Phase field simulation of single bubble behavior under an electric field

Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.     

Comparison between level set and phase field method for simulating bubble movement behavior under electric field

In this study, based on different numberical simulation methods, the gas-liquid two-phase flow is taken as the research object. By coupling the continuity equation of incompressible fluid, Navier-Stokes equation, electric field equation and other control equations, a multi-field coupling model for rising bubbles in viscous fluids is established, and numerical simulations are carried out. The two-phase popularity of coupled electric field is studied, and the effect of electric field on bubble motion is analyzed.The Level-set and phase field method are used to track the changes of deformation and rupture during the rising of the bubble. The accuracy and validity of the two methods are verified by mass conservation. At the same time, the calculation area is determined for the accuracy of calculation, and the optimal mesh size is calculated by using mesh independence test. Compared with the level set method, the phase field method has a certain improvement in the calculation efficiency and accuracy. Among them, the calculation efficiency of the phase field calculation method in the same grid is increased by 5 times, and by 3 times in the vertical electric field environment. Moreover, using the phase field method is easier to capture the bubbles slight changes while they are rising, and the quality of the simulation results is better.The simulation analysis of bubble rising process under coupled electric field by two methods shows that under the interaction of electrostatic force, buoyancy and surface tension, the bubble is stretched into an ellipsoid along the direction of the electric field line, and the ratio of the length to the short axis is proportional to the applied electric field strength. In addition, the bubble rising velocity is affected by the electric field, and the vertical electric field accelerates the rising of the bubble.     

Real-time measurement of bubbling phenomena in a three-dimensional gas-fluidized bed using ultrafast magnetic resonance imaging

Ultrafast magnetic resonance imaging has been applied for the first time to measure simultaneously both the rise velocities and coalescence of bubbles, and the dynamics of the solid phase in a gas-solid two-phase flow. Here, we consider the hydrodynamics within a gas-fluidized bed of particles of diameter 0.5 mm contained within a column of internal diameter 50 mm; gas velocities in the range of 0.18-0.54 m/s were studied. The data are of sufficient temporal and spatial resolution that bubble size and the evolution of bubble size and velocity following coalescence events are determined.     

Effect of a uniform magnetic field on dielectric two-phase bubbly flows using the level set method

In this study, the behavior of a single bubble in a dielectric viscous fluid under a uniform magnetic field has been simulated numerically using the Level Set method in two-phase bubbly flow. The two-phase bubbly flow was considered to be laminar and homogeneous. Deformation of the bubble was considered to be due to buoyancy and magnetic forces induced from the external applied magnetic field. A computer code was developed to solve the problem using the flow field, the interface of two phases, and the magnetic field. The Finite Volume method was applied using the SIMPLE algorithm to discretize the governing equations. Using this algorithm enables us to calculate the pressure parameter, which has been eliminated by previous researchers because of the complexity of the two-phase flow. The finite difference method was used to solve the magnetic field equation. The results outlined in the present study agree well with the existing experimental data and numerical results. These results show that the magnetic field affects and controls the shape, size, velocity, and location of the bubble.     

导电流体中气泡径向振动行为的磁场控制

液态金属中气泡行为是磁流体力学的重要方面。为对磁场条件下导电流体中气泡动力学行为作全面理解,基于磁流体动力学方法建立了磁场条件下导电流体中气泡径向振动的无量纲化动力学方程,数值研究了磁场对导电流体中气泡径向非线性振动稳定性、泡内温度、泡内气压及液体空化阈值的影响。结果显示:磁场增强了气泡非线性振动的稳定性,随着磁场增强且当作用在泡上的电磁力与惯性力数量级可比时,气泡运动为稳定的周期性振动;同时,磁场引起泡内温度、泡内压力及液体空化阈值变化。研究表明,可用磁场调节和控制液态金属中气泡的运动使其满足工程应用需求。      

匀强磁场对水中气泡运动的影响

基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.     

