Dynamics of soluble gas bubbles

The problem of the mass, thermal and dynamic interaction between a bubble containing a soluble gas and a liquid is considered. It is shown that this problem can be reduced to the problem of the behavior of a vapor bubble with phase transitions investigated in detail in [1–3]. Expressions are obtained for the rate of decay of the radially symmetric oscillations of the bubbles due to the solubility of the gas in the liquid. The effective coefficients of mass transfer between the radially pulsating bubbles and the liquid are determined. A numerical solution is obtained for the problem of the radial motion of a bubble created by a sudden change of pressure in the liquid which, in particular, corresponds to the behavior of the bubbles behind the shock front when a shock wave enters a bubble screen.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–59, November–December, 1985.     

Heat exchange between a gas bubble and a liquid

The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.     

Dynamics of vapor-gas bubbles

The nonlinear problem of thermal, mass, and dynamic interaction between a vapor-gas bubble and a liquid is considered. The results of numerical solution of the problem of radial motion of the bubble caused by a sudden pressure change in the liquid, illustrating the behavior of vapor-gas bubbles in compression and rarefaction waves, are presented. The corresponding problem for single-component gas and vapor bubbles was considered in [1, 2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 56–61, November–December. 1976.     

海洋大气间气泡的气体输运

研究球形小气泡在理想流体的波浪场中的气体扩散过程,把小雷诺数下均匀来流绕流球形气泡的气体交换结果与气泡运动方程耦合在一起进行求解．讨论了溶解于水中的气体浓度、波浪、气泡半径、气泡初始深度对单个气泡气体扩散量的影响．由于气泡云对气体的输运,溶解于水中的气体可出现过饱和状态．对１０ｍ／ｓ风速下气泡云的气体输运量进行了计算,得到水中Ｏ２的过饱和度可达１．８９％～３９２％,与实际观测值一致．     

Generator geometry effect on wave dispersion of a gas in a liquid

The influence of the channel diameter and length of the hydrodynamic oscillation generator on gas bubble dimensions in the case of wave dispersion of a gas in a liquid is experimentally investigated. The technique of measuring the bubble diameters based upon the computer analysis of the gas-liquid jet photos is presented. It is shown that on the gas flow rate range from 0.5 to 32 dm³/min the mean diameter of the gas bubbles produced by wave dispersers in water is estimated by an interval from 0.45 to 0.75 mm in optimum performance regimes.     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Acoustics of a Bubbly Liquid with a Weak Chemical Reaction in the Gaseous Phase

The influence of the composition and thermophysical properties of gas-liquid bubbly systems with a dissociating component in the gaseous phase on the laws of small-disturbance propagation and attenuation is investigated. It is found that the reacting gas component in the bubbles significantly affects the sonic-wave attenuation coefficient in the bubbly liquid. This follows from the fact that when a gas bubble is compressed isothermally, a recombination reaction occurs which prevents pressure growth in the bubble.Small-disturbance propagation in bubbly liquids was investigated in a number of publications discussed in review [1]. The acoustics of a bubbly liquid with a gas phase containing active admixtures are of both methodical and practical interest. The dynamics of such multicomponent bubbles were investigated in [2].     

Unsteady waves in a liquid containing vapor bubbles

Unsteady wave processes in vapor-liquid media containing bubbles are investigated taking into account the unsteady interphase heat and mass transfer. A single velocity model of the medium with two pressures is used for this, which takes into account the radial inertia of the liquid with a change in volume of the medium and the temperature distribution in it [1]. The system of original differential equations of the model is converted into a form suitable for carrying out numerical integration. The basic principles governing the evolution of unsteady waves are studied. The determining influence of the interphase heat and mass transfer on the wave behavior is demonstrated. It is found that the time and distance at which the waves reach a steady configuration in a vapor-liquid bubble medium are considerably less than the correponding characteristics in a gas-liquid medium. The results of the calculation are compared with experimental data. The propagation of acoustic disturbances in a liquid with vapor bubbles was studied theoretically in [2]. The evolution of waves of small but finite amplitude propagating in one direction in a bubbling vapor-liquid medium is investigated in [3, 4] on the basis of the generalization of the Burgers-Korteweg-de Vries equation obtained by the authors. An experimental investigation of shock waves in such a medium is reported in [5, 6], and the structure of steady shock waves is discussed [7].Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Zhidkosti i Gaza, No. 5, pp. 117–125, September–October, 1984.     

