Bubble formation in cocurrently upward flowing liquid

The effects of liquid velocity, nozzle diameter, gas chamber volume and gas flow rate on volumes, shapes and growth curves of bubbles formed at a nozzle submerged in a cocurrently upward flowing liquid in a bubble column were experimentally investigated. The bubble volume decreases with increasing liquid flow velocity. The effect of liquid flow velocity on the volume of bubble increases with an increase in the gas flow rate. To simulate bubble formation at a nozzle submerged in cocurrently upward flowing liquid, a revised non-spherical bubble formation model was proposed. Bubble volumes, bubble growth curves and shapes experimentally obtained in this study, as well as in previous experimental studies, are well predicted by the present model.     

A simple bimodal model for the evolution of non-spherical particles undergoing nucleation,coagulation and coalescence

A simple and efficient particle dynamics model is developed accounting for simultaneous nucleation, coagulation, and coalescence or sintering of non-spherical particles. In this model two discrete monodisperse modes are used to represent the non-spherical particle size distributions approximately: a size-fixed nucleation mode and a moving accumulation mode. The size-fixed nucleation mode accounts for the introduction of newly generated particles and the moving accumulation mode characterizes the particle growth by coagulation and coalescence. The simulation results for titania particle formation and growth using the proposed bimodal model are compared with those using the previous monodisperse non-spherical particle dynamics model and non-spherical polydisperse sectional model. The present bimodal model results in a very good agreement with the polydiserse sectional model even when particle nucleation coexists with coagulation process while the monodisperse model shows significant differences. It successfully predicts the morphological change of the non-spherical particles by coalescence. The present model is also shown to be capable of predicting the polydispersity of non-spherical particle distribution. The present non-spherical bimodal model requires the same level of the computation time that the simple monodisperse model does.     

Modelling of the continuous foaming operation by dimensional analysis

In this study, a dimensional analysis of the continuous foaming operation by whipping was performed. Newtonian model fluids were formulated with controlled rheology and interfacial properties. The viscosity has been modified by changing the dilution of glucose syrup and surface tension has been modified by using two different surfactant species (whey protein and sucrose ester). Foams have been produced on an instrumented industrial rotor–stator mixer by varying the rotation speed, flow rates and pressure. An image analysis method which makes possible to characterize accurately the bubble sizes was performed on each samples. A dimensional analysis allowed to describe in a general way the foaming operation with dimensionless ratios and also enabled to weigh the magnitude of each operating parameter. A model which predicts bubble size, depending on process parameters and those related to the products has been established. This model offers a new definition of capillary number. The major influence of this number provides information on the mechanisms involved in the process. However, the approach also shows that other phenomena affect the bubble size.     

Ammonia absorption from a bubble expanding at a submerged orifice into water

To investigate the mechanism of gas absorption from a bubble containing soluble and insoluble components, a gaseous mixture of ammonia and nitrogen was bubbled into water. The growth curve, volume, surface area and shape of the growing bubbles were measured with parameters such as inlet gas composition, gas flow rate and gas chamber volume. The bubble volume decreased with the increasing composition of ammonia in a bubble, decreasing gas chamber volume and decreasing gas flow rate.To reasonably express the mass transfer from the bulk of a gas in a bubble to the bulk of a liquid, the overall mass transfer resistance was evaluated by the mass transfers in the gas phase, interface and liquid phase.The non-spherical bubble formation model combined with the overall mass transfer resistance estimated well experimental bubble shape, bubble volume at its detachment from an orifice, growth rate and mass transfer rate.Moreover, the change of concentration with bubble growth time and the fractional absorption during bubble formation were simulated.     

Modelling the bubble formation dynamics in non-Newtonian fluids

A theoretical model is developed for modelling the non-spherical bubble formation at an orifice submerged in non-Newtonian fluids under constant flowrate conditions. The equations of motion are, respectively, the radial expansion and vertical ascension of the bubble interface. They are combined with the thermodynamic equations for the gas in the bubble and the chamber below the orifice as well as the fluid rheological equation. In particular, the influence of in-line interactions between bubbles due to the fluid memory effects of the viscoelastic characteristics is taken into account for the first time. The present model is able to compute the instantaneous growing shape of the bubble during its formation and determine the final size of detachment as well as the frequency of bubble formation. The values predicted by this model compare satisfactorily with the experimental results obtained under different operating conditions.     

