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1
Salamatin, Andrey N., Vladimir Ya Lipenkov, and Paul Duval. "Bubbly-ice densification in ice sheets: I. Theory." Journal of Glaciology 43, no. 145 (1997): 387–96. http://dx.doi.org/10.1017/s0022143000034961.
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AbstractDry snow on the surface of polar ice ice sheets is first densified and metamorphosed to produce firn. Bubbly ice is the next stage of the transformation process which takes place below the depth of pore closure. This stage extends to the transition zone where, due to high pressures and low temperatures. air trapped in bubbles and ice begins to form the mixed air clathrate hydrates, while the gas phase progressively disappears. Here we develop a model of bubbly-ice rheology and ice-sheet dynamics taking into account glacier-ice compressibility. The interaction between hydrostatic compression of air bubbles, deviatoric (uniaxial) compressive deformation of the ice matrix and global deformations of the glacier body is considered. The ice-matrix pressure and the absolute-load pressure are distinguished. Similarity theory and scale analysis are used in examine the resultant mathematical model of bubbly-ice densification. The initial rate of bubble compression in ice sheets appears to be relatively high, so that the pressure (density) relaxation process takes place only 150-200 m in depth (below pore close-off) to reach its asymptotic phase, wherein the minimal drop between bubble and ice pressures is governed by the rate of loading (ice accumulation). This makes it possible to consider densification under stationary (present-day) conditions of ice formation as a special case of primary interest. The computational tests performed with the model indicate that both ice-porosity and bubble-pressure profiles in ice sheets are sensitive to variations of the rheological parameters of pure ice. However, only the bubble-pressure distinguishes between the rheological properties at low and high stresses. The porosity profile at the asymptotic phase is mostly determined by the air content in the ice. In the companion paper (Lipenkov and others, 1997), we apply the model to experimental data from polar ice cores and deduce, through an inverse procedure, the rhelogical properties of pure ice as well as the mean air content in Holocene and glacial ice sediments at vostok Station (Antarctica).
2
Salamatin, Andrey N., Vladimir Ya Lipenkov, and Paul Duval. "Bubbly-ice densification in ice sheets: I. Theory." Journal of Glaciology 43, no. 145 (1997): 387–96. http://dx.doi.org/10.3189/s0022143000034961.
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AbstractDry snow on the surface of polar ice ice sheets is first densified and metamorphosed to produce firn. Bubbly ice is the next stage of the transformation process which takes place below the depth of pore closure. This stage extends to the transition zone where, due to high pressures and low temperatures. air trapped in bubbles and ice begins to form the mixed air clathrate hydrates, while the gas phase progressively disappears. Here we develop a model of bubbly-ice rheology and ice-sheet dynamics taking into account glacier-ice compressibility. The interaction between hydrostatic compression of air bubbles, deviatoric (uniaxial) compressive deformation of the ice matrix and global deformations of the glacier body is considered. The ice-matrix pressure and the absolute-load pressure are distinguished. Similarity theory and scale analysis are used in examine the resultant mathematical model of bubbly-ice densification. The initial rate of bubble compression in ice sheets appears to be relatively high, so that the pressure (density) relaxation process takes place only 150-200 m in depth (below pore close-off) to reach its asymptotic phase, wherein the minimal drop between bubble and ice pressures is governed by the rate of loading (ice accumulation). This makes it possible to consider densification under stationary (present-day) conditions of ice formation as a special case of primary interest. The computational tests performed with the model indicate that both ice-porosity and bubble-pressure profiles in ice sheets are sensitive to variations of the rheological parameters of pure ice. However, only the bubble-pressure distinguishes between the rheological properties at low and high stresses. The porosity profile at the asymptotic phase is mostly determined by the air content in the ice. In the companion paper (Lipenkov and others, 1997), we apply the model to experimental data from polar ice cores and deduce, through an inverse procedure, the rhelogical properties of pure ice as well as the mean air content in Holocene and glacial ice sediments at vostok Station (Antarctica).
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DELALE, C. F., G. H. SCHNERR, and J. SAUER. "Quasi-one-dimensional steady-state cavitating nozzle flows." Journal of Fluid Mechanics 427 (January 25, 2001): 167–204. http://dx.doi.org/10.1017/s0022112000002330.
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Quasi-one-dimensional cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model. The nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation that takes into account bubble/bubble interactions by a local homogeneous mean-field theory and the various damping mechanisms by a damping coefficient, lumping them together in the form of viscous dissipation. The resulting system of quasi-one-dimensional cavitating nozzle flow equations is then uncoupled leading to a nonlinear third-order ordinary differential equation for the flow speed. This equation is then cast into a nonlinear dynamical system of scaled variables which describe deviations of the flow field from its corresponding incompressible single-phase value. The solution of the initial-value problem of this dynamical system can be carried out very accurately, leading to an exact description of the hydrodynamic field for the model considered.A bubbly liquid composed of water vapour–air bubbles in water at 20 °C for two different area variations is considered, and the initial cavitation number is chosen in such a way that cavitation can occur in the nozzle. Results obtained, when bubble/bubble interactions are neglected, show solutions with flow instabilities, similar to the flashing flow solutions found recently by Wang and Brennen. Stable steady-state cavitating nozzle flow solutions, either with continuous growth of bubbles or with growth followed by collapse of bubbles, were obtained when bubble/bubble interactions were considered together with various damping mechanisms.
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Delale, Can F., Kohei Okita, and Yoichiro Matsumoto. "Steady-State Cavitating Nozzle Flows With Nucleation." Journal of Fluids Engineering 127, no. 4 (April 2, 2005): 770–77. http://dx.doi.org/10.1115/1.1949643.
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Quasi-one-dimensional steady-state cavitating nozzle flows with homogeneous bubble nucleation and nonlinear bubble dynamics are considered using a continuum bubbly liquid flow model. The onset of cavitation is modeled using an improved version of the classical theory of homogeneous nucleation, and the nonlinear dynamics of cavitating bubbles is described by the classical Rayleigh-Plesset equation. Using a polytropic law for the partial gas pressure within the bubble and accounting for the classical damping mechanisms, in a crude manner, by an effective viscosity, stable steady-state solutions with stationary shock waves as well as unstable flashing flow solutions were obtained, similar to the homogeneous bubbly flow solutions given by Wang and Brennen [J. Fluids Eng., 120, 166–170, 1998] and by Delale, Schnerr, and Sauer [J. Fluid Mech., 427, 167–204, 2001]. In particular, reductions in the maximum bubble radius and bubble collapse periods are observed for stable nucleating nozzle flows as compared to the nonnucleating stable solution of Wang and Brennen under similar conditions.
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Toalá, J. A., M. A. Guerrero, H. Todt, L. Sabin, L. M. Oskinova, Y.-H. Chu, G. Ramos-Larios, and V. M. A. Gómez-González. "The Bubble Nebula NGC 7635 – testing the wind-blown bubble theory." Monthly Notices of the Royal Astronomical Society 495, no. 3 (April 17, 2020): 3041–51. http://dx.doi.org/10.1093/mnras/staa752.
