Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session GQ: Bubbles I |
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Chair: Eric Johnsen, University of Michigan Room: Long Beach Convention Center 203B |
Monday, November 22, 2010 8:00AM - 8:13AM |
GQ.00001: Interference between vibrational modes in bubble break-up Samuel D. Oberdick, Lipeng Lai, Wendy W. Zhang Recent works reveal that the dynamics near the break-up of an underwater bubble does not evolve into a singular, universal form independent of initial conditions. Instead, any initial azimuthal distortion excites vibrations in the neck shape that dominate the final break-up. Here we investigate how the final break-up is affected by the presence of several different vibrational modes. Approximating the Hamiltonian evolution of the interface as integrable by treating the amplitudes and the phases of the vibrations as action-angle variables gives a simple model of the break-up dynamics. We find that the outcomes of the model are in reasonable agreement with simulation results for most initial distortions. The cross-section of the bubble neck shrinks radially while vibrating. The first break-up occurs when two opposing sides of the interface osculate, creating a smooth contact. One consequence of this vibration-induced break-up is that there exists narrow intervals of initial distortions that evolve into ``near-miss'' events. In such an event, the two sides of the vibrating interface nearly osculate but pull back just in time. For such initial conditions, the simulated evolution deviates significantly from the model prediction. The action-angle variable approximation also fails. [Preview Abstract] |
Monday, November 22, 2010 8:13AM - 8:26AM |
GQ.00002: Shape instability of a collapsing bubble Arpit Tiwari, Carlos Pantano, Jonathan B. Freund A low pressure gas or vapor spherical bubble becomes aspherical during the final stages of the collapse owing to its inherent dynamical instability. We study the nonlinear dynamics of compressible bubble collapses simulated with a three-dimensional HLLC based Riemann solver on an adaptively refined Cartesian mesh. A new interface capturing algorithm is used to preserve the integrity of the Eulerian representation of the gas-liquid interface. The gas is air, which is assumed to be ideal, and the surrounding liquid is water, which is modeled by a stiffened equation of state. Departure from the spherically symmetric Gilmore/Keller--Miksis model is quantified via spherical harmonic spectra of the surface shape. Broadening, and redistribution, of the initial modes as a function of time is observed during the collapse. Simulation results indicate that unexpected care is require to avoid spurious excitation of modes by the far-field boundaries of the computational domain. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GQ.00003: Stability of surface nanobubbles Detlef Lohse, Joost Weijs, Hanneke Gelderblom, Jacco Snoeijer Surface nanobubbles are spherical-cap-shaped gas bubbles of typical diameter of 100 nm and with typical thickness of 10 nm that can form in water at hydrophobic surfaces. Their stability is a mystery as due to Laplace pressure they should dissolve in microseconds. Brenner and Lohse (Phys. Rev. Lett. 101, 214505 (2008)) had suggested that the nanobubbles are stabilized by a gas influx at the contact line, which compensates for the diffusive gas outflux. Here we give numerical support for this dynamic equilibrium stabilization mechanism from Molecular Dynamics (MD) simulations with Lennard-Jones particles: Indeed, in these MD simulations we find a strong gas influx at the contact line. We also present analytical considerations on the diffusive gas fluxes around the bubble. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GQ.00004: Numerical simulations of single-bubble collapse in liquid metal Eric Johnsen Bubble collapse following a thermal shock in liquid mercury is investigated to understand the resulting cavitation erosion. A conservative high-order accurate interface- and shock-capturing scheme is used to carry out direct simulations of the three-dimensional collapse of a single bubble. Both the shock-induced collapse due to the propagating shock and acoustic waves and the inertial Rayleigh collapse of a cavitation bubble are studied in stationary and laminar flow configurations near a rigid wall. The non-spherical collapse and emitted shock waves are characterized for the given configurations. The stresses measured along the solid surface provide indications of the potential damage of bubble collapse and are related to the erosion patterns observed experimentally in the Spallation Neutron Source at Oak Ridge National Laboratory. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GQ.00005: Surface stability of an encapsulated bubble subjected to an ultrasonic pressure wave Yunqiao Liu, Kazuyasu Sugiyama, Shu Takagi, Yoichiro Matsumoto A theoretical study on the shape stability of a nearly spherical bubble encapsulated by a hyperelastic membrane in an ultrasound field is performed. To describe the dynamic balance on the bubble surface, the membrane effects of the in-plane stress and the bending moment are incorporated into the equation set for the perturbed spherical flow of viscous incompressible fluid (Prosperetti, 1977). The spherical motion of the bubble is numerically obtained by solving the Rayleigh-Plesset equation with the elastic stress. The deflection therefrom is linearized and expanded with respect to the Legendre polynomial. Two amplitudes for each shape mode are introduced since the membrane has mobilities not only in the radial direction but also in the tangential direction. The eigenvalue analysis on the system determines the higher-order natural frequency. The derived system is applied to the temporal evolution of the higher-order shape mode. Stability diagrams for the higher-order shape mode are mapped out in the driving amplitude versus driving frequency phase space for various elastic moduli of the membrane. The most unstable driving frequency is found to be approximately integer multiples of the higher-order natural