Numerische Berechnung physikalischer Schäumungsprozesse auf unterschiedlichen Größenskalen

A simulation method for numerical calculation of physical foaming processes is presented. A micro‐scale model is used to predict the time‐dependent change in foam volume by describing the growth of a single foam bubble as a function of given process conditions. In order to visualize the three‐dimensional foam expansion at the macro scale, the calculated growth dynamics is integrated into a simulation model based on the finite volume method. The calculation procedure is validated using discontinuous and continuous foam experiments.     

Bubble growth model and its influencing factors in a polymer melt under nonisothermal conditions

Traditionally, in order to simplify the bubble growth process in a polymer melt, an isothermal model is typically used. In fact, the temperature of the polymer melt is changing during the foaming process. In order to accurately study the growth mechanism of bubbles in polymer melts, we build a physical and mathematical model of bubble growth in a polymer melt under nonisothermal conditions. The parameters of pressure, zero-shear viscosity, relaxation time, Henry's constant, diffusion coefficient, and surface tension were determined. The fourth-order Runge–Kutta method was used to solve the nonisothermal bubble model in the polymer melt. A computational program is developed to find the dimensional change during the bubble growth process, and the correctness of the model is verified. The nonisothermal growth mechanism of and factors influencing bubbles in the polymer melt are analyzed. Combined with the design of experiment (DOE) analysis method, the transfer function of the bubble radius and the maximum growth rate of bubbles with the process parameters were obtained, such as cooling rate, system pressure, and gas concentration. The results show that system pressure has the most significant effect on bubble growth. At the same time, a bubble growth prediction model is built, which can be used to predict the growth of bubbles. Through optimization analysis, it can be used to control the growth of bubbles. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47210.     

Dissolution of Multicomponent Bubbles

The behavior of an isolated, stationary, multicomponent gas bubble in a glassmelt containing several dissolved gases is considered. The relevant mass-transport equations are formulated and calculations are performed for the case of two diffusing gases using a quasi-stationary model and a numerical solution of the exact mass-transfer equations. The results obtained from these two approaches are compared. The factors which govern the dissolution or growth of a bubble are thermodynamic and kinetic in origin. The tendency of a bubble to grow or shrink at long times is controlled by departure from overall equilibrium, whereas the short-time bubble dynamics may be dominated by kinetic effects. As a result of the existence of these dual influences, maxima and/or minima occur in the functional dependence of the bubble radius on time.     

Bubble measurement in three-phase fluidized beds using a u-shaped optical fiber

A photometric technique is being developed to study bubble behaviour in three-phase fluidized beds constituted by fine particles. A custom made U-shaped single core silica fiber (400 μm diameter) is used as the bubble sensor. A helium-neon laser beam is introduced at one end of the U probe and the variation of the light intensity, occurring when a gas bubble contacts the sensor, is detected at the other end of the fiber. The velocity and axial length (cord) of the bubbles were measured by four such probes in a two dimensional bed. This technique could be applied to study the bubble behaviour and to provide experimental data for estimating the performance of reactors with severe operating conditions of high temperature and pressure.     

气-固流化床的气泡参数测定——直射式光纤探头在流化床研究中的应用

在鼓泡域中,从直射式光纤探头在二维床的测试与图像分析的结果得到气泡的平均直径与平均刺穿长度的关系为:d_b=1.6E[l]气泡的球形度为0.96。通过反射式和直射式光纤探头信号的比较表明,直射式探头的信号便于处理,并可用来测定气泡内的粒子含量。直射式光纤探头在二维床和三维床的测定结果对比表明,两种塔内的气泡行为规律一致但有明显的差异。     

微小有限空间内微气泡控制生长的界面追踪与数值模拟

通过对微机电系统微流体器件中气泡生长实验结果的分析,考虑加热元表面液体微层的作用,将微气泡生长分为晶核形成、球形气泡、受侧壁挤压的气泡、沿微通道生长的气泡4个阶段,建立了矩形微通道内微气泡控制生长物理模型;采用Level Set Method模拟了矩形微通道内微气泡控制生长过程,获得了微气泡生长特性。数值模拟结果表明：微气泡初期生长速率较快,后期由于凝结率增大使生长速率减缓;液体温度、微通道宽度、微加热元宽度、加热电压等均对气泡生长始点和生长速率有显著影响。     

运动气泡近界面湍流场的激光测量及其湍流结构特性

运用二维激光多普勒测速仪,测定了运动气泡近界面的动力学特性,其中包括时均特性及湍流场结构.实验表明,尾涡区的时均流速呈非均匀分布,湍流场由双结构组成,即由完全随机的湍流涡及规律性的相干涡构成,这种双结构现象在尾涡的中心及边缘部又有所变化,其相关函数、谱密度函数及统计尺度亦随不同的部位而变化.泡前区受尾涡区周期性Karman涡脱落的影响,呈现相同频率的周期波动.这种特性存在于切向及法向速度中.     

