Topological singularities occur in a broad range of physical systems, including collapsing stars and pinching fluid interfaces. They are important for being able to concentrate energy into a small region. Underwater air bubbles in particular appear in many practical applications, including new technologies to reduce skin drag on cargo ships. Previous theories show that just before an air bubble pinches off, the neck looks like a cylinder at its very smallest point. Unusually, however, the neck approaches this shape so gradually that the theoretical cylinder solution is not reached in practice; the singularity spends its entire lifetime in a transient phase. Therefore, in order to understand the evolution, we study the transient effects in detail. This paper details the simulation results of bubbles with initial conditions far from the cylindrical solution: squat, up--down asymmetric neck shapes, with imposed vertical flow. We find that the asymmetry is transient: the neck quickly shifts vertically to become up--down symmetric. Importantly, we find that the resulting symmetric singularity is a blend of the initial top and bottom sides, with a weighting factor that is tunable by adjusting the airflow through the neck. This effect should have implications for the later stages of evolution, including the generation of satellite bubbles and the formation of the Worthington jet.
Approach to Universality in Axisymmetric Bubble Pinch-Off
夹断的轴对称气泡包围的无粘流体进行了比较，在四个物理实现：（i）空腔崩溃后的冲击盘，（ii）气泡通过小孔注入，（iii）气泡破裂的应变流，和（iv）气泡与最初的颈缩形状。我们的边界积分模拟表明，所有系统最终都遵循以[Eggers et al.，PRL 98，094502（2007）]。然而，这个最终制度的开始的时间尺度被发现根据所讨论的系统的数量级而变化：而对于冲击盘，它是在毫秒范围内，对于气体注射针的通用行为集在夹断之前只有几微秒。这些发现调和了最近文献中关于气泡夹断的普遍性的不同观点。
The impact of droplets on a liquid pool is ubiquitous in nature and important in many industrial applications. A droplet impacting on a liquid pool can result in the pinch-off of a regular bubble or entrap a large bubble under certain impact conditions. In this study, the cavity deformation and the bubble entrapment during the impact of droplets on a liquid pool are studied by combined experimental measurements and numerical simulations. The time evolution of the free surface profile obtained in the numerical simulation is in good agreement with the experimental results. The cavity created by …
The stability of high-end piezo-acoustic drop-on-demand (DOD) inkjet printing is sometimes compromised by the entrainment of an air bubble inside the ink channel. Here, bubble pinch-off from an acoustically driven meniscus is studied in an optically transparent DOD printhead as a function of the driving waveform. We show that bubble pinch-off follows from low-amplitude higher-order meniscus oscillations on top of the global high-amplitude meniscus motion that drives droplet formation. In a certain window of control parameters, phase inversion between the low and high frequency components leads…
Analytical considerations and potential flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, $r_n$, decreases as $τ\propto r_n^2 \, (-\ln{r_n^2})^{1/2}$, where $τ$ is the time to break-up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a $r_n\proptoτ^{1/3}$ power law. These findings are verified experimentally.
We study a model for the evolution of an axially symmetric bubble of inviscid fluid in a homogeneous porous medium otherwise saturated with a viscous fluid. The model is a moving boundary problem that is a higher-dimensional analogue of Hele-Shaw flow. Here we are concerned with the development of pinch-off singularities characterised by a blow-up of the interface curvature and the bubble subsequently breaking up into two; these singularities do not occur in the corresponding two-dimensional Hele-Shaw problem. By applying a novel numerical scheme based on the level set method, we show that sol…
The oscillatory flows present in an inkjet printhead can lead to strong deformations of the air-liquid interface at the nozzle exit. Such deformations may lead to an inward directed air jet with bubble pinch-off and the subsequent entrainment of an air bubble, which is highly detrimental to the stability of inkjet printing. Understanding the mechanisms of bubble entrainment is therefore crucial in improving print stability. In the present work, we use ultrafast X-ray phase-contrast imaging and direct numerical simulations based on the Volume-of-Fluid method to study the mechanisms underlying t…
To further understand their nature, micro cavitation bubbles were systematically diffused around the exterior of a test body (tube) fully submerged in a water tank. The primary purpose was to assess the feasibility of applying micro cavitation as a means of depth control for underwater vehicles, mainly but not limited to submarines. Ideally, the results would indicate the use of micro cavitation as a more efficient alternative to underwater vehicle depth control than the conventional ballast tank method. The current approach utilizes the Archimedes' principle of buoyancy to alter the density o…
We study singular jets from the collapse of drop-impact craters, when the drop and pool are of different immiscible liquids. These jets emerge from a dimple at the bottom of the rebounding crater, when no bubble is pinched off. The parameter space is considerably more complex than for identical liquids, revealing intricate compound-dimple shapes. In contrast to the universal capillary-inertial drop-regime, where the pinch-off neck radius scales as $R\sim t^{2/3}$, a purely inertial air-dimple has $R \sim t^{1/2}$ and is sensitive to initial and boundary conditions. Capillary waves can therefor…
Acoustic Signatures of Pinch-Off Cavities During Water-Entry
College of Shipbuilding Engineering, Harbin Engineering University（哈尔滨工程大学船舶工程学院）；Nanhai Institute of Harbin Engineering University（哈尔滨工程大学南海研究院）；Southampton Ocean Engineering Joint Institute, Harbin Engineering University（哈尔滨工程大学南安普顿海洋工程联合学院）；National Key Lab of Ship Structural Safety, Harbin Engineering University（哈尔滨工程大学船舶结构安全国家重点实验室）
We report a detailed experimental characterization of the periodic bubbling regimes that take place in an axisymmetric air-water jet when the inner air stream is forced by periodic modulations of the pressure at the upstream air feeding chamber. When the forcing pressure amplitude is larger than a certain critical value, the bubble formation process is effectively driven by the selected frequency, leading to the formation of nearly monodisperse bubbles whose volume is reduced by increasing the forcing frequency. We reveal the existence of two different breakup modes, M1 and M2, under effective…
All children enjoy blowing soap bubbles that also show up in our bath and when we wash dishes. We analyze the thinning and breaking of soap bubble neck when it is stretched. To contrast with the more widely studied film whose boundaries are open, we concentrate on the bubble with a conserved air volume V. Like film (F), non-equilibrium state can be divided into four regimes for bubble (B): (1) roll-off, (2) cusp approach, (3) pinch-off and (4) breakup. We establish the existence of self-similarity in F-1, B-1 and B-3, and universal property in F-1 and B-1 for the profile of soap membrane. The …