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ABSTRACT We present a multiwavelength study of the iconic Bubble Nebula (NGC 7635) and its ionizing star BD+60○2522. We obtained XMM–Newton EPIC X-ray observations to search for extended X-ray emission as in other similar wind-blown bubbles around massive stars. We also obtained San Pedro Mártir spectroscopic observations with the Manchester Echelle Spectrometer to study the dynamics of the Bubble Nebula. Although our EPIC observations are deep, we do not detect extended X-ray emission from this wind-blown bubble. On the other hand, BD+60○2522 is a bright X-ray source similar to other O stars. We used the stellar atmosphere code PoWR to characterize BD+60○2522 and found that this star is a young O-type star with stellar wind capable of producing a wind-blown bubble that in principle could be filled with hot gas. We discussed our findings in line with recent numerical simulations proposing that the Bubble Nebula has been formed as the result of the fast motion of BD+60○2522 through the medium. Our kinematic study shows that the Bubble Nebula is composed by a series of nested shells, some showing blister-like structures, but with little signatures of hydrodynamical instabilities that would mix the material producing diffuse X-ray emission as seen in other wind-blown bubbles. Its morphology seems to be merely the result of projection effects of these different shells.
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Ye, Zhen, and Li Ding. "A study of multiple scattering in bubbly liquids by many-body theory." Canadian Journal of Physics 74, no. 3-4 (March 1, 1996): 92–96. http://dx.doi.org/10.1139/p96-014.
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In this paper it is suggested that acoustic-wave propagation in bubbly liquids can be easily studied using the diagram method in many-body theory. The merit of this method is that it allows convenient inclusion of any higher order bubble interactions. In particular consideration is given to a higher order correction due to the mutual interaction of bubbles. It is shown that under certain circumstances, this correction could be rather significant. Other higher order interactions are also briefly discussed.
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Burkard, M. E., and H. D. Van Liew. "Oxygen transport to tissue by persistent bubbles: theory and simulations." Journal of Applied Physiology 77, no. 6 (December 1, 1994): 2874–78. http://dx.doi.org/10.1152/jappl.1994.77.6.2874.
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Persistent gas bubbles able to traverse capillaries can be prepared from a slowly permeating gas or with a mechanical structure surrounding a gas phase. If they are permeable to gases, such bubbles will carry O2 from the lungs to the tissues via the blood stream. Using a mathematical model based on physical laws, we present simulations of the behavior of bubbles stabilized by a slowly permeating gas (gas X). We show that the bubble persists longer if the tissue and venous blood contain N2 to dilute gas X and slow its outward diffusion. A 6-microns -diam bubble carries 0.11 pl of O2 during the breathing of pure O2, so 4.6 x 10(8) bubbles/ml in the blood will supply a normal arteriovenous difference. In conditions used for hyperbaric O2 therapy, a bubble carries approximately 0.26 pl of O2. Stabilized bubbles have the potential to transport O2 efficiently; they release O2 to tissue at high PO2 and require injection of only small amounts of a foreign substance.
8
Bailey, R. C., and P. B. Garces. "On the theory of air‐gun bubble interactions." GEOPHYSICS 53, no. 2 (February 1988): 192–200. http://dx.doi.org/10.1190/1.1442454.
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Calculation of the seismic signatures of marine air‐gun arrays often requires that the interactions among the bubbles from air guns be taken into account. The standard method of doing this is to use the Giles‐Johnston approximation in which a time‐dependent effective ambient pressure is calculated for each bubble as the sum of the true ambient pressure and the local pressure signals of all the other bubbles in the array. These effects of interaction have a relative importance in the dynamics proportional to (R/D), where R and D are the typical bubble radius and interbubble separation, respectively. To ensure that current methods of calculating signatures are accurate, it is necessary to know how good this approximation is. This paper shows that there are no interaction terms in the full dynamical equations proportional to [Formula: see text] or [Formula: see text], and that the errors of the Giles‐Johnston approximation are only of order [Formula: see text]. The Giles‐Johnston approximation is therefore justified even for fairly accurate signature calculations for noncoalescing bubbles. The analysis here also shows how to incorporate bubble motions and deformations into the dynamical equations, so that the errors can be reduced to order [Formula: see text] if desired.
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Fuster, D., and F. Montel. "Mass transfer effects on linear wave propagation in diluted bubbly liquids." Journal of Fluid Mechanics 779 (August 19, 2015): 598–621. http://dx.doi.org/10.1017/jfm.2015.436.
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In this article we investigate the importance of mass transfer effects in the effective acoustic properties of diluted bubbly liquids. The classical theory for wave propagation in bubbly liquids for pure gas bubbles is extended to capture the influence of mass transfer on the effective phase speed and attenuation of the system. The vaporization flux is shown to be important for systems close to saturation conditions and at low frequencies. We derive a general expression for the transfer function that relates bubble radius and pressure changes, solving the linear version of the conservation equations inside, outside and at the bubble interface. Simplified expressions for various limiting situations are derived in order to get further insight about the validity of the common assumptions typically applied in bubble dynamic models. The relevance of the vapour content, the mass transfer flux across the interface and the effect of variations of the bubble interface temperature is discussed in terms of characteristic non-dimensional numbers. Finally we derive the various conditions that must be satisfied in order to reach the low-frequency limit solutions where the phase speed no longer depends on the forcing frequency.
10
Lu, Tianshi, Roman Samulyak, and James Glimm. "Direct Numerical Simulation of Bubbly Flows and Application to Cavitation Mitigation." Journal of Fluids Engineering 129, no. 5 (October 25, 2006): 595–604. http://dx.doi.org/10.1115/1.2720477.
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The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two- and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed.
11
KLASEBOER, EVERT, SIEW WAN FONG, CARY K. TURANGAN, BOO CHEONG KHOO, ANDREW J. SZERI, MICHAEL L. CALVISI, GEORGY N. SANKIN, and PEI ZHONG. "Interaction of lithotripter shockwaves with single inertial cavitation bubbles." Journal of Fluid Mechanics 593 (November 23, 2007): 33–56. http://dx.doi.org/10.1017/s002211200700852x.
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The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.
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Cheng, Feng, and Weixi Ji. "Numerical and experimental study on dynamic characteristics of cavitation bubbles." Industrial Lubrication and Tribology 70, no. 6 (August 13, 2018): 1119–26. http://dx.doi.org/10.1108/ilt-11-2016-0291.
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Purpose Cavitation bubbles cannot be avoided in the hydraulic system. Because of instability of flow and variation of water pressure, the jet often occurs in a bubble collapse. This study aims to accurately predict the shape, velocity and time of the resulting jet, so as to inhibit cavitation erosion. Design/methodology/approach In the study, a theoretical model of cavitation bubbles in the water has been developed by applying a periodic water film pressure into the Rayleigh–Plesset equation. A fourth-order in time Runge–Kutta scheme is used to obtain an accurate computation of the bubble dynamic characteristics. The behavior of the proposed theory is further simulated in a high-speed photography experiment by using a cavitation bubble test rig. The evolution with time of cavitation bubbles is further obtained. Findings A comparison with the available experimental results reveals that the bubble evolution with time has a duration of about 0.3T0, that well predicts the expanding and compressing process of cavitation bubbles. The results also show that the initial bubble radius in the water influences the moving velocity of the bubble wall, whereas the perturbation frequency of the water pressure has less effect on the velocity of the bubble wall. Originality/value A theoretical model well predicts dynamic characteristics of cavitation bubbles. The bubble evolution with time has a duration of about 0.3T0, Initial bubble radius influences the velocity of bubble wall. Perturbation frequency has less effect on the velocity of bubble wall.
