Session M39: Drops, Bubbles, and Interfacial Fluid Mechanics I

Condensed droplet jumping: Capillary to inertial energy transfer

When condensed droplets coalesce on a superhydrophobic nanostructured surface, the resulting droplet can jump from the surface due to the release of excess surface energy. This behavior has been shown to follow a simple inertial-capillary scaling. However, questions remain regarding the nature of the energy conversion process linking the excess surface energy of the system before coalescence and the kinetic energy of the jumping droplet. Furthermore, the primary energy dissipation mechanisms limiting this jumping behavior remain relatively unexplored. In this work, we present new experimental data from a two-camera setup capturing the trajectory of jumping droplets on nanostructured surfaces with a characteristic surface roughness length scale on the order of 10 nm. Coupled with a model developed to capture the main details of the bridging flow during coalescence, our findings suggest that: 1. the excess surface energy available for jumping is a fraction of that suggested by simple scaling due to incomplete energy transfer, 2. internal viscous dissipation is not a limiting factor on the jumping process at droplet sizes on the order of 10 $\mu$m and 3. jumping performance is strongly affected by forces associated with the external flow and fields around the droplet. This work suggests bounds on the heat transfer performance of superhydrophobic condensation surfaces.   

How does an air film evolve into a bubble during drop impact?

When a liquid drop impacts on a solid substrate, a tiny air film is generally entrapped between the drop and the substrate and eventually evolves into a bubble by surface energy minimization. We investigated how air evolves into a bubble during drop impact using ultrafast x-ray phase-contrast imaging that enables us to track the detailed morphological changes of air with high temporal and spatial resolutions. We found that the evolution takes place through complicated three stages: inertial retraction of the air film, contraction of the top air surface into a toroidal bubble, and pinch-off of a daughter droplet inside the bubble. The collapse and the pinch-off can be explained by energy convergence that is associated with Ohnesorge number (Oh) regarding capillary waves and viscous damping. We measured a critical Oh number, Oh* $\sim$ 0.026 $\pm$ 0.003, above which the generation of the daughter droplet is suppressed. Interestingly we found that the bubble is detached favorably from wettable surfaces, which suggests a feasible way to eliminate bubbles for many applications by controlling surface wettability. The threshold angle for bubble detachment was measured as $\sim$ 40 $\pm$ 5$^{\circ}$ for water, which agrees with a geometrical estimation.   

Swirls and splashes: air vortices created by drop impact

A drop impacting a solid surface with sufficient velocity will splash and emit many small droplets. While liquid and substrate properties are clearly important for determining the splashing threshold, it has been shown that removing the ambient air suppresses splashing completely [1]. However, the mechanism underlying how the surrounding gas affects splashing remains unknown. As has been recently shown, there is no air beneath the liquid that could cause the splash [2] -- thus where does the air matter? We use modified Schlieren optics combined with high-speed video imaging to visualize the air vortices created by the rapid spreading of the drop after it hit the substrate. In the first moments after impact, these vortices remain bound to the spreading drop, creating a low-pressure zone that travels with the advancing lamella. At a later time, after the occurrence of the splash, the vortices detach from the drop. We discuss possible connections between the forces generated by the vortices on the liquid lamella and the initiation of a splash. [1] L. Xu, W. W. Zhang and S. R. Nagel, Phys. Rev. Lett. 94, 184505 (2005) [2] M. M. Driscoll and S. R. Nagel, Phys. Rev. Lett. 107, 154502 (2011)   

Stability of electrically charged toroidal droplets in a viscous liquid.

Droplets and bubbles are spherical due to surface tension. As a result, making non spherical droplets and understanding their evolution is a challenge. Nevertheless, we were able to develop a method to generate toroidal droplets in a viscous liquid and study their stability. Recently, we have extended this method to generate charged toroidal droplets suspended in an electrically insulating and highly viscous liquid, and have studied the evolution of these droplets subject to constant charge or constant voltage constraints. In this talk I will be presenting the initial results on the stability of charged toroidal droplets.   

Clapping wet hands: dynamics of a fluid curtain

Droplets splash around when a fluid volume is quickly compressed. This has been observed during common activities such as kids clapping with wet hands. The underlying mechanism involves a resting fluid volume being compressed vertically between two objects. This compression causes the fluid volume to be ejected radially, thereby generating fluid ligaments and droplets at a high speed. In this study, we designed and performed experiments to observe the process of ligament and drop formation while a fluid is squeezed. A thicker rim at the outer edge forms and moves after the squeezing, and then becomes unstable and breaks into smaller drops. We compared experimental measurements with theoretical models over three different stages; early squeezing, intermediate ejection, and later break-up of the fluid. We found that drop spacing set by the initial capillary instability does not change in the course of rim expansion; consequently final ejected droplets are very sparse compared to the size of the rim.   