Experimental investigation on flow boiling bubble motion under ultrasonic field in vertical minichannel by using bubble tracking algorithm

Bubble dynamics is important in flow boiling of minichannel, and ultrasonic field effects bubble behaviors. However, flow boiling bubble movements in minichannels under ultrasonic field have received little research attention and are still poorly understood. In this paper, the effects of ultrasonic field on bubble dynamics are experimentally studied by capturing the bubble motion behaviors of the flow boiling bubbles. The ultrasonic frequencies are set to 23, 28, 32, and 40 kHz. Bubble tracking algorithm, which studies the growth, trajectories, velocities, and traveled distances for bubbles, is created to qualitatively describe bubble motion behavior of flow boiling in minichannel. It is found that after the application of ultrasound, the detachment frequency, velocity, and travel distance of the bubbles significantly increases, and the growth behavior and trajectory are extremely complex, the two-phase gas-liquid flow is extremely unstable. The bubbles gain kinetic energy as the ultrasound frequency increases. Finally, numerical simulations are used to quantitatively investigate the mechanism of bubble motion in microchannels under ultrasonic fields.     

A new pressure formulation for gas-compressibility dampening in bubble dynamics models

We formulated a pressure equation for bubbles performing nonlinear radial oscillations under ultrasonic high pressure amplitudes. The proposed equation corrects the gas pressure at the gas–liquid interface on inertial bubbles. This pressure formulation, expressed in terms of gas-Mach number, accounts for dampening due to gas compressibility during the violent collapse of cavitation bubbles and during subsequent rebounds. We refer to this as inhomogeneous pressure, where the gas pressure at the gas–liquid interface can differ to the pressure at the centre of the bubble, in contrast to homogenous pressure formulations that consider that pressure inside the bubble is spatially uniform from the wall to the centre. The pressure correction was applied to two bubble dynamic models: the incompressible Rayleigh–Plesset equation and the compressible Keller and Miksis equation. This improved the predictions of the nonlinear radial motion of the bubble vs time obtained with both models. Those simulations were also compared with other bubble dynamics models that account for liquid and gas compressibility effects. It was found that our corrected models are in closer agreement with experimental data than alternative models. It was concluded that the Rayleigh–Plesset family of equations improve accuracy by using our proposed pressure correction.     

Flow of an electrically conducting bubble liquid in the field of an electromagnetic force

Physical processes accompanying the flow of a conducting bubble liquid in crossed electric and magnetic fields are considered. Based on the general equations of mechanics of multiphase media, we develop a one-dimensional model of the flow of and heat exchange in a compressible bubble liquid when the phases are not in thermal and velocity equilibrium. The model is numerically investigated. It is demonstrated that, when the bubble liquid flows along the electromagnetic force vector, the bubbles lag behind the carrying flow and are compressed and warmed up. This causes oscillations of the bubble volume, as well as oscillations of the parameters of both the disperse and carrying phase. In particular, the compression of the bubbles reduces the volumetric gas content, as well as increases the effective conductivity of the flow and the electromagnetic force in the downstream direction. This sets conditions for crisis of the bubble flow when the electromagnetic force expels the bubbles against the main stream. On the basis of the solutions obtained, the efficiency of a gas compressor is calculated.     

超声场下刚性界面附近溃灭空化气泡的速度分析

为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

强电场下气泡形变对液体绝缘的影响

 基于液体气泡击穿的椭球模型,推导了气泡形变的流体动力学方程;利用软件Comsol模拟了气泡受力后的形变;根据模拟结果,结合气体击穿的帕邢定律,讨论了气泡形变对液体绝缘的影响。结果表明:气泡在静电引力和表面张力的作用下,沿电场线方向拉伸成椭球,椭球长短轴之比与外加电场强度和气泡初始半径成正比;形变导致电场方向气体通道延长,气泡更容易击穿,外加气压是避免气泡击穿的有效途径之一,外加气压的大小与电场强度和气泡初始半径成正比。     

复杂微通道内气泡在浮力作用下上升行为的格子Boltzmann方法模拟

本文采用气-液两相流格子Boltzmann方法模拟了复杂微通道内气泡在浮力作用下的上升过程,主要研究障碍物表面润湿性、浮力大小、障碍物尺寸和气泡初始位置对气泡变形、分裂、合并的动力学行为以及对气泡上升速度、终端速度和气泡剩余质量的运动特性的影响.研究发现,障碍物表面接触角较小时气泡能够完整地通过障碍物通道,随着障碍物表面接触角增加,气泡通过障碍物通道时严重变形,并会发生分裂行为,使得部分气泡黏附在障碍物表面,从而导致气泡到达终端时质量减少.相应地,气泡上升速度以及终端速度也随着微通道表面接触角的增加而减小.另一方面,随着浮力的增加,气泡在上升过程中更容易发生分裂和合并现象,且气泡剩余质量和终端速度随着浮力的增加呈对数形式增加.此外,随着微通道障碍物半径增加,气泡剩余质量首先缓慢减小然后快速减小,而气泡终端速度近似呈线性减小.最后,数值结果还表明当气泡初始位置偏离管道中间时,其上升速度、气泡剩余质量以及气泡终端速度都与初始位置在管道中间时的变化趋势一致,然而对应的数值均减小,且气泡在上升过程中变形更严重.     