13
Mou, Wenjie. "Effect of shear factor on bubble nucleation of polystyrene using supercritical fluid as a foaming agent." Journal of Polymer Engineering 34, no. 5 (July 1, 2014): 387–94. http://dx.doi.org/10.1515/polyeng-2013-0126.
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Abstract The effect of shear factor on bubble nucleation during the foaming extrusion process with polystyrene (PS) using the supercritical fluid (SCF) carbon dioxide (CO2) as a foaming agent was studied based on the energy transformation in this article. The influence of shear factor (which is caused by the velocity gradient in a conical die) on the dynamics of bubble nucleation was investigated and determined. The critical radius for bubble nucleation is presented through the Taylor deformation theory by using a nuclear embryo to represent the state in the bud of the appearance of the nuclear bubble. Theoretical analysis shows that a spherical nuclear bubble can split into two new nuclear bubbles after the deformation in the shear flow field; the radius of the new nuclear bubble is greater than the critical radius, so it can finally grow into a larger nuclear bubble. The shear factor increased the number of the nuclear bubbles in the polymer melt and so increased the density of the bubbles and decreased the diameters of the bubbles. This article proposes a qualitative judgment which indicates that the shear factor in a conical die has a beneficial effect on bubble nucleation, and helps to produce foamed plastics with fine bubbles.
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d’Auria, Fabrizio, Luca d’Agostino, and Christopher E. Brennen. "Dynamic Response of Ducted Bubbly Flows to Turbomachinery-Induced Perturbations." Journal of Fluids Engineering 118, no. 3 (September 1, 1996): 595–601. http://dx.doi.org/10.1115/1.2817800.
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The present work investigates the dynamics of the three-dimensional, unsteady flow of a bubbly mixture in a cylindrical duct subject to a periodic pressure excitation at one end. One of the purposes is to investigate the bubbly or cavitating flow at inlet to or discharge from a pump whose blade motions would provide such excitation. The flow displays various regimes with radically different wave propagation characteristics. The dynamics effects due to the bubble response may radically alter the fluid behavior depending on the void fraction of the bubbly mixture, the mean bubble size, the pipe diameter, the angular speed of the turbomachine and the mean flow Mach number. This simple linearized analysis illustrates the importance of the complex interactions of the dynamics of the bubbles with the average flow, and provides information on the propagation and growth of the turbopump-induced disturbances in the feed lines operating with bubbly or cavitating liquids. Examples are presented to illustrate the influence of the relevant flow parameters. Finally, the limitations of the theory are outlined.
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Chen, Huiting, Shiyu Wei, Weitian Ding, Han Wei, Liang Li, Henrik Saxén, Hongming Long, and Yaowei Yu. "Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons." Entropy 23, no. 9 (August 25, 2021): 1106. http://dx.doi.org/10.3390/e23091106.
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Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.
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Gubaidullin, Damir Anvarovich, and Ramil Nakipovich Gafiyatov. "Reflection and Transmission of Acoustic Waves through the Layer of Multifractional Bubbly Liquid." MATEC Web of Conferences 148 (2018): 15001. http://dx.doi.org/10.1051/matecconf/201814815001.
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The mathematical model that determines reflection and transmission of acoustic wave through a medium containing multifractioanl bubbly liquid is presented. For the water-water with bubbles-water model the wave reflection and transmission coefficients are calculated. The influence of the bubble layer thickness on the investigated coefficients is shown. The theory compared with the experiment. It is shown that the theoretical results describe and explain well the available experimental data. It is revealed that the special dispersion and dissipative properties of the layer of bubbly liquid can significantly influence on the reflection and transmission of acoustic waves in multilayer medium
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Abdel-Latif, Lotfie Ahmed, Heinz Peeken, and Joachim Benner. "Thermohydrodynamic Analysis of Thrust-Bearing With Circular Pads Running on Bubbly Oil (BTHD-Theory)." Journal of Tribology 107, no. 4 (October 1, 1985): 527–37. http://dx.doi.org/10.1115/1.3261124.
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This paper considers the steady-state bubble-thermohydrodynamic behavior of rigid circular pad thrust bearing and presents an iterative numerical scheme to solve the governing equations. The Reynolds equation, the energy equation of the oil film, and the heat conduction equation of the pad are converted by means of finite difference method and solved numerically. The air/gas bubbles included in the lubricant are assumed to be evenly dispersed. The variation in the oil density and viscosity due to bubble presence as well according to pressure differentials and temperature rise is considered. The surface tension of the bubbles is taken into account in the analysis. Typical graphs showing the influence of the bubble content on the most important design criteria of the bearing: load W, friction loss F, pressure center location Xp and temperature rise within the oil film are presented. The load carrying capacity, outlet temperature or friction loss does not change much with increasing bubble content. The pressure distributions predicted in earlier work by To̸nder [1–4] etc. is confirmed. The pressure center location, however, shifts more downstream, making the bearing more unstable for smaller loads.
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TOMITA, Y., P. B. ROBINSON, R. P. TONG, and J. R. BLAKE. "Growth and collapse of cavitation bubbles near a curved rigid boundary." Journal of Fluid Mechanics 466 (September 10, 2002): 259–83. http://dx.doi.org/10.1017/s0022112002001209.
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Laser-induced cavitation bubbles near a curved rigid boundary are observed experimentally using high-speed photography. An image theory is applied to obtain information on global bubble motion while a boundary integral method is employed to gain a more detailed understanding of the behaviour of a liquid jet that threads a collapsing bubble, creating a toroidal bubble. Comparisons between the theory and experiment show that when a comparable sized bubble is located near a rigid boundary the bubble motion is significantly influenced by the surface curvature of the boundary, which is characterized by a parameter ζ, giving convex walls for ζ < 1, concave walls for ζ > 1 and a flat wall when ζ = 1. If a boundary is slightly concave, the most pronounced migration occurs at the first bubble collapse. The velocity of a liquid jet impacting on the far side of the bubble surface tends to increase with decreasing parameter ζ. In the case of a convex boundary, the jet velocity is larger than that generated in the flat boundary case. Although the situation considered here is restricted to axisymmetric motion without mean flow, this result suggests that higher pressures can occur when cavitation bubbles collapse near a non-flat boundary. Bubble separation, including the pinch-off phenomenon, is observed in the final stage of the collapse of a bubble, with the oblate shape at its maximum volume attached to the surface of a convex boundary, followed by bubble splitting which is responsible for further bubble proliferation.
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Diwan, Sourabh S., and O. N. Ramesh. "Relevance of local parallel theory to the linear stability of laminar separation bubbles." Journal of Fluid Mechanics 698 (April 5, 2012): 468–78. http://dx.doi.org/10.1017/jfm.2012.110.
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AbstractLaminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.
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Wang, Binbin, Chris C. K. Lai, and Scott A. Socolofsky. "Mean velocity, spreading and entrainment characteristics of weak bubble plumes in unstratified and stationary water." Journal of Fluid Mechanics 874 (July 3, 2019): 102–30. http://dx.doi.org/10.1017/jfm.2019.461.
