Axisymmetric bubble pinch-off at high Reynolds numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau 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 rn proportional to tau1/3 power law. These findings are verified experimentally.     

Satellites in the inviscid breakup of bubbles

In this Letter, we stress the essential role played by gas inertia in the breakup of gas bubbles. Our results reveal that, whenever the gas to liquid density ratio Lambda=rhog/rhol is different from zero, tiny satellite bubbles may be formed as a result of the large gas velocities that are reached close to pinch-off. Moreover, we provide a closed expression for the characteristic satellite diameter, which decreases when decreasing Lambda and which shows order of magnitude agreement with the micron-sized satellite bubbles observed experimentally.     

Giant bubble pinch-off

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a downward jet. Only in the limiting case of large Froude numbers does the purely inertial scaling h(-logh)(1/4) proportional tau(1/2) for the neck radius h [J. M. Gordillo et al., Phys. Rev. Lett. 95, 194501 (2005)] become visible. For any finite Froude number the collapse is slower, and a second length scale, the curvature of the void, comes into play. Both length scales are found to exhibit power-law scaling in time, but with different exponents depending on the Froude number, signaling the nonuniversality of the bubble pinch-off.     

Detailed simulation of primary atomization mechanisms in Diesel jet sprays (isolated identification of liquid jet tip effects)

In this study, the atomization characteristics of Diesel jet front tip have been investigated to elucidate the physical mechanisms by detailed numerical simulation. The computations are carried out with the finest grid resolutions ever that can resolve the final droplet generation by surface tension. The numerical methods are based on level-set interface tracking. The methods were validated by test cases and the grid resolution survey shows that the resolutions for the present study are sufficient. The present flow setup excludes nozzle disturbances to investigate how the disturbances from the liquid jet front would lead to atomization where the liquid jet impacts against the quiescent gas. The liquid jet front becomes an umbrella-like shape. From the front umbrella tip edge, ligament breakup first occurs. Ligament breakup is strongly correlated with the gas motion in the vicinity. The gas region behind the front is highly disturbed by atomization. By the gas recirculation motion here, air and some droplets are entrained and mixed. Also, the disturbances are fed back to the front umbrella by this motion and become synchronized with the breakup. Droplet pinch-off is mainly in the short-wave mode, but some ligaments are elongated by local gas stretch to finally have a long-wave mode shape, namely a mode shift occurs. The above findings of liquid jet front umbrella formation, atomization at the umbrella edge, mixing and atomization loop in the recirculation flow region and droplet generation mode give an insight to the modeling of droplet generation in actual sprays.     

Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761–780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed.     

Role of dimensionality and axisymmetry in fluid pinch-off and coalescence

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.     

Scaling and instabilities in bubble pinch-off

We have used a 100 000 frame-per-second video to analyze the pinch-off of nitrogen gas bubbles in fluids with a wide range of viscosity. If the external fluid is highly viscous (eta(ext)>100 cP), the bubble neck radius is proportional to the time before break, tau, and decreases smoothly to zero. If the external fluid has low viscosity (eta(ext)<10 cP), the radius scales as tau(1/2) until an instability develops in the gas bubble, which causes the neck to rupture and tear apart. Finally, if the viscosity of the external fluid is in an intermediate range, an elongated thread is formed, which breaks apart into micron-sized bubbles.     

