such as PCB (printed circuit board) and electronic packages. Therefore, an effective way to represent solder interconnects for FEA is needed which would be relatively simpler yet detailed. Comparable board-level drop tests are conducted after equipping test vehicles with various fixtures considering PBA mounting structures, which make it possible to apply different loading conditions to BGA packages. The results show different drop impact life for solder interconnects depending on the mounting design of the PBA. Particularly, the solder interconnect of the component located at the middle of the PCB exhibits the shortest impact life where the highest tensile stress occurs. Also, the mounting design restraining PBA deflections shows better reliability under the drop impact loading. Sequentially, simulating with a PBA composed of the BGA package and the PCB is considered to assess the feasibility of the solder ball failure modeling when the drop impact load is applied. Especially, for the modeling of the solder balls, detailed solid model and simple beam model are compared regarding computational efficiency and numerical accuracy. We found that the simple beam model significantly shortens computational time from 110 h to less than an hour. Accordingly, the feasibility of the beam model for the solder balls is shown by correlating the stress level and the drop impact life obtained from the experiments.

The capillary wave and initial spreading velocity in the spreading phase of drop impacting on a glass surface are studied experimentally, while the drop photos are obtained by using a high-speed video camera, which can catch up to 9000 images per second with an exposure time of 4 µs. A wide range of impact velocities are studied by varying the fall height, showing different capillary waves. All attention is given to the capillary wave and initial spreading velocity of drop. A non-linear relation between the wavelength and the impact velocity is found experimentally. Combined with the minimum spreading radius theory, a linear relation between the initial spreading velocity and the impact velocity is acquired.

The rim breakup of an impacting drop is experimentally investigated by comparing the impacts on superheated and superhydrophobic surfaces. The objective of the present study is to experimentally examine whether the Bo = 1 criteria holds for the rim breakups of drops impacting on the surfaces. A transparent sapphire plate was heated to achieve the Leidenfrost impact, which enables us to observe with a high-speed camera from below. The characteristics of the rim breakup were evaluated quantitatively using a particle tracking velocimetry method for both the rim and the drops generated. As a result, we clarified that Bo of the rim increases in the spreading phase and marks the highest value of 0.5 on a superheated surface, which is smaller than that on a pillar, where Bo ≈ 1. On a superhydrophobic surface, the highest Bo was 1.2, which is smaller than that on a wettable solid surface, 2.5, but close to the value on a pillar. We also revealed that diameters of generated drops collapse on a master curve when plotted as a function of pinch-off time for both the impacts on superheated and superhydrophobic surfaces.

Numerical solutions of high-speed microdroplet impact onto a smooth solid surface are computed, using the interFoam VoF solver of the OpenFOAM(R) CFD package. Toward the solid surface, the liquid microdroplet is moving with an impinging gas flow, simulating the situation of ink droplets being deposited onto substrate with a collimated mist jet in the Optomec Aerosol Jet(R) printing process. For simplicity and computational efficiency, axisymmetric incompressible flow is assumed here for the free-surface fluid dynamic problem. The computed values of maximum spread factor [xi], for the range of parameters relevant to Aerosol Jet(R) printing, are found in good agreement with some of the correlation formulas proposed by previous authors in the literature. A formula of improved accuracy is then obtained for evaluating [xi] of Aerosol Jet(R) deposited droplets, by combining selected formulas from different authors with appropriate modifications. The computational results also illustrate droplet impact dynamics with lamella shape evolution throughout the spreading, receding-relaxation, and wetting equilibrium phases, consistent with that observed and described by many authors. This suggests a scale-invariant nature of the basic droplet impact behavior such that experiments with larger droplets at the same nondimensional parameter values may be applicable for studying microdroplet impact dynamics. Significant free surface oscillations can be observed with low viscosity droplets. The border line between free surface oscillations and aperiodic creeping to the capillary equilibrium shape appears at Oh ~ 0.25. Droplet bouncing after receding is prompted with large contact angles at solid surface (as consistent with findings reported in the literature), but can be suppressed by increasing the droplet viscosity.

Significance Liquid drops always splash when they impact smooth surfaces with high enough speeds. This common phenomenon is crucial in many important fields such as agriculture, printing, surface coating, and spray cooling. However, despite extensive studies over one century, the origin of splashing remains a big mystery. Combining experiment with model, we show that the air trapped under the liquid drop forms a special flow within a nanoscale gap. This airflow produces a stress 10 times stronger than the common airflow and generates small Kelvin–Helmholtz instabilities that trigger splash. Our model agrees quantitatively with the experimental verifications and brings a fundamental understanding to the general phenomenon of drop splashing on smooth surfaces. When a fast-moving drop impacts onto a smooth substrate, splashing will be produced at the edge of the expanding liquid sheet. This ubiquitous phenomenon lacks a fundamental understanding. Combining experiment with model, we illustrate that the ultrathin air film trapped under the expanding liquid front triggers splashing. Because this film is thinner than the mean free path of air molecules, the interior airflow transfers momentum with an unusually high velocity comparable to the speed of sound and generates a stress 10 times stronger than the airflow in common situations. Such a large stress initiates Kelvin–Helmholtz instabilities at small length scales and effectively produces splashing. Our model agrees quantitatively with experimental verifications and brings a fundamental understanding to the ubiquitous phenomenon of drop splashing on smooth surfaces.

Many biological surfaces of animals and plants (e.g., bird feathers, insect wings, plant leaves, etc.) are superhydrophobic with rough surfaces at different length scales. Previous studies have focused on a simple drop-bouncing behavior on biological surfaces with low-speed impacts. However, we observed that an impacting drop at high speeds exhibits more complicated dynamics with unexpected shock-like patterns: Hundreds of shock-like waves are formed on the spreading drop, and the drop is then abruptly fragmented along with multiple nucleating holes. Such drop dynamics result in the rapid retraction of the spreading drop and thereby a more than twofold decrease in contact time. Our results may shed light on potential biological advantages of hypothermia risk reduction for endothermic animals and spore spreading enhancement for fungi via wave-induced drop fragmentation.

Raindrop impact on infected plants can disperse micron-sized propagules of plant pathogens (e.g., spores of fungi). Little is known about the mechanism of how plant pathogens are liberated and transported due to raindrop impact. We used high-speed photography to observe thousands of dry-dispersed spores of the rust fungus Puccinia triticina being liberated from infected wheat plants following the impact of a single raindrop. We revealed that an air vortex ring was formed during the raindrop impact and carried the dry-dispersed spores away from the surface of the host plant. The maximum height and travel distance of the air-borne spores increased with the aid of the air vortex. This unique mechanism of vortex-induced dispersal dynamics was characterized to predict trajectories of spores. Finally, we found that the spores transported by the air vortex can reach beyond the laminar boundary layer of leaves, which would enable the long-distance transport of plant pathogens through the atmosphere.