Session AH: Drops I: Impact

Thin Sheet Formation in Viscous Splash

Ambient air is crucial for creating a splash on smooth dry surfaces for both viscous and inviscid liquids.\footnote{L. Xu, \textit{Phys. Rev. E} \textbf{75}, 056316 (2007); L. Xu \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{94}, 184505 (2005).} In a viscous splash, the drop initially spreads in the form of a thick lamella until $t_{ejt}$ at which time it emits a thin fluid sheet. We have previously shown that $t_{ejt}$ is set by the ambient pressure and the liquid viscosity, and shows only a weak dependence on drop impact velocity and surface tension.\footnote{M. Driscoll \textit{et al.}, \textit{DFD 2008} BAPS.2008.DFD.AG.5} We have measured the thickness of the ejected sheet using absorption measurements of a dyed liquid drop. The ejected sheet has a thickness $\sim10 ~ \mu m$ that is approximately a tenth the thickness of the lamella preceding it. Using high-resolution, high-speed photography we have observed that as the ejected sheet expands, air bubbles are entrained into the trailing lamella. The bubble size increases as the lamella velocity decreases. Air entrainment ceases at a critical lamella velocity, $v_c \sim 1.2 ~ m/s$, which appears to be independent of drop impact velocity as well as the ambient pressure. At the critical velocity, the bubble radius is approximately 30 $\mu m$.   

The dependence of Mesler entrainment on Weber number and drop axis ratio

The impact of a water drop on a flat water surface can result in a variety of subsurface bubble formation events. Under certain conditions, the impact results in the formation of a large number of micron-scale bubbles, often referred to as Mesler entrainment. An experimental study is presented revealing that the existence of Mesler entrainment depends on both the drop Weber number and the drop axis ratio. Specifically, Mesler entrainment was observed for Weber numbers greater than 8 and less than 26. Within this range, the occurrence of Mesler entrainment was more frequent for axis ratios close to unity, that is for spherical drops. Drops of a prolate or oblate shape showed significantly less frequent Mesler entrainment. The working fluid for all experiments was water with a constant concentration of the soluble surfactant Triton X-100. This was done to avoid the influence of contaminating surfactants which tend to accrue when pure water is used as the working fluid.   

A computational study of high speed droplet impact

When a droplet impacts a solid surface at high speed, the contact periphery expands very quickly and liquid compressibility plays an important role in the initial dynamics and the formation of lateral jets. Impact results in high pressures that can damage the surface. In this study, we numerically investigated a high speed droplet impacts on a solid wall. The multicomponent Euler equations are computed by a FV-WENO scheme with an HLLC Riemann solver [Johnsen {\&} Colonius, J. Comp. Phys. (2006)] that accurately captures shocks and interfaces. Stiffened equation of state is employed to model of gas, liquid and solid components. In order to compare the available theory and experiments, 1D, 2D and axisymmetric solutions are obtained. The generated pressures, shock speeds, and the lateral jetting mechanism are investigated. In addition, the effect of target compliance is evaluated.   

Events before droplet splashing on a solid surface

A high velocity impact between a liquid droplet and a solid surface produces a splash. Classical observations traced the origin of this splash to a thin sheet of fluid ejected near the impact point, though the fluid mechanical mechanism leading to the sheet is not known. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. In this paper, we theoretically and numerically study the events within 1 $\mu$s of contact. The droplet initially tries to contact the substrate by either draining gas out of a thin layer or compressing it, with the local behavior described by a self similar solution of the governing equations. This similarity solution is not asymptotically consistent: forces that were initially negligible become relevant and dramatically change the behavior. Depending on the radius and impact velocity of the droplet, we show that the solution is overtaken by either the surface tension of the liquid--gas interface or viscous forces in the liquid. At low impact velocities surface tension stops the droplet from impacting the surface, whereas at higher velocities viscous forces become important before surface tension.   

Oscillating Effects on the Bubble Induced by A Free Falling Drop

The impact of a droplet on a liquid pool can result in different fantastic phenomena. Many investigations have been conducted since decades; however, none has been studied for the effects of oscillating drop on the big bubble induced by the impacting droplet since Worthington (1908). In the present study, big bubble induced by the droplet impact has been experimentally studied and systematically analyzed. Effects of impact velocity, drop size, oscillation parameters and depth of target liquid have been investigated and discussed. New characteristic regimes in the V (impact velocity)-d (diameter of droplet)-map have been discovered. Two geometry parameter oscillation parameters sharpness-ratio and offset-ratio of the free-falling droplet have been found to be the most important controlling parameters. Their results are revealed and compared in this study.   