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In this paper we present an experimental and theoretical study of weak bubble plumes in unstratified and stationary water. We define a weak bubble plume as one that spreads slower than the linear rate of a classic plume. This work focuses on the characteristics of the mean flow in the plume, including centreline velocity, plume spreading and entrainment of ambient water. A new theory based on diffusive spreading instead of an entrainment hypothesis is used to describe the lateral spreading of the bubbles and the associated plume. The new theory is supported by the experimental data. With the measured data of liquid volume fluxes and the new theory, we conclude that the weak bubble plume is a decreasing entrainment process, with the entrainment coefficient $\unicode[STIX]{x1D6FC}$ in the weak bubble plume decreasing with height $z$, following $\unicode[STIX]{x1D6FC}\sim z^{-1/2}$, and taking on values much smaller than those in a classic bubble plume. An additional non-dimensional diffusion coefficient, $\hat{E_{t}}\sim E_{t}U_{s}^{2}/B_{0}$, is also needed to describe the evolution of the volume and kinematic momentum fluxes for the mean flow in the weak bubble plume. Here, $E_{t}$ is the effective turbulent diffusion coefficient, $U_{s}$ is the terminal rise velocity of the bubbles, and $B_{0}$ is the kinematic buoyancy flux of the source. Finally, we provide a unified framework for the mean flow characteristics, including volume flux, momentum flux and plume spreading for the classic and weak bubble plumes, which also provides insight on the transition from classic to weak bubble plume behaviour.
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Su, Yanwen, Xuelin Tang, Fujun Wang, Xiaoqin Li, and Xiaoyan Shi. "Three-Dimensional Cavitation Bubble Simulations based on Lattice Boltzmann Model Coupled with Carnahan-Starling Equation of State." Communications in Computational Physics 22, no. 2 (June 21, 2017): 473–93. http://dx.doi.org/10.4208/cicp.oa-2016-0112.
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AbstractThe Shan-Chen multiphase lattice Boltzmann model (LBM) coupled with Carnahan-Starling real-gas equation of state (C-S EOS)was proposed to simulate three-dimensional (3D) cavitation bubbles. Firstly, phase separation processes were predicted and the inter-phase large density ratio over 2×104was captured successfully. The liquid-vapor density ratio at lower temperature is larger. Secondly, bubble surface tensions were computed and decreased with temperature increasing. Thirdly, the evolution of creation and condensation of cavitation bubbles were obtained. The effectiveness and reliability of present method were verified by energy barrier theory. The influences of temperature, pressure difference and critical bubble radius on cavitation bubbles were analyzed systematically. Only when the bubble radius is larger than the critical value will the cavitation occur, otherwise, cavitation bubbles will dissipate due to condensation. According to the analyses of radius change against time and the variation ratio of bubble radius, critical radius is larger under lower temperature and smaller pressure difference condition, thus bigger seed bubbles are needed to invoke cavitation. Under higher temperature and larger pressure difference, smaller seed bubbles can invoke cavitation and the expanding velocity of cavitation bubbles are faster. The cavitation bubble evolution including formation, developing and collapse was captured successfully under various pressure conditions.
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Fan, Yu Guang, Zhao Liu, Jing Ming Li, San Ping Zhou, Bing Chen, and Hong Xian Lin. "Research on the Change of Energy in the Process of the Micro Bubble Formation with Dissolved Air Method." Advanced Materials Research 664 (February 2013): 390–94. http://dx.doi.org/10.4028/www.scientific.net/amr.664.390.
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The generation method of dissolved gas micro bubble is introduced in the paper. The micro bubble producing process can be divided into two stages-nucleation and expansion through analysis. The formation process and the free energy change of the micro bubble is analyzed according to the homogeneous nucleation theory, free energy change formula of the two process is derived, and relation between bubble radius and formation bubble number under certain conditions is also discussed. It is concluded that the smaller the radius of formed bubbles, the more free energy change and initial energy are needed according to the analysis of the relation above.
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SMEULDERS, D. M. J., and M. E. H. VAN DONGEN. "Wave propagation in porous media containing a dilute gas–liquid mixture: theory and experiments." Journal of Fluid Mechanics 343 (July 25, 1997): 351–73. http://dx.doi.org/10.1017/s0022112097005983.
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The influence of a small amount of gas within the saturating liquid of a porous medium on acoustic wave propagation is investigated. It is assumed that the gas volumes are spherical, homogeneously distributed, and that they are within a very narrow range of bubble sizes. It is shown that the compressibility of the saturating fluid is determined by viscous, thermal, and a newly introduced Biot-type damping of the oscillating gas bubbles, with mean gas bubble size and concentration as important parameters. Using a super-saturation technique, a homogeneous gas–liquid mixture within a porous test column is obtained. Gas bubble size and concentration are measured by means of compressibility experiments. Wave reflection and propagation experiments carried out in a vertical shock tube show pore pressure oscillations, which can be explained by incorporating a dynamic gas bubble behaviour in the linear Biot theory for plane wave propagation.
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WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave." Journal of Fluid Mechanics 659 (July 27, 2010): 191–224. http://dx.doi.org/10.1017/s0022112010002430.
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Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described by the linear wave equation, also for the first and second orders. Matching between the two expansions provides the model for the non-spherical bubble behaviour in a compressible fluid. A numerical model using the mixed Eulerian–Lagrangian method and a modified boundary integral method is used to obtain the evolving bubble shapes. The primary advantage of this method is its computational efficiency over using the wave equation throughout the fluid domain. The numerical model is validated against the Keller–Herring equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the fourth oscillation. Numerical analyses are further performed for non-spherical oscillating acoustic bubbles. Bubble evolution and jet formation are simulated. Outputs also include the bubble volume, bubble displacement, Kelvin impulse and liquid jet tip velocity. Bubble behaviour is studied in terms of the wave frequency and amplitude. Particular attention is paid to the conditions if/when the bubble jet is formed and when the bubble becomes multiply connected, often forming a toroidal bubble. When subjected to a weak acoustic wave, bubble jets may develop at the two poles of the bubble surface after several cycles of oscillations. A resonant phenomenon occurs when the wave frequency is equal to the natural oscillation frequency of the bubble. When subjected to a strong acoustic wave, a vigorous liquid jet develops along the direction of wave propagation in only a few cycles of the acoustic wave.
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Branger, Annette B., Christian J. Lambertsen, and David M. Eckmann. "Cerebral gas embolism absorption during hyperbaric therapy: theory." Journal of Applied Physiology 90, no. 2 (February 1, 2001): 593–600. http://dx.doi.org/10.1152/jappl.2001.90.2.593.
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Cerebral gas embolism is a serious consequence of diving. It is associated with decompression sickness and is assumed to cause severe neurological dysfunction. A mathematical model previously developed to calculate embolism absorption time based on in vivo bubble geometry is used in which various conditions of hyperbaric therapy are considered. Effects of varying external pressure and inert gas concentrations in the breathing mixtures, according to US Navy and Royal Navy diving treatment tables, are predicted. Recompression alone is calculated to reduce absorption times of a 50-nl bubble by up to 98% over the untreated case. Lowering the inhaled inert gas concentration from 67.5% to 50% reduces absorption time by 37% at a given pressure. Bubbles formed after diving and decompression with He are calculated to absorb up to 73% faster than bubbles created after diving and decompression with air, regardless of the recompression gas breathed. This model is a useful alternative to impractical clinical trials in assessing which initial step in hyperbaric therapy is most effective in eliminating cerebral gas embolisms should they occur.
