Dissolution of bubbles in glassmelts with equilibrium redox reactions: approximations for a moving bubble boundary

The solutions of the diffusion equations with a moving boundary for bubble dissolution (or growth) accompanied by a chemical reaction, were examined. From the viewpoint of the interaction between the convective transport and the chemical reactions, some approximations introduced to solve numerically the equations governing the bubble dissolution (or growth) were studied. For bubble dissolution in glassmelts with equilibrium redox reactions due to refining agents, the applicability of the convection transport approximations employed in the literature was discussed. It was found that our previously proposed model, in which the convective transport is neglected, agrees well with the rigorous finite-difference solution and is more reasonable compared with the approximate models proposed in the literature. Comparisons between our approximate model and the rigorous numerical solution indicate better agreement for dissolution of a bubble by simultaneous mass transfer and chemical reaction, compared with that by only mass transfer. © 1998 Chapman & Hall     

Rise of an elipsoidal air bubble (a thermal) in the atmosphere

An idealized three-dimensional model of an air bubble (a thermal) rising in the atmosphere is considered. The shape of the thermal is taken to be ellipsoidal. The additional mass, the energy of the circulating motion of the air inside the bubble, the energy of the compensating motion of the air downward in the region of streamlining, and the total energy of the process of rising are determined.     

Some problems of convective diffusion to a spherical particle with Pe ≤ 1000

The problem of convective heat and mass exchange during the slow motion of a single drop in a uniform and a shear stream, as well as during the motion of a gas bubble in a power-law liquid, is solved using finite-difference methods.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 6, pp. 1053–1058, June, 1977.     

Lateral motion and interaction of gas bubbles growing over spherical and plate heaters

This work investigates the motion of CO₂ bubbles emerging in n-heptane when a heat pulse given to a submerged heater creates local supersaturation. The ensuing slow diffusion-induced bubble expansion makes bubble motion easy to observe. The low gravity environment of a parabolic flight allows bubbles to reach large sizes without departing from the heater while retaining their spherical shape. A fast lateral displacement of single bubbles has often been noticed on two type of heaters. In cases where many bubbles grow adjacent to each other, they soon start to interact. Phenomena such as bubbles clustering, coalescence and lift-off from the heater of a large bubble induced by neighboring small ones, have been repeatedly observed. An interesting thermocapillary attraction has also been noticed between bubbles adhering to the heater and others free-floating in the nearby liquid.     

Collective effects in a dense system of large bubbles

The rising velocity and interphase transport of a dense bubble swarm in a homogeneous liquid are investigated, along with the motion and external mass transfer in an inhomogeneous porous medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 6, pp. 1057–1066, December, 1981.     

Bubble Motion near a Wall Under Microgravity: Existence of Attractive and Repulsive Forces

A numerical simulation for a bubble motion near a wall under microgravity, relevant to material processing such as crystal growth in space, is presented based on a mass conservation level set algorithm to predict the bubble behavior affected by the near wall. The simulation for the wall effect on the bubble driven by an external acceleration parallel with the near wall referred to as g-jitter confirms for the first time the existence of the wall attractive force to the bubble near the wall under certain conditions such as the initial distance between the bubble and the wall, density and viscosity ratios between the bubble and surrounding liquid under microgravity. The wall effect mechanism is explained, and the results show that the wall attractive force increases with the increasing of density ratio. Moreover, the simulation for the wall repulsive effect on the bubble near the wall under microgravity has been carried out as well.     

Effective Mass of an Electron Bubble in Superfluid Helium-4

We present the results of computer simulations of the motion of an electron bubble through superfluid helium-4 when acted upon by an electric field. The simulations are based on an extended version of the Gross–Pitaevskii equation. The temperature is assumed to be sufficiently low for the drag exerted on the bubble by thermal excitations to be negligible, and the calculations are made for velocities below the critical velocitie for nucleation of vortices and roton production. We calculate the effective mass \(m*\) of the bubble and obtain results in excellent agreement with the measurements of Poitrenaud and Williams, and Ellis, McClintock, and Bowley.     

Separation of a vapor bubble and calculation of the critical bubble radius

On the basis of the solution to the equation of motion of a variable mass, a formula is derived for analytically calculating the critical radius of a vapor bubble in a boiling liquid during free flow of the latter.Translated from Ihzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 5, pp. 831–835, May, 1973.     