Drop impact on sand: from donut to pie

We have studied the impact of water drops onto granular layers. Depending on the impact energy, various shapes are observed for the resulting craters. Experimental parameters that have been considered are : the size of the millimetric droplets; the height of the free fall, ranging from $1.5$~cm to $100$~cm; and, the depth of the granular layers, ranging from tenth of millimeters to a few centimeters. As the drop is impacting the sand layer, energy is dissipated and a splash of sand occurs. Meanwhile, surface tension, inertia and viscosity compete, leading to strong deformations of the drop which depend on the experimental conditions. Just after the drop enters into contact with the sand, imbibition takes place and increases the apparent viscosity of the fluid. Soon, the drop motion is stopped by this process. Images and fast-video recordings of the impact allowed us to draw scaling laws for the crater morphology and size.   

Suppressing Viscous Drop Splashing with Surface Roughness

The splashing of a liquid drop on a smooth, dry surface depends on a host of factors: the speed, surface tension, viscosity and size of the drop, but also, surprisingly, the pressure and molecular weight of the surrounding gas.\footnote{ L. Xu, W.W. Zhang, S.R. Nagel, PRL 94, 184505 (2005).}$^,$\footnote{ L. Xu, PRE 75, 056316 (2007).} In the case of a viscous drop splashing on a smooth surface, a thin sheet of fluid is first ejected from the rim of the expanding drop and then breaks up into droplets to form a splash.\footnote{M. Driscoll et al., BAPS DFD AG.00005 (2008).} When the surface is rough, different behavior, known as prompt splashing, may also be observed.$^{2,}$\footnote{ L. Xu, L. Barcos, and S.R. Nagel, PRE 76 066311 (2007).} Here we explore the splashing of a viscous liquid as the surface roughness, $R_a$, is varied. We find that a small degree of roughness, $R_a < 1 ~ \mu m$, can completely suppress the thin-sheet ejection occurring on smooth surfaces. The degree of roughness necessary for this suppression decreases with increasing viscosity. In some cases, the roughness is great enough to suppress the thin sheet, but insufficient to produce a prompt splash, thus suppressing the splash entirely.   

The effects of wind on the impact of a single drop on a water surface

The impact of single water drops on a water surface was studied experimentally in a wind tunnel. Water drops were generated from a needle oriented vertically from the top surface of the wind tunnel test section. The wind speed ranged from 0 to 10.0 m/s. After leaving the needle, the drops move downward due to gravity and downstream due to the effect of the wind, eventually hit a shallow pool of water on the bottom of the test section. The drop impacts were backlit with a halogen lamp and photographed with a high-speed movie camera at 1,000 frames per second. It is shown that the water drop obliquely impacts the water surface and the impingement angle relative to vertical increases with increasing wind speed. After the drop hits the water surface, a chain of secondary drops are formed and move in the leeward direction. This is followed by a stalk formation at the location of the water drop impact. It is found that the shape of the secondary-drop chain and the appearance of the stalk are markedly affected by wind speed. The effects of wind speed and initial drop size on a number of parameters, including the number, diameter and total mass of secondary drops were investigated. The dynamics of secondary drops in the presence of wind are discussed.   

Droplet impact on a porous substrate: a capillary tube model

The dynamics of impacting (spreading, penetrating) a droplet on a porous substrate, modeled by an array of capillary tubes, is studied numerically using diffuse interface methods. The absorption rate depends on the diameter ratio of the capillary tube to the droplet, wettability, and liquid properties. The flow dynamics is resolved by solving the Navier-Stokes equations and interface capturing is governed by the Cahn-Hilliard equation. Contact-angle hysteresis is included (Ding{\&}Spelt 2008) and the stress singularity at moving contact lines is relieved using a diffuse interface model (Seppecher 1996; Jaqcmin 2000). The model is validated by studying the evolution of a droplet initially resting on a porous substrate and by comparison to drop-impact experiments involving just one capillary tube (Kogan et al 2008). Comparisons with analytical solutions and results available in the literature (e.g. Hilpert {\&} Ben-David 2009) are presented. Through parametric simulations over relevant ranges of Reynolds and Ohnesorge numbers and contact angles, impact regime maps are derived.   

Impact of Droplets on a Vertical Capillary Tube

We experimentally study whether it is possible to force liquid impregnation of a porous media using the kinetics energy of an impacting drop. We study impregnation at the local scale and only consider a unique pore, a vertical glass capillary tube with thick walls. The forced impregnation is achieved with droplet of water impacting with an initial velocity on the tube. We focus both on forced impregnation of hydrophilic or hydrophobic capillary tubes. For small impact velocities, the classical results of impregnation are recovered. For large impact velocities, we observe new regimes due to the initial kinetics energy of the droplet. In particular, a liquid index disconnected from the upper part of the drop, which spreads on the horizontal flat surface, is observed both for the hydrophilic and hydrophobic tubes. To quantify the efficiency of the forced impregnation, we answer the following questions i) what is the volume of liquid eventually trapped within the porosity? ii) How deep this liquid is located in the pore?