气体中心式离心喷嘴喷雾实验与三维仿真

在实验的基础上, 基于RNG k-ε模型对常压下气体中心式同轴离心(gas-centered swirl coaxial,GCSC)喷嘴喷雾形态和破碎模式进行了三维仿真研究。采用网格自适应加密(adaptive mesh refinement,AMR)技术、耦合水平集和流体体积(coupled level-set and volume of fluid, CLSVOF)方法对气液界面进行捕捉。结果表明, 液体质量流率($\dot{m}_{\mathrm{l}}$)不变, 随着气体质量流率($\dot{m}_{\mathrm{g}}$)的增加, 中心气流的引射作用增强, 液膜内外压差增大, 雾化锥角减小, 并对其流动特性进行了分析; 而$\dot{m}_{\mathrm{g}}$不变时, 液膜在喷嘴出口的径向速度与切向速度随$\dot{m}_{\mathrm{l}}$的增大而增大, 导致雾化锥角增大。同时根据气液质量流率比(gas-liquid mass flow rate,GLR), 将喷雾的破碎模式分为穿孔破碎、气泡破碎和气动破碎。      

液体横向射流在气膜作用下的破碎过程

为了研究液体横向射流在气膜作用下的破碎过程,采用背景光成像技术及VOF TO DPM方法进行了实验研究和仿真研究,模拟介质为水和空气.研究结果表明,液体射流在气膜作用下主要存在两种破碎过程:柱状破碎和表面破碎.Rayleigh-Taylor(R-T)不稳定性产生的表面波是液体射流发生柱状破碎的主要原因,气流穿透表面波的波谷导致射流柱破碎,破碎后的液丝沿流向逐渐发展呈带状分布.Kelvin-Helmholtz(K-H)不稳定性产生的表面波是液体射流发生表面破碎的主要原因,液丝和液滴从射流表面剥离.局部动量比对液体横向射流的破碎过程具有重要影响,当局部动量比较低时,液体射流的破碎由K-H不稳定性主导;随着局部动量比的增大液体射流的破碎逐渐由R-T不稳定性主导.液体射流的破碎长度及穿透深度均随局部动量比的增大而增大.     

Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method

Simulations of the pinch-off of an inviscid fluid column are carried out based upon a potential flow model with capillary forces. The interface location and the time evolution of the free surface boundary condition are both approximated by means of level set techniques on a fixed domain. The interface velocity is obtained via a Galerkin boundary integral solution of the 3D axisymmetric Laplace equation. A short-time analytical solution of the Raleigh–Taylor instability in a liquid column is available, and this result is compared with our numerical experiments to validate the algorithm. The method is capable of handling pinch-off and after pinch-off events, and simulations showing the time evolution of the fluid tube are presented.     

Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids

We contrast the extensional and shear dynamics of non-Brownian suspensions as a function of particle concentration. We show that the thinning rate selected during the viscoelastic pinch-off of a liquid bridge is related to the shear rate at which normal stresses become positive, which differs from the shear rate at the onset of shear thickening. By tracking particles, we demonstrate that the extensional flow is heterogeneous, with local variations of the volume fraction consistent with self-dilution. This nonuniform structure is the cause of the buckling of the threads formed after breakup.     

Gate control characteristics in GaAs nanometer-scale Schottky wrap gate structures

Gate control characteristics of GaAs-based quantum wire transistors (QWRTrs) controlled by a nanometer-scale Schottky wrap gate (WPG) are investigated theoretically and experimentally. Gate bias dependence of the effective wire width of fabricated WPG QWRTrs determined theoretically as well as experimentally from Landau plots showed that the nanometer-scale WPG controls the potential very tightly near channel pinch-off and that the pinch-off threshold voltage is strongly dependent on the gate length, L_G, when L_G is shorter than 400 nm. The theory based on the three-dimensional (3D) potential simulation pointed out that Fermi level pinning on the semiconductor surface around the WPGs strongly affects the gate controllability in the nanometer-scale Schottky WPG structure.     