Evolution of finite perturbations in a viscoelastic relaxing liquid with gas bubbles

The propagation of one-dimensional perturbations in a viscoelastic relaxing liquid containing gas bubbles is investigated within the framework of the homogeneous model of the medium when the wavelength of the perturbation is much larger than the distance between the bubbles and the bubble radius. The evolution of stationary and nonstationary waves is investigated analytically and with the use of numerical integration; shock waves are also investigated. The results are compared with the behavior of perturbation waves in a Newtonian liquid with gaseous inclusions. The models of the gas-liquid medium [1, 2] are generalized to the case when the liquid phase is a viscoelastic liquid, for example, a weak aqueous solution of polymers. The propagation of longwave perturbations of finite amplitude in such a mixture is investigated using the technique developed in [3].     

台阶式并行微通道内气泡群自组装行为及其对气泡生成的反馈效应

台阶式微通道乳化装置因易于高通量生产均一性的气泡及液滴而受到关注.本文利用高速摄像仪研究了台阶式并行微通道装置空腔内的气泡群复杂行为及其对气泡生成的反馈效应.实验设计的操作变量为气液相进出口位置、气相流速和液相流速.在实验操作范围内,共发现了气泡的单管生成模式和多管生成模式.研究了空腔内气泡群复杂行为随操作条件的变化趋势.发现在受限空间内,气泡在水平面内发生挤压堵塞能够自组装成具有特定几何特点的二维晶格,分别为有序的行三角晶格、有序的竖三角晶格和无序的三角晶格.晶格结构与气相压力密切相关;同时,气泡界面能量随着气相压力的增大而增大.运用介尺度、能量和活化等概念分析了气泡群复杂行为对气泡生成方式的影响,充分阐释了受限空间内气泡群的介尺度效应.以变异系数CV来表示气泡的均匀性特征,考察了气泡晶格自组装行为的控制因素.结果表明:气泡的自组装路径由气泡尺寸及其分布决定,有序的三角晶格变异系数小于5%,无序的三角晶格变异系数大于5%.     

Numerical study of the dynamics of a vapor envelope round a heated solid particle in a liquid

A study is made of the radial motion of a vapor envelope surrounding an isolated spherical particle in an unbounded mass of liquid. It is assumed that the liquid is viscous and incompressible and that the temperature is distributed uniformly in the solid particle. A model of a calorifically perfect gas is used for the vapor phase. The same assumptions are made as in Rayleigh's formulation for the problem of the dynamics of a single bubble: that the process is spherically symmetric and that the pressure P₂ (t) in the vapor phase is homogeneous. The justification for making these assumptions in problems of the dynamics of gas, vapor, and vaporgas bubbles is discussed in [1–5]. In this paper, the collapse of the vapor layer and the boiling of the liquid on the surface of the heated particle are not considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 154–157, July–August, 1985.     

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

Oscillations of a gas-vapor bubble in an acoustic field

It is shown that at large vapor contents, as a result of the combined action of phase transitions and capillary effects, the small radially symmetric oscillations of gas-vapor bubbles in an acoustic field are unstable in amplitude. The critical vapor concentration in the bubble separating regions of qualitatively different bubble behavior in the acoustic field is determined. Expressions are obtained for the decay rate of the radial oscillations of the gas-vapor bubble and the growth rate characterizing the rate of increase of oscillation amplitude in the region of instability. It is shown that adding only a slight amount of gas to the vapor bubble leads to a marked decrease in the growth rate. It is found that in the particular case of a vapor bubble the tine growth rate characterizing the development of the instability is of the same order as the second resonance frequency of the vapor bubble. This may serve to explain why in the case of vapor bubble oscillations the second resonance effect, which has been established in a number of theoretical studies and is widely discussed in the literature, has not yet been experimentally confirmed. The problem of spherically symmetrical processes around gasvapor bubbles was posed in [1], and their small oscillations are investigated in detail in [2–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 79–33, May–June, 1986.The authors are grateful to R. I. Nigmatulin for useful discussions.     

