A theoretical model for bubble formation at an orifice submerged in an inviscid liquid

A new theoretical model for calculating bubble formation at an orifice submerged in an inviscid liquid is presented. Simplified equations of motion for the gas—liquid interface were developed, and together with thermodynamic equations for the gas in the bubble and the chamber below the orifice plate, the instantaneous shape of the bubble during its formation was calculated. In contrast with previous models, the present model is able to determine the instant of detachment as the moment at which the neck of the bubble closes. The present model gives also a more detailed treatment of the flow through the orifice, and is suitable for low as well as high chamber volumes. Calculated results are presented for a wide range of orifice radii (0.0175–0.48 cm), gas flow rates (0.4–100 cm³/sec) and chamber volume (1–5000 cm³), including examples of calculated bubble shapes. The present model is restricted to single bubble formation, but it is able to calculate the critical flow rates and critical chamber volumes which limit this region.     

Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate

Extensive numerical simulations were carried out to study the problem of bubble formation at submerged orifices under constant inflow conditions. A combined volume-of-fluid and level-set method was applied to simulate the formation process, the detachment and the bubble rise above the orifice in axisymmetric coordinates. On the one hand, the operating conditions of the formation process such as orifice flow rate, orifice radius and wettability of the orifice plate were investigated for the working fluids of air and water at 20 °C. On the other hand, the influence of the variation of fluid properties (liquid density and viscosity, surface tension) was examined individually. In this frame, the present work focused on low and medium flow rate conditions, at which the formation takes place in a periodic manner, in contrast to aperiodic or double periodic modes. The results of the computations provide information on the influence of various conditions on the bubble shapes, the bubble volume and the transition from a single to a double periodic formation process. The numerical results were extensively validated with experimental data available in the literature.     

Influence of fluid properties on bubble formation,detachment, rising and collapse; Investigation using volume of fluid method

Numerical simulations have been carried out to investigate the formation and motion of single bubble in liquids using volume-of-fluid (VOF) method using the software platform of FLUENT 6.3. Transient conservation mass and momentum equations with considering the effects of surface tension and gravitational force were solved by the pressure implicit splitting operator (PISO) algorithm to simulate the behavior of gas-liquid interface movements in the VOF method. The simulation results of bubble formation and characteristics were in reasonable agreement with experimental observations and available literature results. Effects of fluid physical properties, operation conditions such as orifice diameter on bubble behavior, detachment time, bubble formation frequency and bubble diameter were numerically studied. The simulations showed that bubble size and bubble detachment times are linear functions of surface tension and decrease exponentially with the increase in liquid density. In contrast, only a small influence of the fluid viscosity on bubble size and detachment time was observed. Bubble collapse at a free surface simulation with VOF method was also investigated.     

The formation and growth of bubbles at a submerged orifice

A model has been developed to describe the formation of single bubbles at a submerged orifice. The model is based on a modified Rayleigh equation for bubble growth and describes the effect of gas momentum by assuming that the flow field inside the growing bubble is in the form of a circulating toroidal vortex. The equations describing the bubbling system are solved numerically using an explicit finite-difference technique. The model shows that bubble growth is characterised by an initial outward movement of the base of the bubble along the plate floor followed by an inward movement back towards the orifice which leads to a severing of the bubble from the orifice and termination of the growth cycle.Computed bubble growth rates, formation times and chamber pressure fluctuations are shown to be in good agreement with available experimental data for a wide range of system pressure (0–1.37 MN/m²) and computed bubble shapes are similar to those observed experimentally.     

Equilibrium shapes and quasi-static formation of bubbles at submerged orifice

A detailed analysis of the effect of chamber volume, orifice radius, orifice submergence and contact angle on quasi-static formation of bubbles is presented. It is shown, that many aspects of slow bubble formation, involving phenomena leading to various modes of the bubble release, as well as the maximum orifice diameter which sustains a bubble at equilibrium, can be explained on the basis of information on equilibrium shapes and conditions. Scaling rules enabling adoption of results for water to other liquids are also presented.     

Experimental Investigations of Regimes of Bubble Formation on Submerged Orifices Under Constant Flow Condition

Regimes of bubble formation on a submerged orifice under constant flow conditions were investigated experimentally. The effects of orifice diameter, surface characteristics (contact angle and roughness) and surface tension on the regimes of bubble formation were studied for a wide range of gas flow rates. In particular, the transitions of period‐1 to period‐2 bubbling regime, with pairing or with coalescence at the orifice, and period‐2 to chaotic bubbling were investigated in detail. An attempt is made to provide a generalized bubble formation regime map constructed using appropriate dimensionless numbers. The physical understanding of various bubbling regimes and the experimental data on the effects of various system parameters are expected to contribute to the development and validation of analytical and CFD models     

BUBBLE FORMATION FROM AN ORIFICE SUBMERGED IN LIQUIDS

The phenomena of the bubble formation from an orifice submerged in a liquid is classified according to their formation mechanisms and the estimation expressions of the bubble volume are reviewed