Dry microfoams: formation and flow in a confined channel

We present an experimental investigation of the agglomeration of microbubbles into a 2D microfoam and its flow in a rectangular microchannel. Using a flow-focusing method, we produce the foam in situ on a microfluidic chip for a large range of liquid fractions, down to a few percent in liquid. We can monitor the transition from separated bubbles to the desired microfoam, in which bubbles are closely packed and separated by thin films. We find that bubble formation frequency is limited by the liquid flow rate, whatever the gas pressure. The formation frequency creates a modulation of the foam flow, rapidly damped along the channel. The average foam flow rate depends non-linearly on the applied gas pressure, displaying a threshold pressure due to capillarity. Strong discontinuities in the flow rate appear when the number of bubbles in the channel width changes, reflecting the discrete nature of the foam topology. We also produce an ultra flat foam, reducing the channel height from 250 μm to 8 μm, resulting in a height to diameter ratio of 0.02; we notice a marked change in bubble shape during the flow.     

Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Sonoluminescence: Two sources of light

The model of sonoluminescence with two sources of light is presented. The first of them is gas inside the bubble heated during collapse. The second source (main) is plasma in the breakdown channel in liquid.     

Noncontinuous froude number scaling for the closure depth of a cylindrical cavity

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude(1/3) power law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary wave effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the nonuniversality of the void collapse.     

Measurement of the absolute branching fraction of Ds+ --> tau+ nutau decay

Using a sample of tagged D(s)(+) decays collected near the D(s)(*+/-)D(s)(-/+) peak production energy in e(+)e(-) collisions with the CLEO-c detector, we study the leptonic decay D(s)(+)-->tau(+)nu(tau) via the decay channel tau(+)-->e(+)nu(e)nu(tau). We measure B(D(s)(+)-->tau(+)nu(tau))=(6.17+/-0.71+/-0.34)%, where the first error is statistical and the second systematic. Combining this result with our measurements of D(s)(+)-->mu(+)nu(mu) and D(s)(+)-->tau(+)nu(tau) (via tau(+)-->pi(+)nu(tau)), we determine f(D(s))=(274+/-10+/-5) MeV.     

Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions

This Letter describes a quasistationary breakup of an immiscible, inviscid fluid at low capillary numbers. The breakup proceeds in a coflowing, viscous liquid, in a confined geometry of a long and narrow orifice. In contrast to the capillary instability in an unbounded fluid, the collapse proceeds through a series of equilibria, each yielding the minimum interfacial energy of the fluid-fluid interface. The process is slow in comparison to typical relaxation speeds of the interface, and it is reversible. Its quasistatic character of collapse forms the basis for controlled, high-throughput generation of monodisperse fluid dispersions.     

Physical investigation of acoustic waves induced by the oscillation and collapse of the single bubble

The objective of this paper is to apply both experimental and numerical methods to investigate acoustic waves induced by the oscillation and collapse of a single bubble. In the experiments, the schlieren technique is used to capture the temporal evolution of the bubble shapes, and the corresponding acoustic waves. The results are presented for the single bubble generated by a low-voltage bubble generator in the free field of water. During the numerical simulations, a three-dimensional (3D) weakly compressible model is introduced to investigate the single bubble dynamics, including the generation and propagation of acoustic waves. The results show that (1) Compression wave, rarefaction wave and shock wave are generated during expansion stage, collapse stage and rebound stage of the bubble respectively. (2) Compression waves are induced by the rapid expansion of the bubble and eventually steepen into one shock wave propagating outward in the liquid, then another strong shock wave is emitted at the final collapse stage. The velocity and pressure of the liquid field increases after the shock wave. (3) Rarefaction waves are generated during the collapse stage due to the contraction of the bubble. The rarefaction wave reduces the liquid pressure and its spatial distribution is dispersive. The pressure of these acoustic waves and their effect on the liquid velocity attenuate with the increase of propagation distance.     

Three-body breakup in the dissociative recombination of the covalent triatomic molecular ion O3+

We report the first observation of almost exclusive three-body breakup in the dissociative recombination of a covalent triatomic molecular ion O3+. The three-body channel, constituting about 94% of the total reactivity, has been investigated in detail. The atomic fragments are formed in only the first two electronic states, 3P and 1D, while formation in the 1S state has not been observed. The breakup predominantly proceeds through dissociative states with linear geometry.