Dynamics of Drops/Bubbles Studied by Ultrafast X-ray Imaging

Abstract

Drops and bubbles are small masses of liquid and gas, respectively, bounded by other phases or materials. They are ubiquitous everywhere in nature and our daily life, for example, in form of raindrops, tap water, breaking waves, liquid jets, foam, boiling water, carbonated drink, and cavitation bubbles. Different from typical fluid flow, the behaviors of drops and bubbles are not simply described by Newton’s law, instead unusual, unexpected, and interesting. For these reasons, the behaviors of drops and bubbles have attracted many scientists for a long time, however, many phenomena related with them are still remain a puzzle.The most remarkable feature for the dynamics of drops and bubbles is that surface tension plays very important roles in their behaviors. First of all, they prefer to maintain spherical shapes as a result of surface energy minimization. For that reason, when two or more drops (bubbles) get together, they easily coalesce into one mass. Moreover we can see that a long column of liquid (gas) can split into several drops (bubbles) and form liquid (bubble) jets. The internal structure and the dynamics of liquid jets or sprays are also important issues in industrial applications. Because their dynamics are extremely fast and complex, however, many questions still remain unsolved now.One of the challenging issues of drops & bubbles is direct visualization of the structure or flow behaviors of the fluids. Different from the solid state physics, the visualization has been relying on the observations by naked eyes or imaging with optical microscopy for a long time. However, it is difficult to acquire exact images or sufficient information of the drops and bubbles with conventional visible-light imaging techniques because of the several critical problems, such as high scattering including reflection and refraction of the visible light, a short depth of focus of optical lenses, and limitation of the spatial resolution (~1 μm) arising from long wavelength (400nm < λ < 700nm) of the visible lights.In this thesis, important issues related with drops and bubbles are studied, including air bubble entrapment during drop impact on solid / liquid surfaces, bubble bursting and jet formation, vortex rings made by drop impact, and coarsening law of 3-D liquid foam. The key idea is ultrafast X-ray imaging which enables direct visualizing of air/liquid interfaces in high spatial and temporal resolutions thanks to its high penetration ability, little refraction, and strong irradiance.First, with ultrafast phase-contrast X-ray imaging, the profile of air layer during drop impact on solid surface is directly visualized. A complicated evolution process of the air is identified that it consists of three stages: inertial retraction of the air film, collapse of the top air surface into a bubble, and pinch-off of a daughter droplet in the bubble. Energy convergence during retraction drives the collapse and pinch-off of a daughter droplet. The wettability of the solid surface affects the detachment of the bubble, suggesting a bubble elimination method in many drop-impact applications.Second, the evolution of air during drop impact on liquid surface is also studied. It is revealed that the evolution of the air film does not only simply contracts in radius, but shows many unexpected dynamic singularities. The retraction of the film radius crosses from inertial to viscous regime on the increase of liquid viscosity. During the retraction, the strong azimuthal instability develops along the thin rim of the air film, and a daughter droplet is pinched-off by convergence of capillary waves. Moreover, the bubble breaks up into two bubbles by inertia of the retraction and Rayleigh instability. A phase diagram is demonstrated to characterize the various types of morphological air evolutions in terms of surface tension, viscous dissipation and inertial force. Third, it is demonstrated that the liquid jet formation is inhibited by bubble size

a jet is not formed from bursting bubbles smaller than a critical size. A phase diagram for jetting and the absence of jetting is built for the first time. The size limitation of jetting is critically dependent on the momentum transfer from capillary waves, as described by a critical Ohnesorge number below which jetting occurs. The results demonstrate that jetting in bubble bursting is analogous to pinching-off in liquid coalescence. Next, the formation of vortex rings during drop impact is clearly visualized for the first time. It is found that the critical conditions for vortex ring formation are small Ohnesorge number, as Oh < 0.011. The capillarity induced lamella that independently formed without merging with the ejecta is another requirement. It is also shown that the circulation dynamics of the vortex core well follows the Stoke’s drag, enabling prediction of the circulation angle as a function of time. The decrease of vorticity with time shows a large oscillation due to the spreading of the drop.Finally, using newly developed fast tomography, it is demonstrated that the growth of 3-D infant foams is in the self-similar regime, as observed for 2-D foams. The growth rate and distributions of bubble sizes and face numbers show scale-invariance with time.As shown in this thesis, X-ray imaging has a great potential and performances in study of drops and bubbles. It is still under development by many scientists and technicians. I believe that X-ray imaging may open great opportunities to much better understand the underlying physics of drops and bubbles.