Origin of the negative wake behind a bubble rising in non-Newtonian fluids

The present work aims at understanding the behavior of individual bubbles in non-Newtonian fluids. By means of a Particle Image Velocimetry (PIV) device, the complete flow field around either a single non-spherical bubble rising in polyacrylamide (PAAm) solutions or a solid sphere settling down in the same fluids shows for the first time the similar coexistence of three distinct zones: a central downward flow behind the bubble or the sphere (negative wake), a conical upward flow surrounding the negative wake zone, and an upward flow zone in front of the bubble or the sphere. This excludes then the possible influence of the interface deformation on the negative wake. A theoretical lattice Boltzmann scheme coupled to a sixth-order Maxwell model was developed for computing the complex flow field around a solid sphere. The good agreement with the experimental measurements provides evidence that the physical mechanism responsible for the negative wake in such fluids could be related to the fluid's viscoelastic properties.     

Numerical simulation of bubble growth in a limited amount of liquid

In this study, we examined the growth of a spherical bubble in a limited amount of liquid by using a finite‐element‐based numerical simulation method. The bubble growth was assumed to be controlled by both momentum and mass transfer. A truncated power‐law constitutive equation was used to describe the rheology of the melt. The gas inside the bubble followed the ideal gas law. The gas concentration at the bubble surface obeyed Henry's law. A computer code was programmed to solve the equations with the Galerkin method. A backward Euler scheme was used to discretize time. Grids were remeshed after each incremental time step to ensure the accuracy of the numerical results. The bubble growth process was simulated with the code. The numerical results, such as the instantaneous bubble size, gas pressure inside the bubble, and gas concentration profile in the liquid, were predicted. The influences of the liquid volume, initial gas pressure, temperature, and rheology of the melt on bubble growth were also studied. The results of the bubble growth simulation in this study were in satisfactory agreement with others' work. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Analysis of non-spherical polydisperse particle growth in a two-dimensional tubular reactor

Polydisperse aggregate particle growth considering coalescence, coagulation, generation and spatial transport processes is studied in a two-dimensional reactor for the first time. Effects of two-dimensional spatial transport processes, such as convection, diffusion, deposition and thermophoresis as well as nucleation, coagulation and coalescence are of primary interests. An efficient particle dynamics model based on two sets of coupled sectional equations (J. Aerosol Sci. 32 (2001) 565) is used to facilitate the severe computation loads for analyzing the growth of non-spherical polydisperse particles in an axi-symmetric two-dimensional geometry. Fluid dynamics calculations indicate the existence of non-uniform distributions of temperature and flow fields in the radial direction as well as in the axial direction inside the reactor. Particle dynamics simulations also demonstrate the significant inhomogeneous spatial distributions of the characteristics of aggregate particles. The present two dimensional calculations for reactor temperatures and particle size distributions are in agreement with the previous experimental data. The validity of simplified one-dimensional analysis is also evaluated against the present two-dimensional analysis. While the one-dimensional analysis agreed well with the spatially two-dimensional one for the cases of low flow rates, it resulted in significant errors for high flow rates.     

Viscous co‐current downward Taylor flow in a square mini‐channel

This article presents a computational study of the co‐current downward Taylor flow of gas bubbles in a viscous liquid within a square channel of 1 mm hydraulic diameter. The three‐dimensional numerical simulations are performed with an in‐house computer code, which is based on the volume‐of‐fluid method with interface reconstruction. The computed (always axi‐symmetric) bubble shapes are validated by experimental flow visualizations for varying capillary number. The evaluation of the numerical results for a series of simulations reveals the dependence of the bubble diameter and the interfacial area per unit volume on the capillary number. Correlations between bubble velocity and total superficial velocity are also provided. The present results are useful to estimate the values of the bubble diameter, the liquid film thickness and the interfacial area per unit volume from given values of the gas and liquid superficial velocities. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Bubble growth in reaction injection molded parts foamed by ultrasonic excitation

Processing of microcellular foam was studied for polyurethane. Assuming that the bubble growth is controlled by diffusion, theoretical prediction was carried out numerically to understand the bubble growth mechanism in the cavity during mold filling. Final bubble sizes were also predicted by considering the gelation time and the diffusion boundary. Viscosity change of the mixed polyurethane resin during polymerization reaction was predicted by considering reaction kinetics. The gelation time was determined to terminate the numerical calculation. The diffusion boundary was predicted based on the number of nucleated bubbles that had been determined both theoretically and experimentally. For processing of polyurethane foam by reaction injection molding, ultrasonic excitation was applied to the mixture of polyol and isocyanate. The polyol resin was supersaturated with nitrogen gas at an elevated pressure and ultrasonic excitation was applied to the mixture after impingement mixing of two components of the selected polyurethane system. Bubble nucleation was induced by the ultrasonic excitation and the bubbles were grown as the gas was supplied to the bubble from the resin.     