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

Spatio-temporal dynamics of an encapsulated gas bubble in an ultrasound field

Coupled equations describing the radial and translational dynamics of an encapsulated gas bubble in an ultrasound field are derived by using the Lagrangian formalism. The equations generalize Church's theory by allowing for the translation motion of the bubble and radiation losses due to the compressibility of the surrounding liquid. The expression given by Church for the inner bubble radius corresponding to the unstrained state of the bubble shell is also refined, assuming that the shell can be of arbitrary thickness and impermeable to gas. Comparative linear analysis of the radial equation is carried out relative to Church's theory. It is shown that there are substantial departures from predictions of Church's theory. The proposed model is applied to evaluate radiation forces exerted on encapsulated bubbles and their translational displacements. It is shown that in the range of relatively high frequencies encapsulated bubbles are able to translate more efficiently than free bubbles of the equivalent size.     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.     

电场对注入气泡和沸腾气泡影响的实验研究

本文主要研究了直流电场对冷态注入氮气气泡和R113沸腾气泡行为的影响.利用高速摄像机拍摄了冷态注入气泡和热态沸腾气泡在不同场强作用下的实验图像,并对气泡的脱离进行了定量分析.实验结果表明:注入氮气气泡和沸腾气泡沿电场方向显著伸长,其脱离长径比随着场强升高而增大,并且电场对沸腾气泡伸长行为的影响更显著.此外,注入气泡和沸腾气泡的脱离体积随着场强增大都具有减小的趋势,而且注入气泡体积随场强减小的行为更明显.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Effect of dissolved gases in water on acoustic cavitation and bubble growth rate in 0.83 MHz megasonic of interest to wafer cleaning

Changes in the cavitation intensity of gases dissolved in water, including H₂, N₂, and Ar, have been established in studies of acoustic bubble growth rates under ultrasonic fields. Variations in the acoustic properties of dissolved gases in water affect the cavitation intensity at a high frequency (0.83 MHz) due to changes in the rectified diffusion and bubble coalescence rate. It has been proposed that acoustic bubble growth rates rapidly increase when water contains a gas, such as hydrogen faster single bubble growth due to rectified diffusion, and a higher rate of coalescence under Bjerknes forces. The change of acoustic bubble growth rate in rectified diffusion has an effect on the damping constant and diffusivity of gas at the acoustic bubble and liquid interface. It has been suggested that the coalescence reaction of bubbles under Bjerknes forces is a reaction determined by the compressibility and density of dissolved gas in water associated with sound velocity and density in acoustic bubbles. High acoustic bubble growth rates also contribute to enhanced cavitation effects in terms of dissolved gas in water. On the other hand, when Ar gas dissolves into water under ultrasound field, cavitation behavior was reduced remarkably due to its lower acoustic bubble growth rate. It is shown that change of cavitation intensity in various dissolved gases were verified through cleaning experiments in the single type of cleaning tool such as particle removal and pattern damage based on numerically calculated acoustic bubble growth rates.     

气泡在超声场中绕圈运动的高速摄影及其图像分析

借助高速摄影和图像分析技术对首次发现的附壁气泡的绕圈现象进行了实验研究,重点研究游移气泡的运动轨迹、附壁气泡的布阵过程、气泡的来源以及气泡的振动细节.研究发现游移绕圈气泡的运动轨迹呈现出不稳定、不规则、不光滑的特点.阵列气泡源于游移气泡,而游移气泡变成阵列气泡的方式主要是通过合并增大体积,从而减小所受的Bjerknes力,降低活性的方式实现的.游移气泡源于ALF(acoustic lichtenberg figure)空化云中大量空泡的合并,使以径向振动为主的空泡逐渐过渡到以表面波动为主的气泡.阵列气泡在Bjerknes力的作用下呈现出规则的表面波动,而体积更小受力更大的游移空泡的表面完全失稳,呈现极不规则的形貌,并对附近阵列气泡的表面波动产生影响.阵列气泡呈现出十分规则的排布,相邻阵列气泡之间的振动相位是相反的,表现为相互排斥.