Visual Observation of a Sound-Induced Bubble in Liquid 3He–4He Mixtures

We report visual observation of a sound-induced bubble in superfluid ³He–⁴He liquid mixtures using a high-speed camera at a rate of 1 msec/frame. The experiments were performed in the ³He dilute phase of phase-separated mixtures at 300 mK. The resonant frequency of the piezoelectric transducer was 9.36 MHz and the diameter of the active electrode was about 4 mm. When an acoustic wave pulse of sufficient magnitude was applied to the dilute phase from the transducer under saturated vapor pressure, a single bubble was nucleated on the active area. The bubble expanded almost spherically on the transducer, as it reached maximum size, it started shrinking, detached from the transducer, and collapsed. We also investigated the motion of the bubble in mixtures with a ³He concentration of 25% at 750 mK. In this case, the bubble grew elliptically on the transducer and detached from it without much change in shape.     

The motion of bubbles in a sinusoidally oscillating liquid in microgravity

The sinusoidal motion of single, spherical bubbles in microgravity was studied experimentally aboard the U.S. Space Shuttle. Tests were performed to determine the effect of frequency, acceleration amplitude, bubble size, and fluid viscosity on bubble motion. Five test cells each containing a single bubble were subjected to rectilinear, sinusoidal oscillations. Three nominal bubble sizes and three liquids were used to cover a range of Stokes numbers from 1.3 to 21 and Reynolds numbers from 0.6 to 75. Bubble motion was recorded by video. The ratio of bubble motion amplitude to container motion amplitude was found to be essentially independent of the actual container motion amplitude. Therefore, this ratio could be plotted against frequency to obtain a frequency response for each case. This ratio was found to rise sharply from zero at zero frequency and then approach an asymptote at high frequencies. The strong effect of the walls in these experiments caused the amplitude of bubble motion to be reduced somewhat from that expected for an infinite fluid.     

Effects of Reduced Gravity Conditions on Bubble Dispersion Characteristics in the Bubble Column

Bubble-liquid turbulent flow has an excellent heat and mass transfer behaviors than single gas or liquid flow. In order to analyze the effects of normal and reduced gravity on cold bubble-liquid two-phase turbulent flow in bubble column a second-order moment cold bubble-liquid two-phase turbulent model was developed to disclose the bubble dispersion characteristics. Under the reduced gravity condition, volume fraction caused by the decrease of buoyance force is larger than normal gravity level due to bigger bubble solid volume. In addition, bubble frequency is also decreased by in decrease of buoyance force. Normal and shear stresses have strongly anisotropic characteristics at every directions and have larger values under normal gravity than reduced gravity. The liquid turbulent kinetic energy has the two-peak bimodal distribution and weaker than bubble turbulent kinetic energy with one peak unimodal, which is caused by vigorous wake fluctuations. The correlation of fluctuation velocities between bubble and liquid has clearly anisotropic behaviors Under reduced gravity, the bubble motion has a little impact on liquid turbulent flow caused by slight buoyancy force, however, it will greatly reduce the liquid turbulent intensity due to energy cascade transport, which was transformed into bubbles or dissipated by interface friction. Bubble formation and detachment mechanisms affected by gravity conditions lead to the different levels of bubble dispersion distributions.     

Bubble motion under the action of a gradient in surface-active material concentration

The problem of bubble motion under the action of a gradient in surface-active material concentration is considered. The bubble drift velocity is determined. The possibility of calculating bubble velocity with simultaneous action of temperature and concentration gradients is considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 4, No. 6, pp. 1040–1044, December, 1981.     

Optimum design considerations for dual conductor bubble devices

A design for dual conductor, current-access bubble devices with 8-μm periods has been optimized with a numerical calculation method for bubble motion in a propagating magnetic field, generated around hole patterns in conductor layers. Magnetic bias field distributions are calculated for an oval hole chain in the conductor layers. Bubble motion equations are obtained with analytical field distribution functions approximating the calculated field distributions. Minimum drive current density Jminfor normal bubble propagation is determined by a solution to the equations. The hole shape has been optimized by the minimization of the drive power Pmin, the product of Jminand conductor resistance, which is calculated from current distributions around the hole pattern. Optimum layer thickness have also been obtained for 8-μm period bubble devices. Both registration tolerance between the two conductor layers and bubble skew effects have been studied semiquantitatively on the basis of the equations of motion. The numerical calculation method developed here is found to be a highly effective means to optimize pattern design for smaller period devices.     