Controlled electrochemical gas bubble release from electrodes entirely and partially covered with hydrophobic materials

This paper deals with an experimental study on millimetre-size electrochemically evolved hydrogen bubbles. A method to generate gas bubbles controlled in number, size at detachment and place on a flat electrode is reported. Partially wetted composite islands are implemented on a polished metal substrate. As long as the island size is lower than a limit depending on its wettability, only one bubble spreads on the island and its size at detachment is controlled by the island perimeter. The composite, a metal–polytetrafluoroethylene (Ni–PTFE), is obtained by an electrochemical co-deposition process. On the contrary to predictions of available models for co-deposition, at current densities beyond Ni²⁺ limiting current density, the mass ratio of PTFE in the deposit strongly increases. A mechanism is proposed to describe co-deposition when hydrogen bubbles are co-evolved. The observation of gas evolution on fully hydrophobic electrodes highlights the fact that bubbles growth rate on such electrodes differs from growth rates when bubble growth is controlled by mass transport of dissolved gas. The more a bubble grows by coalescence the more its foot expands on the electrode the bigger its size at detachment. This triple line creeping mechanism explains why, when attached bubbles coalesce many times before detaching, their size at detachment increases with current density.     

BUBBLE DYNAMICS AND ELUTRIATION STUDIES IN GAS-FLUID1ZED BEDS

In order to adequately interpret the heat and mass transfer data taken in a gas-fluidized bed, it is essential to know the bubble dynamics and solids movement in the bed, and solids elutriation from the bed. To generate information on these aspects, an experimental facility has been designed, fabricated and successfully tested. This consists of a two-dimensional fluidized bed with its gas supply and cleanup system. The bubble dynamics and solids projection from the bed are recorded by a high-speed movie camera. The films are analyzed on a photo-optical data analyser and digitizer provided with an electronic graphics calculator connected to tape printer and a Teletype terminal interfaced with a computer. The analysis of recorded bed dynamics suggests that for large particles the bubbles grow to be non-spherical and these rise almost above the bed surface before bursting when the wake remains intact while the solids bulge at the bubble nose ruptures to release the bubble gas. It is concluded unambiguously that the solids projected in the freeboard originate from the bubble bulge, and not from the bubble wake as commonly believed. A series of experiments is proposed which will facilitate the development of a general quantitative theory for solids elutriation from industrial fluidized beds.

In addition, a fairly complete review of the work done on bubble dynamics, solids movement in the bed, and solids projection from the bed surface in two- and three-dimensional fluidized beds is presented. Thus, on the whole the present work reviews the state-of-the-art of these three different fluid-bed aspects, and reports new data.     

BUBBLE DYNAMICS AND ELUTRIATION STUDIES IN GAS-FLUID1ZED BEDS

In order to adequately interpret the heat and mass transfer data taken in a gas-fluidized bed, it is essential to know the bubble dynamics and solids movement in the bed, and solids elutriation from the bed. To generate information on these aspects, an experimental facility has been designed, fabricated and successfully tested. This consists of a two-dimensional fluidized bed with its gas supply and cleanup system. The bubble dynamics and solids projection from the bed are recorded by a high-speed movie camera. The films are analyzed on a photo-optical data analyser and digitizer provided with an electronic graphics calculator connected to tape printer and a Teletype terminal interfaced with a computer. The analysis of recorded bed dynamics suggests that for large particles the bubbles grow to be non-spherical and these rise almost above the bed surface before bursting when the wake remains intact while the solids bulge at the bubble nose ruptures to release the bubble gas. It is concluded unambiguously that the solids projected in the freeboard originate from the bubble bulge, and not from the bubble wake as commonly believed. A series of experiments is proposed which will facilitate the development of a general quantitative theory for solids elutriation from industrial fluidized beds.

In addition, a fairly complete review of the work done on bubble dynamics, solids movement in the bed, and solids projection from the bed surface in two- and three-dimensional fluidized beds is presented. Thus, on the whole the present work reviews the state-of-the-art of these three different fluid-bed aspects, and reports new data.