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WANG, HAN, ZHEN-YU ZHANG, YONG-MING YANG, and HUI-SHENG ZHANG. "NUMERICAL INVESTIGATION OF THE INTERACTION MECHANISM OF TWO BUBBLES." International Journal of Modern Physics C 21, no. 01 (January 2010): 33–49. http://dx.doi.org/10.1142/s0129183110014938.
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In the frame of inviscid and incompressible fluids without taking into consideration of surface tension effects, the axisymmetric evolution of two buoyancy-driven bubbles in an infinite and initially stationary liquid are investigated numerically by VOF method. The numerical experiments are performed for two bubbles with same size, with the following one being half of the leading one, and with the leading one being half of the following one, and for different bubble distances. The ratio of gas density to liquid density is 0.001. It is found by numerical experiment that when the distance between the two bubbles is greater than or equal to one and half of the bigger bubble radius, the interaction is very weak and the two bubbles evolute like isolated ones rising in an infinite liquid. When the two bubbles come closer, the leading bubble itself evolutes like an isolated one rising in an infinite liquid. However, due to the smaller distance between the two bubbles, large pressure gradient forms in the liquid region near the top of the following bubble, which causes the upward stretch of its top part no matter what sizes of the two bubbles are. When the distance between the two bubbles is less than or equal to three-tenth of the bigger bubble radius, before the liquid jet behind the leading bubble fully developed, the top part of the following bubble has already been sucked into the leading one, giving a pear-like shape. Soon after the following bubble merges with the leading one. It is also found that for the smaller bubble, its transition to toroidal is always faster than that of the bigger one because of its smaller size. The mechanism of the above phenomena has been analyzed numerically.
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Nie, Lei, Yu Ning Zhong, and Ye Peng Zhang. "Gas Bubble Behavior Model in Adhesive Bonding Using Thermosetting Polymer." Advanced Materials Research 291-294 (July 2011): 527–31. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.527.
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Gas bubbles entrapped in polymer intermediate layer often lead to voids which are severe defects of adhesive bonding qualities. Although the empirical method had been used for a long time to eliminate the bubbles, theoretic analysis considering the bubble behavior during bonding process is more preferable because of the better universality. The interrelationships between processing parameters and bubble deformation were investigated. A theoretic model describing those interrelationships was developed reasonably using gas diffusion theory to predict the bubble behavior. The mathematic equations of this model were deduced and the solution was obtained with some proper simplifications. Experiments under different conditions were carried out and the experimental results were contrasted with the theoretical predictions. It was obvious that when choosing temperatures and pressures carefully, the model could predict the bubble behavior accurately.
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Wang, Ya Wei, Yuan Yuan Xu, Xing Long Zhu, Shou Wang Jiang, Yu Jiao Chen, Xue Fu Shang, Wei Feng Jin, Cui Hong Lv, Min Bu, and Ying Zhou Chen. "Phase Microscopy Method of Micro-Nano Sized Bubbles Based on Hilbert Phase Microscopy (HPM)." Advanced Materials Research 586 (November 2012): 316–21. http://dx.doi.org/10.4028/www.scientific.net/amr.586.316.
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Measuring shape of bubbles is very important in many industrial processes, because that its behavior in the fluid is closely related to its morphology. Phase microscopy imaging (PMI) method is one of the best useful methods in this field. In the paper, considering on PMI idea, it is put out a new method which improves an ordinary light microscope into a dual function that can do both PMI and its ordinary microscopy function. Its optical structure is designed by using Mach-Zehnder interferometer method which can be added on the platform of ordinary microscope. A glass hole (bubble) is used as a sample to do phase microscopy imaging via the improved device. The results of the experiment and theory show that the phase distribution of bubble is closely related to the shape of it, which is very useful to detect the bubble’s behavior in the flow field. Besides bubbles, the improved microscope can be also used to observe the phase body such as cells.
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Wang, Tao, Jian Hua Zhang, Yi Zhang, and Xiu Hua Ren. "Optimization of Bubble Amount in Resin Mineral Composite Based Vacuum Pouring Procedure." Applied Mechanics and Materials 395-396 (September 2013): 60–63. http://dx.doi.org/10.4028/www.scientific.net/amm.395-396.60.
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With good vibration alleviating property, resin mineral composite has been used to produce main components of machine tools to satisfy the requirements of machining efficiency. Bubble in RMC is one of the key influences on compression strength, its amount and distribution determines the overall mechanical properties of the composite directly. In this article, bubble nucleation and free energy theory are used to explain the generation mechanism of bubbles by subdividing them into two parts, bubbles generated in granite and bubbles generated in resin. Mechanical model of single raised bubble in micro cylinder channel is established based on the flow characteristics of non-newtonian fluid. In order to validate the aforementioned assumptions, typical RMC samples are produced. Strength test and draining method are used to get their compression strength and bulk density. Experimental results show that sample with vacuum pouring process has smaller bubble amount and better compression strength performance, which is consistent with the mechanical model.
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Nov, Yuval, and Oded Nov. "Living in a bubble? Toward a unified bubble theory." International Journal of General Systems 37, no. 5 (October 2008): 627–35. http://dx.doi.org/10.1080/03081070802037696.
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CHATZIDAI, N., Y. DIMAKOPOULOS, and J. TSAMOPOULOS. "Viscous effects on the oscillations of two equal and deformable bubbles under a step change in pressure." Journal of Fluid Mechanics 673 (March 1, 2011): 513–47. http://dx.doi.org/10.1017/s0022112010006361.
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According to linear theory and assuming the liquids to be inviscid and the bubbles to remain spherical, bubbles set in oscillation attract or repel each other with a force that is proportional to the product of their amplitude of volume pulsations and inversely proportional to the square of their distance apart. This force is attractive, if the forcing frequency lies outside the range of eigenfrequencies for volume oscillation of the two bubbles. Here we study the nonlinear interaction of two deformable bubbles set in oscillation in water by a step change in the ambient pressure, by solving the Navier–Stokes equations numerically. As in typical experiments, the bubble radii are in the range 1–1000 μm. We find that the smaller bubbles (~5 μm) deform only slightly, especially when they are close to each other initially. Increasing the bubble size decreases the capillary force and increases bubble acceleration towards each other, leading to oblate or spherical cap or even globally deformed shapes. These deformations may develop primarily in the rear side of the bubbles because of a combination of their translation and harmonic or subharmonic resonance between the breathing mode and the surface harmonics. Bubble deformation is also promoted when they are further apart or when the disturbance amplitude decreases. The attractive force depends on the Ohnesorge number and the ambient pressure to capillary forces ratio, linearly on the radius of each bubble and inversely on the square of their separation. Additional damping either because of liquid compressibility or heat transfer in the bubble is also examined.
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Etienne, Xiaoli Liao, Scott H. Irwin, and Philip Garcia. "$25 spring wheat was a bubble, right?" Agricultural Finance Review 75, no. 1 (May 5, 2015): 114–32. http://dx.doi.org/10.1108/afr-12-2014-0042.