On the migration of a single gas bubble in water

A theoretical model of a single gas bubble rising in open water is considered. It is revealed that methane bubble rising is accompanied by the formation of the hydration shell on its surface under the thermobaric conditions of the stability of hydrates. Numerical solutions for two limiting cases were obtained and analyzed, when the formation rate of the hydrated crust on the bubble surface is limited by the intensity of heat removal released in the process of hydrate formation by the surrounding liquid or the diffusion resistance of the gas hydrate crust to the transfer of hydrate-forming components. The comparison of numerical results with experimental data showed that the scheme of the diffusion transfer of hydrate-forming components through the crust describes most adequately the process of the growth of the gas hydrate particle observed in experiments of methane bubbles rising in sea water. It is established that argon bubble rising under the corresponding thermobaric conditions can occur without the formation of the hydrate on its surface. The migration of the gas bubble is accompanied by its dissolution in water. Numerical estimates for the values of the argon diffusion coefficient in water and reduced diffusion coefficients of gas (methane) and water through the hydrate crust are obtained from the conditions of matching theoretical and experimental data from the change of the argon bubble radius and the gas hydrate particle.     

近场气泡载荷下柔性结构耦合响应实验研究

通过电火花气泡装置和高速摄像设备对气泡与附近刚性/柔性边界间的耦合现象进行实验观测和研究。针对不同材质平板和不同距离参数下气泡脉动实验数据进行整理,对气泡动力学特性如撕裂现象、射流方向特性及气泡迁移特性等进行机理分析;并借助MATLAB开发图片数字化识别程序,分析总结了整个气泡脉动载荷下柔性板的整体运动响应模式和结构中心测点的响应特征。实验结果表明:气泡在柔性板附近收缩时出现“棒槌”状或气泡撕裂及远离对向射流现象;探究气泡载荷下柔性结构响应模式,发现气泡膨胀时柔性板呈一阶响应,收缩时呈现三阶响应及双峰值迁移现象。     

Mass transfer correlation of NH3–H2O bubble absorption

The objectives of this paper are to study the effect of key parameters on absorption performance and to develop an experimental correlation of mass transfer coefficient for ammonia–water bubble absorption. The orifice diameter, liquid concentration and vapor velocity are considered as the key parameters. This study successfully visualized the bubble behavior and measured the volumetric diameter of bubbles during the bubble absorption process. The bubble absorption is grouped into two processes, bubble growth (process I) and bubble disappearance (process II), respectively. The following conclusions were drawn from the present study. A new experimental correlation for the volumetric bubble diameter was proposed with ±15% error band, which could be applied to calculate the mass transfer coefficient. The mass transfer coefficient increased with a decrease of the liquid concentration. In process II, the mass transfer coefficient increased with an increase of the Galileo number. Finally, experimental correlations of mass transfer coefficient were developed for processes I and II with ±18% error bands.     

A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid

This paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three-dimensional problems. Finally, we illustrate our method with some typical numerical results.     

Some dynamical characteristics of a non-spherical bubble in proximity to a free surface

The motions of a gas bubble in proximity to a free surface with and without buoyancy force, as well as in shallow water are simulated based on a numerical time integration coupled with three-dimensional boundary integral spatial solution. The fluid is assumed to be inviscid, incompressible, and the flow irrotational. The unsteady Bernoulli equation is applied on the free surface and bubble surface as one of the boundary conditions of the Laplace equation for the potential. Improvements have been made in the mesh generation of the free surface and rigid boundary, the modeling of the toroidal bubble after the jet impact and the investigation into the combined effects on the motion of a bubble in the presence of the rigid bottom and free surface. The growth and collapse of a gas bubble together with the formation of the toroidal bubble after the jet impact are simulated. The shapes and positions of the bubble, the trajectories and velocities of the poles of the bubble as well as the pressure distributions in the fluid under different standoff distances and buoyancy parameters are obtained to better illuminate the mechanism underlying the motions of gas bubble and free surface. When a bubble is initiated sufficiently close to a free surface, the free surface spike and the second accelerating phenomenon of the free surface during the collapse phase can be observed. The buoyancy force has significant effects on the jet formation and development within the bubble and it may reverse the direction of the liquid jet when exceeding the effect of the Bjerknes force induced by the free surface. The large contortions in the shallow water and the formation of the high-pressure region between the bubble and the free surface are captured when the bubble is close enough to the rigid bottom and the free surface.     

Transient subharmonic and ultraharmonic acoustic emission during dissolution of free gas bubbles

This work concerns the study of free gas bubble behavior, a basic step in contrast agent study. In order to improve the understanding of microbubble-ultrasound interaction, we propose an acoustic dynamic observation of microbubble behavior performed by a high frame-rate acquiring and processing system. Results from ultrasonic observations of free gas microbubbles are discussed and compared with theoretical simulation. Peculiar radio frequency (RF) echo signals back-propagated from bubbles during dissolution up to their destruction are shown and their behavior is discussed. In particular, the different orders of subharmonic emissions related to changes in bubble sizes during dissolution were observed.