Mass transfer from a pulsating drop

The primary difficulty in solving the problem of mass transport through an isolated drop (or bubble) moving in a fluid medium at high Reynolds numbers lies in the extreme complexity of the hydrodynamic pattern of the phenomenon. For sufficiently high velocities a separation of the external flow will occur in the rear portion of the drops and bubbles, which leads to the appearance of a turbulent wake and a sharp increase of the hydrodynamic resistance. Beginning with those dimensions for which the resistance force acting per unit surface of the drop or bubble from the external medium becomes greater than the capillary pressure, the surface of the drops and bubbles begins to deform and pulsate. The local variations of the surface tension, resulting either from the process of convective diffusion or from adsorption of surface-active substances, have a large effect on the hydrodynamics of drops and bubbles (particularly on the deformation of their surface) [1, 2], The presence of vortical, and possibly even turbulent, motion within the drops and bubbles may, under certain conditions [1], lead to their fractionation.Naturally, at the present time such complex hydrodynamics cannot be described by exact quantitative relations. Several authors have attempted to solve this problem approximately within the framework of certain assumptions. In particular [3–6], a theory was developed for the boundary layer on the surface of spherical and ellipsoidal gaseous bubbles moving in a liquid, studies were made [7, 8] of the hydrodynamics of drops located in a gas flow and the conditions were found for which fractionation of such drops takes place. Of considerable practical interest is the development of the theory of mass transfer in pulsating drops and bubbles and finding in explicit form the dependence of the mass transfer coefficients on the hydrodynamic characteristics of these systems. Until this relationship is established, every theory which ignores the effect of hydrodynamics on the mass transfer rate from an individual drop or bubble cannot be considered in any way well-founded. This relates particularly to the theories [9, 10] which consider mass transfer in systems with concentrated streams of drops and bubbles. The present paper is devoted to the study of mass transport through the surface of an isolated drop in an irrotational gas or liquid stream for large Peclet numbers P.In conclusion the authors wish to thank V. G. Levich for his helpful discussions.     

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.     

A numerical study of weak shock wave propagation in a reactive bubbly liquid

A numerical study is presented on the response of a weakly shock compressed liquid column that contains reactive gas bubbles. Both the liquid and gas are considered compressible. Compressibility of the liquid allows calculation of shock and rarefaction waves in the pure liquid as well as in the gas/liquid mixture. A microscopic model for local bubble collapse is coupled with a macroscopic model of wave propagation through the gas/liquid mixture. In the particular cases presented here, the characteristic times of propagation of the shock wave and bubble collapse are of the same order of magnitude. Consequently, the coupling between various phenomena is very strong. The present model based on fundamental principles of two-phase fluid mechanics takes into account the coupling of localized bubble oscillations. This model is composed of a microscopic one in the scale of a bubble size, and a macroscopic one which is based on the mixture theory. The liquid under study is water, and the gas is a reactive mixture of argon, hydrogen and oxygen. Received 18 December 1995 / Accepted 2 June 1996     

Flow characteristics of gas-liquid-particle mixing in a gas-stirred ladle system with throughflow

An experimental study is performed on air-liquid-particle mixing, resulting from an air-particle mixture injected into a liquid flowing through a slender ladle. Flow visualization combined with image processing is employed to investigate the bubble and particle behavior at the nozzle outlet. Effort is directed to particle discrimination in both the liquid and the bubbles to determine particle distribution, which affects the mixing performance of gas bubbles, solid particles and liquid. A real-time movement of bubble and particle behavior can be visualized by means of image processing with the use of a slow-motion video recording. It is disclosed that the particles injected through the nozzle may stick on the inner surface of the gas bubble, break through the bubble surface, or mingle with the gas stream to form a two-phase jet, depending on the particle-to-gas mass flow rate ratio. It is observed that when a solid-gas two-phase jet penetrates deeper in the horizontal direction, the particles and bubbles rise along the vertical sidewall and simultaneously spread in the transverse direction, thus promoting a better liquid-particle mixing. The application of the slow-motion video recording results in quantitative evaluations of both the penetration depth of particles or of gas-particles from the injection nozzle and the velocity distribution along the sidewall.List of symbols B Width of water vessel, m - B _n Nozzle location on bottom surface of water vessel, m - d _o Diameter of a gas-particle injection nozzle, m - H Height of water vessel, m - H _n Nozzle location on vertical surface of water vessel, m - L Penetration length of particles or of particles and gas from the nozzle, m - Q _g Volumetric flow rate of gas, m³/s - Q _l Volumetric flow rate of water, m³/s - Q _s Volumetric flow rate of particle, m³/s - Re _g Gas Reynolds number based on inner diameter of the air-particle injection nozzle - t Time, sec. - W Thickness of water vessel, m - x Transverse coordinate, m - y Longitudinal coordinate, m - Mass flow rate ratio of particles to gas Visiting scholar on leave from the Mechanical Engineering Department, Kagoshima University, Kagoshima, JapanThe work reported was supported by the National Science Foundation under the Grant No. CTS-8921584     

Bubble formation in co-fed gas–liquid flows in a rotor-stator spinning disc reactor

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers (Re_ω < 0.4 · 10⁶), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re_ω, small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re_ω, depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.