Electric Charging Effects on Condensed Droplet Jumping

When condensed droplets coalesce on a superhydrophobic surface, the resulting droplet can jump due to the conversion of surface energy into kinetic energy. This frequent out-of-plane droplet jumping has the potential to enhance condensation heat transfer. Furthermore, for more than a century, researchers have shown that droplet-surface interactions can be dominated by electrostatic charge buildup. In this work, we studied droplet jumping dynamics on nanostructured copper oxide and carbon nanotube surfaces coated with tri-chloro silane and PFDA hydrophobic coatings, respectively. Through analysis of droplet trajectories and terminal velocities under various electric fields (0 -- 50 V/cm), we show that condensation on these surfaces having both conducting and insulating substrates results in a buildup of positive surface charge (H$^{\mathrm{+}})$ due to dissociated water ion adsorption on the superhydrophobic coating. Consequently, an accumulation of the opposite charge (OH$^{\mathrm{-}})$ occurs on the condensing droplet interface, which creates an attractive force between the jumping droplet and the condensing surface. Using this knowledge, we demonstrate a novel condensation mechanism whereby an external electric field is used to oppose the droplet-surface attraction, further enhancing the coalescing droplet jumping frequency and overall surface heat transfer.   

Dynamics of a Disturbed Sessile Drop Measured by Atomic Force Microscopy

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r $\sim $ 20 - 30 $\mu $m) attached to an AFM cantilever is brought into contact with a sessile water drop. Immediately after the initial rise of the meniscus, the microsphere oscillates about a fixed average position while partially immersed in the liquid. The small (\textless\ 100 nm) oscillations of the interface are readily measured with AFM. The oscillations correspond to the resonance oscillation of the entire droplet. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 $\mu $L. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.   

How leaves survive falling raindrops

Plant surfaces found in nature often exhibit hydrophobic or hydrophilic wetting properties; a particular example is the surface of leaves. Most leaves are compliant enough to survive while being impacted by rain droplets. Here, we investigate this leaf-drop system exhibiting a unique system of coupled elasticity and drop dynamics. By replacing the leaf with a thin piezoelectric cantilever beam, we further measure and harvest this drop kinetic energy as a workable model for an energy-harvester from rain drops.   

The Vibrating Vapor Layer Beneath a Leidenfrost Drop

The levitation of a liquid drop above a hot surface is known as the Leidenfrost effect. Due to strong evaporation, a vapor layer forms beneath the drop that both levitates and thermally insulates the liquid, resulting in extremely long drop life times. The geometry of this vapor layer has been characterized using high-speed laser-light interference imaging [1], which showed spatial oscillations of the interface. Here we report the evolution of these oscillations using an algorithm we developed for identifying the interference fringes. From these fringes we extract the relative height profile of the vapor layer. We track the time evolution of the spatial-fluctuations and measure the absolute change in the average height of the drop over a time scale of seconds. Large, transient, azimuthal deformations to the bottom of the drop are correlated with the rapid escape of vapor and a change in height above the surface. We also observe and characterize a range of metastable star-like oscillations in the shape. \newline \newline [1] Burton et al., PRL 109, 074301 (2012).   

Coalescence of Two Drops Surrounded by an Outer Fluid

When two liquid drops make contact, a liquid bridge forms and then rapidly expands due to surface-tension forces that are divergent at the point where the drops first touch. This nonlinear process has received a lot of recent attention, especially for two liquid drops coalescing in vacuum or air. However, little is known about how the surrounding fluid influences the singularity when the two drops are surrounded by an external fluid with significant density or dynamic viscosity. We use a combination of high-speed imaging and an ultrafast electrical method to study coalescence in this regime. We find that even if the outer fluid is over 10 times more viscous than the fluid within the drops, the coalescence speed need not be affected, even near the singularity. In order to understand the nature of the flows in the surrounding fluid, we also study the limiting case of air bubbles coalescing inside a very viscous external liquid.   

Measurement of Bubble Size Distribution Based on Acoustic Propagation in Bubbly Medium

Acoustic properties are strongly affected by bubble size distribution in a bubbly medium. Measurement of the acoustic transmission becomes increasingly difficulty as the void fraction of the bubbly medium increases due to strong attenuation, while acoustic reflection can be measured more easily with increasing void fraction. The \textsc{ABS Acoustic Bubble Spectrometer}$^{\mathrm{\mbox{\textregistered }\copyright }}$, an instrument for bubble size measurement that is under development tries to take full advantage of the properties of acoustic propagation in bubbly media to extract bubble size distribution. Properties of both acoustic transmission and reflection in the bubbly medium from a range of short single-frequency bursts of acoustic waves at different frequencies are measured in an effort to deduce the bubble size distribution. With the combination of both acoustic transmission and reflection, assisted with validations from photography, the \textsc{ABS Acoustic Bubble Spectrometer}$^{\mathrm{\mbox{\textregistered }\copyright }}$ has the potential to measure bubble size distributions in a wider void fraction range.   