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Purpose – The purpose of this paper is to test for bubbles in the US hard red spring (HRS) wheat market from 2004 to 2014, with particular focus on 2007-2008 when the market experienced record-high price volatility. Design/methodology/approach – The authors apply a recently developed bubble testing procedure to cash, rolling nearby futures contract, and individual futures contract prices of HRS wheat sampled at daily, weekly, and monthly frequencies. Two critical value (CV) sequences are derived to date-stamp bubbles, one from Monte Carlo simulations, and the other from recursive wild bootstrap procedure. Findings – The authors find that regardless of the price series adopted, sampling frequency chosen, or CVs used, bubbles account for only a small fraction of the HRS wheat price behavior during 2004-2014. However, much sharper differences are detected regarding the key policy question of bubble behavior during 2007-2008. Individual futures contract prices during this period suggest only a minimal number of bubble days, while rolling nearby futures and cash prices indicate bubbles lasting much longer. Since theory suggests that prices for individual futures contracts are more likely to provide a clearer test of bubble components, the authors conclude there is little evidence that the spike in spring wheat prices to $25 per bushel in 2007-2008 was a bubble. Originality/value – This paper is the first in the literature to examine the sensitivity of bubble testing to different types of data, sampling frequencies, and inference procedures.
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HARKIN, ANTHONY, TASSO J. KAPER, and ALI NADIM. "Coupled pulsation and translation of two gas bubbles in a liquid." Journal of Fluid Mechanics 445 (October 16, 2001): 377–411. http://dx.doi.org/10.1017/s0022112001005857.
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We present and analyse a model for the spherical pulsations and translational motions of a pair of interacting gas bubbles in an incompressible liquid. The model is derived rigorously in the context of potential flow theory and contains all terms up to and including fourth order in the inverse separation distance between the bubbles. We use this model to study the cases of both weak and moderate applied acoustic forcing. For weak acoustic forcing, the radial pulsations of the bubbles are weakly coupled, which allows us to obtain a nonlinear time-averaged model for the relative distance between the bubbles. The two parameters of the time-averaged model classify four different dynamical regimes of relative translational motion, two of which correspond to the attraction and repulsion of classical secondary Bjerknes theory. Also predicted is a pattern in which the bubbles exhibit stable, time-periodic translational oscillations along the line connecting their centres, and another pattern in which there is an unstable separation distance such that bubble pairs can either attract or repel each other depending on whether their initial separation distance is smaller or larger than this value. Moreover, it is shown that the full governing equations possess the dynamics predicted by the time-averaged model. We also study the case of moderate-amplitude acoustic forcing, in which the bubble pulsations are more strongly coupled to each other and bubble translation also affects the radial pulsations. Here, radial harmonics and nonlinear phase shifting play a significant role, as bubble pairs near resonances are observed to translate in patterns opposite to those predicted by classical secondary Bjerknes theory. In this work, dynamical systems techniques and the method of averaging are the primary mathematical methods that are employed.
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Chu, You-Hua. "Bubbles and Superbubbles: Observations and Theory." Proceedings of the International Astronomical Union 3, S250 (December 2007): 341–54. http://dx.doi.org/10.1017/s1743921308020681.
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AbstractMassive stars inject energy into the surrounding medium and form shell structures. Bubbles are blown by fast stellar winds from individual massive stars, while superbubbles are blown by fast stellar winds and supernova explosions from groups of massive stars. Bubbles and superbubbles share a similar overall structure: a swept-up dense shell with an interior filled by low-density hot gas. Physical properties of a bubble/superbubble can be affected by magnetic field, thermal conduction, turbulent mixing, inhomogeneous ambient medium, etc. I will review recent progresses on observations and compare them to theoretical expectations for (1) swept-up dense shells, (2) hot interiors, and (3) interface between a dense shell and its interior hot gas.
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Ziolkowski, Anton. "Measurement of air‐gun bubble oscillations." GEOPHYSICS 63, no. 6 (November 1998): 2009–24. http://dx.doi.org/10.1190/1.1444494.
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In this paper, I provide a theoretical basis for a practical approach to measuring the pressure field of an air gun array and present an algorithm for computing its wavefield from pressure measurements made at known positions in the vicinity of the gun ports. The theory for the oscillations of a single bubble is essentially a straight‐forward extension of Lamb’s original paper and provides a continuous, smooth transition from the oscillating wall of the bubble to the far‐field, preserving both the fluid flow and the acoustic radiation, all to the same accuracy and valid for bubbles with initial pressures up to about 200 atm (3000 psi or 20 MPa). The simplifying assumption, based on an argument of Lamb, is that the particle velocity potential obeys the linear acoustic wave equation. This is used then in the basic dynamic and kinematic equations to lead, without further approximations, to the nonlinear equation of motion of the bubble wall and the wavefield in the water. Given the initial bubble radius, the initial bubble wall velocity, and the pressure variation at any point inside or outside the bubble, the algorithm can be used to calculate the bubble motion and the acoustic wavefield. The interaction among air‐gun bubbles and the resultant total wavefield is formulated using the notional source concept, in which each bubble is replaced by an equivalent notional bubble obeying the same equation of motion but oscillating in water of hydrostatic pressure, thus allowing the wavefields of the notional bubbles to be superposed. A separate calibration experiment using the same pressure transducers and firing the guns individually allows the initial values of the bubble radius and bubble wall velocity to be determined for each gun. An appendix to the paper provides a test of the algorithm on real data from a single gun.
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Jones, Theodore G., Jacob Grun, L. Dale Bibee, Charles Manka, Alexandra Landsberg, and Daniel Tam. "Laser-Generated Shocks and Bubbles as Laboratory-Scale Models of Underwater Explosions." Shock and Vibration 10, no. 3 (2003): 147–57. http://dx.doi.org/10.1155/2003/647530.
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Underwater shocks and bubbles were generated using a high energy pulsed laser system. The advantages of this experimental approach are: (1) precisely controlled and measured experimental conditions; (2) improved diagnostics, including extensive imaging capabilities; (3) unique experiments, including a simultaneously detonated line charge; and (4) the ability to provide validation quality data for hydrodynamic simulation codes. Bubble sensitivity to variation of several experimental parameters was examined. Numerical simulations were performed corresponding to the experimental shots, showing that empirical bubble theory, experimental bubble data, and simulations were all in good agreement.
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Kumar, V., and J. Weller. "Production of Microcellular Polycarbonate Using Carbon Dioxide for Bubble Nucleation." Journal of Engineering for Industry 116, no. 4 (November 1, 1994): 413–20. http://dx.doi.org/10.1115/1.2902122.
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A process to produce a family of novel materials from polycarbonate, having a microcellular structure, is described. The process utilizes the high solubility of carbon dioxide in polycarbonate to nucleate a very large number of bubbles, on the order of 1 to 10 × 109 bubbles/cm3, at temperatures well below the glass transition temperature of the original, unsaturated polycarbonate. Microcellular polycarbonate foams with homogeneous microstructure and a wide range of densities have been produced. In this paper experimental results on solubility, bubble nucleation, and bubble growth in the polycarbonate-carbon dioxide system are presented, and the critical ranges of the key process parameters are established. It is shown that the bubble nucleation phenomenon in polycarbonate near the glass transition temperature is not described by classical nucleation theory.
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Guo, Li Jun, Shu Ming Xing, and Pei Wei Bao. "A Study on Bubbles in Semisolid Alloys." Solid State Phenomena 217-218 (September 2014): 302–11. http://dx.doi.org/10.4028/www.scientific.net/ssp.217-218.302.