frequency. [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GQ.00006: Lattice Boltzmann Simulations for High Density Ratio Flows of Multiphase Fluids Yikun Wei, YueHong Qian In the present communication, we will show that the compression effect of the Redlich-Kwong equation of state(EOS) is lower than that of the van der Waals (vdW) EOS. The Redlich-Kwong equation of state has a better agreement with experimental data for the coexistence curve than the van derWaals (vdW) EOS. We implement the Redlich-Kwong EOS in the lattice Boltzmann simulations via a pseudo-potential. As a result, multi-phase flows with large density ratios may be simulated, thus many real applications in engineering problems can be applied. Acknowledgement: This research is supported in part by Ministry of Education in China via project IRT0844 and NSFC project 10625210 and Shanghai Sci and Tech. Com. Project 08ZZ43 [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GQ.00007: Microjet formation in a capillary by laser-induced cavitation Ivo R. Peters, Yoshiyuki Tagawa, Devaraj van der Meer, Andrea Prosperetti, Chao Sun, Detlef Lohse A vapor bubble is created by focusing a laser pulse inside a capillary that is partially filled with water. Upon creation of the bubble, a shock wave travels through the capillary. When this shock wave meets the meniscus of the air-water interface, a thin jet is created that travels at very high speeds. A crucial ingredient for the creation of the jet is the shape of the meniscus, which is responsible for focusing the energy provided by the shock wave. We examine the formation of this jet numerically using a boundary integral method, where we prepare an initial interface at rest inside a tube with a diameter ranging from 50 to 500 $\mathrm{\mu m}$. To simulate the effect of the bubble we then apply a short, strong pressure pulse, after which the jet forms. We investigate the influence of the shape of the meniscus, and pressure amplitude and duration on the jet formation. The jet shape and velocity obtained by the simulation compare well with experimental data, and provides good insight in the origin of the jet. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GQ.00008: Cavitation damage in blood clots under HIFU Hope Weiss, Golnaz Ahadi, Thilo Hoelscher, Andrew Szeri High Intensity Focused Ultrasound (HIFU) has been shown to accelerate thrombolysis, the dissolution of blood clots, \textit{in vitro} and \textit{in vivo}, for treatment of ischemic stroke. Cavitation in sonothrombolysis is thought to play an important role, although the mechanisms are not fully understood. The damage to a blood clot associated with bubble collapses in a HIFU field is studied. The region of damage caused by a bubble collapse on the fibrin network of the blood clot exposed to HIFU is estimated, and compared with experimental assessment of the damage. The mechanical damage to the network caused by a bubble is probed using two independent approaches, a strain based method and an energy based method. Immunoflourescent fibrin staining is used to assess the region of damage experimentally. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GQ.00009: Modeling bubble clusters in compressible liquids Daniel Fuster, Tim Colonius We present a new model to simulate the behaviour of bubble clouds in compressible liquids. The method uses a volume-averaged approach and defines the pressure and void fraction relative to a computational cell. Inside the cell, a generalisation of the Keller-Miksis equation is derived in order to take into account the presence of (one or more) nearby spherical bubbles as well as liquid compressibility effect on the bubble interface motion. The method converges to previous models in two distinct limits. First, it reproduces the bubble radius evolution and pressure disturbances induced by a single bubble subjected to a given far field pressure, irrespective of the relative size of the bubble compared to the grid size. Second, it converges to continuum models based on Ensemble-averaged equations when there are many bubbles in a cell. The main advantage of the model is that it allows to access to the instantaneous pressure profiles in the liquid rather than the averaged behaviour. The local pressures generated and scattered by bubble dynamics is important for predicting the peak pressures that can be locally achieved in some points of the liquid when violent bubble collapses are encountered. [Preview Abstract] |
Monday, November 22, 2010 9:57AM - 10:10AM |
GQ.00010: Modeling bubbles and dissolved gases after a breaking-wave Junhong Liang, James McWilliams, Peter Sullivan, Burkard Baschek We developed a bubble concentration model and a dissolved gas concentration model for the oceanic boundary layer. The bubble model solves a set of concentration equations for multiple gases in bubbles of different sizes, and the dissolved gas concentration model simulates the evolution of dissolved gases and dissolved inorganic carbon. The models include the effects of advection, diffusion, bubble buoyant rising, bubble size changes, gas exchange between bubbles and ambient water, and chemical reactions associated with the dissolved CO$_2$.To study the bubble and dissolved gas evolution after a single wave-breaking event, the model is coupled with a fluid-dynamical Direct Numerical Simulation model with spatially and temporally distributed momentum and bubble injection for a typical breaking wave. The modeled bubble size spectrum compares well with the laboratory measurements. The breaker-induced vortex not only advects the bubble-induced dissolved gas anomalies downstream, but also entrains the surface diffusion layer to greater depth. Due to the hydrostatic pressure and surface tension exerted on bubbles, bubbles do not contribute to the total air-sea gas flux when the water is at a saturation level $\sigma^b_m>100\%$. When the actual saturation level $\sigma_m<\sigma^b_m$, the integrated bubble contribution to gas flux is dissolution. When $\sigma_m>\sigma^b_m$, bubbles add to the venting of dissolved gases. [Preview Abstract] |
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