Experimental and Numerical Investigation of Pressure Wave Attenuation due to Bubbly Layers

In this work, the effects of dispersed microbubbles on a steep pressure wave and its attenuation are investigated both numerically and experimentally. Numerical simulations were carried out using a compressible Euler equation solver, where the liquid-gas mixture was modeled using direct numerical simulations involving discrete deforming bubbles. To reduce computational costs a 1D configuration is used and the bubbles are assumed distributed in layers and the initial pressure profile is selected similar to that of a one-dimensional shock tube problem. Experimentally, the pressure pulse was generated using a submerged spark electric discharge, which generates a large vapor bubble, while the microbubbles in the bubbly layer are generated using electrolysis. High speed movies were recorded in tandem with high fidelity pressure measurements. The dependence of pressure wave attenuation on the bubble radii, the void fraction, and the bubbly layer thickness were parametrically studied. It has been found that the pressure wave attenuation can be seen as due to waves reflecting and dispersing in the inter-bubble regions, with the energy absorbed by bubble volume oscillations and re-radiation. Layer thickness and small bubble sizes were also seen as having a strong effect on the attenuation with enhanced attenuation as the bubble size is reduced for the same void fraction.   

Bubble Augmented Propulsor Mixture Flow Simulation near Choked Flow Condition

The concept of waterjet thrust augmentation through bubble injection has been the subject of many patents and publications over the past several decades, and computational and experimental evidences of the augmentation of the jet thrust through bubble growth in the jet stream have been reported. Through our experimental studies, we have demonstrated net thrust augmentation as high as 70{\%}for air volume fractions as high as 50{\%}. However, in order to enable practical designs, an adequately validated modeling tool is required. In our previous numerical studies, we developed and validated a numerical code to simulate and predict the performance of a two-phase flow water jet propulsion system for low void fractions. In the present work, we extend the numerical method to handle higher void fractions to enable simulations for the high thrust augmentation conditions. At high void fractions, the speed of sound in the bubbly mixture decreases substantially and could be as low as 20 m/s, and the mixture velocity can approach the speed of sound in the medium. In this numerical study, we extend our numerical model, which is based on the two-way coupling between the mixture flow field and Lagrangian tracking of a large number of bubbles, to accommodate compressible flow regimes. Numerical methods used and the validation studies for various flow conditions in the bubble augmented propulsor will be presented.   

Dynamics of a Cylindrical Bubble between Two Parallel Plates for Biomedical Applications

Microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. To study and understand the mechanisms at play in such interactions, a full three- dimensional Boundary Element Method (BEM) has been developed to describe complex bubble deformations, jet formation, and bubble splitting. The present work aims at providing analytical validation for the three-dimensional BEM code, \textsc{3DynaFS}$^{\mathrm{\copyright }}$, when the dynamics of a bubble between two parallel plates is studied. The analytical equations of a cylindrical (2-D) bubble between two flat plates were derived without accounting for any shape deformation. Comparisons between the analytical model and the numerical model were carried out in scenarios where the shape of an expanding/collapsing bubble between two parallel plates is nearly cylindrical (large maximum equivalent bubble radius to plate gap ratio). Interestingly, both the analytical and the numerical methods predict a strong dependence of the bubble period on the plate size.   

Universality Results for Multi-phase Hele-Shaw Flows

Saffman-Taylor instability is a well known viscosity driven instability of an interface separating two immiscible fluids. We study linear stability of displacement processes in a Hele-Shaw cell involving an arbitrary number of immiscible fluid phases. This is a problem involving many interfaces. Universal stability results have been obtained for this multi-phase immiscible flow in the sense that the results hold for arbitrary number of interfaces. These stability results have been applied to design displacement processes that are considerably less unstable than the pure Saffman-Taylor case. In particular, we derive universal formula which gives specific values of the viscosities of the fluid layers corresponding to smallest unstable band. Other similar universal results will also be presented. The talk is based on the following paper.\\[4pt] [1] Prabir Daripa and Xueru Ding, ``Universal Stability Properties for Multi-Layer Hele-Shaw Flows and Application to Instability Control,'' {\it SIAM Journal of Applied Mathematics}, Vol 72, No. 5, pp. 1667-1685, 2012.