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Abstract. Bubble or blowhole is one of the most common defects in the workpiece produced by a semisolid alloy process. Except some bubbles are discharged out of the melt, many of the bubbles remained in the semisolid slurry will be deformed, enlarged or merged in the storage and transport process of the semisolid slurry, and be compressed, burst, flattened into crack which is called as gas induced crack in the further semisolid process. How to control and reduce the bubble defects is a key problem to give full play to the advantages of semisolid processing technology in industrial applications. In this paper, the behaviors of growing, floating, escaping and changing of the bubbles in semisolid alloys were theoretically explored during the smelting, filling and forming, and the mathematical models for predicting bubble dimensions and remained bubble ratio in the semisolid slurry were derived based on the theory of twophase flow and the principle of rheology. Moreover, the mechanism and critical conditions for forming the bubbles defects and gasinduced cracks defects in a workpiece were discussed by mechanics analysis. Finally, the relationships between blowhole defects, cracks defects and process parameters were built through kinetic analysis for the rheology behaviors of the semisolid slurry and bubble growing process. These mathematical models will provide a reference for controlling and preventing defects of the blowhole and cracks in the semisolid process.
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Li, Duan, Zhang, Tang, and Zhang. "Retardant Effects of Collapsing Dynamics of a Laser-Induced Cavitation Bubble Near a Solid Wall." Symmetry 11, no. 8 (August 15, 2019): 1051. http://dx.doi.org/10.3390/sym11081051.
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In the present paper, the dynamic behavior of cavitation bubbles near a wall is experimentally investigated with a focus on the retardant effects of the wall on the collapsing dynamics of the bubble. In the present experiments, a cavitation bubble is generated by a focused laser beam with its behavior recorded through high-speed photography. During the data analysis, the influences of non-dimensional bubble–wall distance on the bubble collapsing dynamics are qualitatively and quantitatively investigated in terms of the interface evolution, the velocities of the poles, and the movement of the bubble centroid. Our results reveal that the presence of the wall could significantly affect the collapsing characteristics, leading to a dramatic difference between the moving velocities of interfaces near and away from the wall. With the decrease of the bubble–wall distance, the effects will be gradually strengthened with a rapid movement of the bubble centroid during the final collapse. Finally, a physical interpretation of the phenomenon is given based on the bubble theory, together with a rough estimation of the induced water hammer pressure by the bubble collapse.
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Jones, Ronald W. "Bubble Diagrams in Trade Theory." Pacific Economic Review 18, no. 5 (November 28, 2013): 561–73. http://dx.doi.org/10.1111/1468-0106.12040.
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WONG, HARRIS, DAVID RUMSCHITZKI, and CHARLES MALDARELLI. "Theory and experiment on the low-Reynolds-number expansion and contraction of a bubble pinned at a submerged tube tip." Journal of Fluid Mechanics 356 (February 10, 1998): 93–124. http://dx.doi.org/10.1017/s0022112097007805.
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The expansion and contraction of a bubble pinned at a submerged tube tip and driven by constant gas flow rate Q are studied both theoretically and experimentally for Reynolds number Re[Lt ]1. Bubble shape, gas pressure, surface velocities, and extrapolated detached bubble volume are determined by a boundary integral method for various Bond (Bo=ρga2/σ) and capillary (Ca=μQ/σa2) numbers, where a is the capillary radius, ρ and μ are the liquid density and viscosity, σ is the surface tension, and g is the gravitational acceleration.Bubble expansion from a flat interface to near detachment is simulated for a full range of Ca (0.01–100) and Bo (0.01–0.5). The maximum gas pressure is found to vary almost linearly with Ca for 0.01[les ]Ca[les ]100. This correlation allows the maximum bubble pressure method for measuring dynamic surface tension to be extended to viscous liquids. Simulated detached bubble volumes approach static values for Ca[Lt ]1, and asymptote as Q3/4 for Ca[Gt ]1, in agreement with analytic predictions. In the limit Ca→0, two singular time domains are identified near the beginning and the end of bubble growth during which viscous and capillary forces become comparable.Expansion and contraction experiments were conducted using a viscous silicone oil. Digitized video images of deforming bubbles compare well with numerical solutions. It is observed that a bubble contracting at high Ca snaps off.
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Zheng, Yuxin, Linya Chen, Xiaoyu Liang, and Hangbo Duan. "Numerical Study of the Interaction between a Collapsing Bubble and a Movable Particle in a Free Field." Water 12, no. 12 (November 27, 2020): 3331. http://dx.doi.org/10.3390/w12123331.
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This study numerically investigates the interactions between a collapsing bubble and a movable particle with a comparable size in a free field, which is associated with the microscopic mechanisms of the synergetic effects of cavitation erosion and particle abrasion on the damages of materials in fluid machineries. A new solver on OpenFOAM based on direct numerical simulations with the volume of fluid (VOF) method capturing the interface of a bubble and with the overset grid method handling the motion of the particle was developed to achieve the fluid–structure interaction (FSI). The results show that bubbles in cases with stand-off parameter χ (defined as (d0−Rp)/R0), where d0 is the initial distance between the centers of the bubble and particle, and Rp,R0 are the particle’s radius and the initial radius of the bubble respectively >1, experience spherical-shaped collapse under the influence of the approaching particle, which is attracted by the collapsing bubble. The bubbles in these cases no longer present non-spherical collapse. Additionally, a force balance model to account for the particle dynamics was established, in which the particle velocity inversely depends on the size of the particle, and approximately on the second power of the initial distance from the bubble. This analytical result accords with the numerical results and is valid for cases with χ>1 only, since it is based on the theory of spherical bubbles. These conclusions are important for further study of the interactions between a bubble and a movable particle near a rigid wall.
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WILSON, MILES, JOHN R. BLAKE, and PETER M. HAESE. "CLOUD CAVITATION DYNAMICS." ANZIAM Journal 50, no. 2 (October 2008): 199–208. http://dx.doi.org/10.1017/s1446181109000133.
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AbstractAn analysis is developed for the behaviour of a cloud of cavitation bubbles during both the growth and collapse phases. The theory is based on a multipole method exploiting a modified variational principle developed by Miles [“Nonlinear surface waves in closed basins”, J. Fluid Mech.75 (1976) 418–448] for water waves. Calculations record that bubbles grow approximately spherically, but that a staggered collapse ensues, with the outermost bubbles in the cloud collapsing first of all, leading to a cascade of bubble collapses with very high pressures developed near the cloud centroid. A more complex phenomenon occurs for bubbles of variable radius with local zones of collapse, with a complex frequency spectrum associated with each individual bubble, leading to both local and global collective behaviour.
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Kruyt, N. P. "On the Shear Modulus of Two-Dimensional Liquid Foams: A Theoretical Study of the Effect of Geometrical Disorder." Journal of Applied Mechanics 74, no. 3 (May 24, 2006): 560–67. http://dx.doi.org/10.1115/1.2424241.
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The shear modulus of two-dimensional liquid foams in the dry limit of low liquid content has been studied theoretically. The focus is on the effect of geometrical disorder on the shear modulus (besides the influence of surface tension). Various theoretical predictions are formulated that are all based on the assumptions of isotropic geometrical characteristics, incompressible bubbles, and negligible edge curvature. Three of these predictions are based on a transformation of Princen’s theory that is strictly valid only for regular hexagonal bubbles. Another prediction takes into account variations in bubble areas by considering the foam as consisting of approximately regular hexagonal bubbles with varying areas. Two other predictions are solely based on the characteristics of the bubble edges. The first of these is based on the assumption of affine movement of bubble vertices, while the second accounts for nonaffine deformation by considering the interaction with neighboring edges. The theoretical predictions for the shear modulus are compared with the result from a single foam simulation. For the single simulation considered, all predictions, except that based on affine movement of bubble vertices, are close to the value obtained from this simulation.
