Interaction between two spherical bubbles rising in a viscous liquid

The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier-Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalized by the bubble radius) and the angle θ (0o ≤ θ ≤ 90o ) formed between the line of centre and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0o ) by Legendre, Magnaudet & Mougin 2003 (J. Fluid Mech., 497,133-166) and for two bubbles moving in line (θ = 90o ) by Yuan & Prosperetti 1994 (J. Fluid Mech., 278, 325-349). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore correction) and a significant wake effect observed on both the drag and the transverse force of the second bubble when located in the wake of the first one

The stability of buoyant bubbles in the atmospheres of galaxy clusters

The buoyant rise of hot plasma bubbles inflated by active galactic nuclei outflows in galaxy clusters can heat the cluster gas and thereby compensate radiative energy losses of this material. Numerical simulations of this effect often show the complete disruption of the bubbles followed by the mixing of the bubble material with the surrounding cluster gas due to fluid instabilities on the bubble surface. This prediction is inconsistent with the observations of apparently coherent bubble structures in clusters. We derive a general description in the linear regime of the growth of instabilities on the surface between two fluids under the influence of a gravitational field, viscosity, surface tension provided by a magnetic field and relative motion of the two fluids with respect to each other. We demonstrate that Kelvin–Helmholtz instabilities are always suppressed, if the fluids are viscous. They are also suppressed in the inviscid case for fluids of very different mass densities. We show that the effects of shear viscosity as well as a magnetic field in the cluster gas can prevent the growth of Rayleigh–Taylor instabilities on relevant scalelengths. Rayleigh–Taylor instabilities on parsec scales are suppressed even if the kinematic viscosity of the cluster gas is reduced by two orders of magnitude compared to the value given by Spitzer for a fully ionized, unmagnetized gas. Similarly, magnetic fields exceeding a few ?G result in an effective surface tension preventing the disruption of bubbles. For more massive clusters, instabilities on the bubble surface grow faster. This may explain the absence of thermal gas in the north-west bubble observed in the Perseus cluster compared to the apparently more disrupted bubbles in the Virgo cluster

Heat transfer mechanisms in bubbly Rayleigh-Benard convection

The heat transfer mechanism in Rayleigh-Benard convection in a liquid with a mean temperature close to its boiling point is studied through numerical simulations with point-like vapor bubbles, which are allowed to grow or shrink through evaporation and condensation and which act back on the flow both thermally and mechanically. It is shown that the effect of the bubbles is strongly dependent on the ratio of the sensible heat to the latent heat as embodied in the Jacob number Ja. For very small Ja the bubbles stabilize the flow by absorbing heat in the warmer regions and releasing it in the colder regions. With an increase in Ja, the added buoyancy due to the bubble growth destabilizes the flow with respect to single-phase convection and considerably increases the Nusselt number.Comment: 11 pages, 14 figure

Cosmic ray confinement in fossil cluster bubbles

Most cool core clusters of galaxies possess active galactic nuclei (AGN) in their centers. These AGN inflate buoyant bubbles containing non-thermal radio emitting particles. If such bubbles efficiently confine cosmic rays (CR) then this could explain ``radio ghosts'' seen far from cluster centers. We simulate the diffusion of cosmic rays from buoyant bubbles inflated by AGN. Our simulations include the effects of the anisotropic particle diffusion introduced by magnetic fields. Our models are consistent with the X-ray morphology of AGN bubbles, with disruption being suppressed by the magnetic draping effect. We conclude that for such magnetic field topologies, a substantial fraction of cosmic rays can be confined inside the bubbles on buoyant rise timescales even when the parallel diffusivity coefficient is very large. For isotropic diffusion at a comparable level, cosmic rays would leak out of the bubbles too rapidly to be consistent with radio observations. Thus, the long confinement times associated with the magnetic suppression of CR diffusion can explain the presence of radio ghosts. We show that the partial escape of cosmic rays is mostly confined to the wake of the rising bubbles, and speculate that this effect could: (1) account for the excitation of the H$\alpha$ filaments trailing behind the bubbles in the Perseus cluster, (2) inject entropy into the metal enriched material being lifted by the bubbles and, thus, help to displace it permanently from the cluster center and (3) produce observable $\gamma$-rays via the interaction of the diffusing cosmic rays with the thermal intracluster medium (ICM).Comment: submitte

Evidence of Fueling of the 2000 New Economy Bubble by Foreign Capital Inflow: Implications for the Future of the US Economy and its Stock Market

Previous analyses of a large ensemble of stock markets have demonstrated that a log-periodic power law (LPPL) behavior of the prices constitutes a qualifying signature of speculative bubbles that often land with a crash. We detect such a LPPL signature in the foreign capital inflow during the bubble on the US markets culminating in March 2000. We detect a weak synchronization and lag with the NASDAQ 100 LPPL pattern. We propose to rationalize these observations by the existence of positive feedback loops between market-appreciation / increased-spending / increased-deficit-of-balance-of-payment / larger-foreign-surplus / increased-foreign-capital-inflows and so on. Our analysis suggests that foreign capital inflow have been following rather than causing the bubble. We then combine a macroeconomic analysis of feedback processes occurring between the economy and the stock market with a technical analysis of more than two hundred years of the DJIA to investigate possible scenarios for the future, three years after the end of the bubble and deep into a bearish regime. We also detect a LPPL accelerating bubble on the EURO against the US dollar and the Japanese Yen. In sum, our analyses is in line with our previous work on the LPPL ``anti-bubble'' representing the bearish market that started in 2000.Comment: 41 Latex pages including 14 eps figure

Physics of beer tapping

The popular bar prank known in colloquial English as beer tapping consists in hitting the top of a beer bottle with a solid object, usually another bottle, to trigger the foaming over of the former within a few seconds. Despite the trick being known for long time, to the best of our knowledge, the phenomenon still lacks scientific explanation. Although it seems natural to think that shock-induced cavitation enhances the diffusion of CO$_2$ from the supersaturated bulk liquid into the bubbles by breaking them up, the subtle mechanism by which this happens remains unknown. Here we show that the overall foaming-over process can be divided into three stages where different physical phenomena take place in different time-scales, namely: bubble-collapse (or cavitation) stage, diffusion-driven stage and buoyancy-driven stage. In the bubble-collapse stage, the impact generates a train of expansion-compression waves in the liquid that leads to the fragmentation of pre-existing gas cavities. Upon bubble fragmentation, the sudden increase of the interface-area-to-volume ratio enhances mass transfer significantly, which makes the bubble volume grow by a large factor until CO$_2$ is locally depleted. At that point buoyancy takes over, making the bubble clouds rise and eventually form buoyant vortex rings whose volume grows fast due to the feedback between the buoyancy-induced rising speed and the advection-enhanced CO$_2$ transport from the bulk liquid to the bubble. The physics behind this explosive process might also be connected to some geological phenomena.Comment: 7 pages, 4 figures, 4 movies Accepted in Physical Review Letter