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Cholewiński, Jarosław. "The Phenomenon of Speculative Bubble in the Light of the Austrian Business Cycle Theory." Equilibrium 4, no. 1 (June 30, 2010): 51–63. http://dx.doi.org/10.12775/equil.2010.004.
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The article presents the modern interpretation of the Austrian business cycle theory and the look at the phenomenon of economic bubble through the lens of that theory. The aim of the article is to answer the question ‘What is the main cause of economic bubbles’. The author suggests that it is a depiction which integrates cyclical fluctuations induced by credit expansion with the phenomenon of speculative bubble. Capital-based macroeconomics proposed by Garrison can become a core of universal economic theorizing. The model presented by the author shows how credit expansion that decreases interest rate of credits below its natural level causes medium-run discoordination of production structure. Disruptions that lies in the strong fluctuations of capital goods during a cyclical episode can be understand as consecutive stages of speculative bubble. In the paper the author conducted a historical analysis of data to investigate whether the dramatic increase in house prices that occurred in the United States after the year 2000 could have been triggered by credit expansion. The author summarizes that such hypothesis can’t be rejected.
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Doinikov, Alexander A., and Ayache Bouakaz. "Microstreaming generated by two acoustically induced gas bubbles." Journal of Fluid Mechanics 796 (May 4, 2016): 318–39. http://dx.doi.org/10.1017/jfm.2016.270.
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A theory is developed that describes microstreaming generated by two interacting gas bubbles in an acoustic field. The theory is used in numerical simulations to compare the characteristics of acoustic microstreaming at different frequencies, separation distances between the bubbles and bubble sizes. It is shown that the interaction of the bubbles leads to a considerable increase in the intensity of the velocity and stress fields of acoustic microstreaming if the bubbles are driven near the resonance frequencies that they have in the presence of each other. Patterns of streamlines for different situations are presented.
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HERRMANN, MARCUS, PARVIZ MOIN, and SNEZHANA I. ABARZHI. "Nonlinear evolution of the Richtmyer–Meshkov instability." Journal of Fluid Mechanics 612 (October 10, 2008): 311–38. http://dx.doi.org/10.1017/s0022112008002905.
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We report analytical and numerical results describing the dynamics of the two-dimensional coherent structure of bubbles and spikes in the Richtmyer–Meshkov instability for fluids with a finite density ratio. The theory accounts for the non-local properties of the interface evolution, and the simulations treat the interface as a discontinuity. Good agreement between the analytical and numerical results is achieved. To quantify accurately the interface dynamics in the simulations, new diagnostics and scalings are suggested. The velocity at which the interface would move if it were ideally planar is used to set the flow time scale as well as the reference point for the bubble (spike) position. The data sampling has high temporal resolution and captures the velocity oscillations caused by sound waves. The bubble velocity and curvature are both monitored, and the bubble curvature is shown to be the relevant diagnostic parameter. According to the results obtained, in the nonlinear regime of the Richtmyer–Meshkov instability the bubbles flatten and decelerate, and the flattening of the bubble front indicates the multiscale character of the coherent dynamics.
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D'Agostino, Luca, Christopher E. Brennen, and Allan J. Acosta. "Linearized dynamics of two-dimensional bubbly and cavitating flows over slender surfaces." Journal of Fluid Mechanics 192 (July 1988): 485–509. http://dx.doi.org/10.1017/s0022112088001958.
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The present work investigates the dynamics of two-dimensional, steady bubbly flows over a surface and inside a symmetric channel with sinusoidal profiles. Bubble dynamics effects are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. Energy dissipation due to viscous, thermal and liquid compressibility effects in the dynamics of the bubbles is included, while the relative motion of the two phases and viscous effects at the flow boundaries are neglected. The results are then generalized by means of Fourier synthesis to the case of surfaces with slender profiles of arbitrary shape. The flows display various flow regimes (subsonic, supersonic and super-resonant) with different properties according to the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms on the flows subject to harmonic excitation. Finally the results for a flow over a surface with a Gaussian-shaped bump are presented and the most important limitations of the theory are briefly discussed.
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Gangloff, John J., Thomas A. Cender, Volkan Eskizeybek, Pavel Simacek, and Suresh G. Advani. "Entrapment and venting of bubbles during vacuum bag prepreg processing." Journal of Composite Materials 51, no. 19 (October 25, 2016): 2757–68. http://dx.doi.org/10.1177/0021998316676325.
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During composites manufacturing with partially pre-impregnated fibers (i.e. “prepregs”) in Out-of-Autoclave processes, non-impregnated fabric cross-sections serve as air pathways to evacuate entrapped bubbles of air, moisture, or volatiles. The bubbles trapped within a laminate during processing lead to decreased structural performance. In this work, the motion of resin and bubbles during the processing of a characteristic prepreg is directly visualized in situ. This is performed utilizing a previously developed flow visualization technique under known pressure and temperature conditions. This study investigates the processing conditions under which a bubble succeeds or fails to meet and coalesce with available air pathways in order to escape the laminate. A key finding of this study is that tunable process parameters, such as pressure and temperature, are less important for successful bubble removal as compared to the initial state of resin impregnation in the prepreg. Prepregs with initially high states of resin impregnation will often fail to draw bubbles into air pathways through the center of fiber tow cross sections, whereas prepregs with initially low states of resin impregnation have clear pathways for bubbles to meet local resin flow fronts, coalesce, and escape. The relevant literature on the motion of bubbles in confined spaces is discussed. It is observed that small Capillary number theory (i.e. Ca < 0.01) under predicts the relative velocity of bubbles, and the faster than expected bubble transport is likely due to effects given by the bubble aspect ratio via the fibrous micro-channel geometry.
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Brożek, Marian, and Anna Młynarczykowska. "The distribution of air bubble size in the pneumo-mechanical flotation machine . Rozkład wielkości pęcherzyków powietrza w pneumo-mechanicznej maszynie flotacyjnej." Archives of Mining Sciences 57, no. 3 (December 1, 2012): 729–40. http://dx.doi.org/10.2478/v10267-012-0047-9.
Full textAbstract:
Abstract The flotation rate constant is the value characterizing the kinetics of cyclic flotation. In the statistical theory of flotation its value is the function of probabilities of collision, adhesion and detachment of particle from the air bubble. The particle - air bubble collision plays a key role since there must be a prior collision before the particle - air bubble adhesion happens. The probability of such an event to occur is proportional to the ratio of the particle diameter to the bubble diameter. When the particle size is given, it is possible to control the value of collision probability by means of the size of air bubble. Consequently, it is significant to find the effect of physical and physicochemical factors upon the diameter of air bubbles in the form of a mathematical dependence. In the pneumo-mechanical flotation machine the air bubbles are generated by the blades of the rotor. The dispergation rate is affected by, among others, rotational speed of the rotor, the air flow rate and the liquid surface tension, depending on the type and concentration of applied flotation reagents. In the proposed paper the authors will present the distribution of air bubble diameters on the grounds of the above factors, according to the laws of thermodynamics. The correctness of the derived dependences will be verified empirically.