The revised two-stage model of bubble formation accompanied by the pressure fluctuation in the gas chamber is presented and the results computed by this model are compared with the experimental results obtained for relatively wider range of gas chamber volume. Effects of some factors on the bubble volume, such as, gas chamber volume, orifice diameter, physical properties of gas and velocity of surrounding liquid are discussed     

Bubble evolution through submerged orifice using smoothed particle hydrodynamics: Basic formulation and model validation

Smoothed particle hydrodynamics is used to simulate the bubble evolution in liquid pool through a submerged orifice. Discontinuities in the physical properties along the interface are taken care using appropriate smoothening functions. Surface tension at the interfacial plane is also added in the momentum equation to track the evolution of the bubbles. To prevent abrupt intrusion of one fluid into the other no penetration force is applied for two closely situated particles of different properties. Solid walls are modelled with two layer of virtual particle along the boundary. Further, the use of corrective form of kernel approximation eradicates the inherent particle deficiency at the interface and solid boundary. The model is capable to simulate the growth of the bubble, neck formation and its detachment from the orifice along with the dynamic velocity field in both the phases. Comparison between the numerical bubble contour and published results shows excellent predictability of the model. The volume of the bubble at the detachment and the bubble frequency are compared satisfactorily with available experimental observations.     

温度与压力对单孔气泡形成过程的影响

温度压力对进气管孔口气泡的生成具有重要影响。以氮气-水、氦气-水、氮气-十四烷为研究体系,采用高速摄像法,观察了恒速流下孔口气泡的形成过程,考察了孔口气速（0~1500 cm/s）、温度(293~393 K)、压力（0~6 MPa）、孔径（1.12, 2.5 mm）、气体类型（N₂、He）对气泡生长过程的影响。实验表明：随着压力增加,气泡直径减小,纵横比增加;温度升高一方面导致黏度、密度和表面张力降低,使气泡直径减小,另一方面加剧了液体汽化,使得气泡直径增大。根据实验结果修正了Gaddis提出的气泡直径模型,引入饱和蒸气压贡献项,得出新的适用于高温高压条件下气泡直径的估算式。     

鼓泡塔反应器分布板的开孔率和液体返混

考察鼓泡塔内鼓泡现象,发现气流经过小孔的速度（称为小孔气速）需大于某一临界值。计算并比较了气流通过多孔板的干板压力降和表面能损耗,提出计算此临界气速的公式和确定最大开孔率的方法。 用脉冲注入法测定鼓泡塔液体停留时间分布,提出非整数串连混合器模型,推导出其停留时间分布曲线方程式,计算结果与实验数据相符。并验证了Towell的轴向分散系数的计算方法。     

Prediction of bubble diameter at detachment from a wall orifice in liquid cross-flow under reduced and normal gravity conditions

Bubble formation and detachment is an integral part of the two-phase flow science. The objective of the present work is to theoretically investigate the effects of liquid cross-flow velocity, gas flow rate embodied in the momentum flux force, and orifice diameter on bubble formation and detachment in a wall-bubble injection configuration. A two-dimensional one-stage theoretical model based on a global force balance on the bubble evolving from a wall orifice in a cross liquid flow is presented in this work. In this model, relevant forces acting on the evolving bubble are expressed in terms of the bubble center of mass coordinates and solved simultaneously. Relevant forces in low gravity included the momentum flux, shear-lift, surface tension, drag and inertia forces. Under normal gravity conditions, the buoyancy force, which is dominant under such conditions, can be added to the force balance. Two detachment criteria were applicable depending on the gas to liquid momentum force ratio. For low ratios, the time when the bubble acceleration in the direction of the detachment angle is greater or equal to zero is calculated from the bubble x and y coordinates. This time is taken as the time at which all the detaching forces that are acting on the bubble are greater or equal to the attaching forces. For high gas to liquid momentum force ratios, the time at which the y coordinate less the bubble radius equals zero is calculated. The bubble diameter is evaluated at this time as the diameter at detachment from the fact that the bubble volume is simply given by the product of the gas flow rate and time elapsed. Comparison of the model's predictions was also made with predictions from a two-dimensional normal gravity model based on Kumar-Kuloor formulation and such a comparison is presented in this work.     

Bubble formation from a flexible hole submerged in an inviscid liquid

In the waste water treatment industry, a novel gas sparger based on flexible membranes has been used for the last 10 years. The objective of the present work is to study the bubble formation generated from a flexible orifice (membrane). Firstly, the membranes are characterised with regard to their properties: wetting critical surface tension, expanding hole diameter, orifice coefficients, flexibility, critical and elastic pressures. The bubble formation phenomenon in an inviscid liquid at rest is studied experimentally for different membranes and gas flow rates. The variation in the bubble diameter, the bubble centre of gravity and the bubble spread on the membrane are determined as a function of time. An analytic model is proposed to describe the bubble growth and its detachment at a flexible orifice. This theoretical approach, developed by Teresaka and Tsuge (J. Chem. Eng. Jpn. 23 (1990) 160) for rigid orifices, is adapted to take into account the membrane features (elastic behaviour and wettability). The predicted bubble diameters at detachment agree with the experimental measurements; however, the model underestimates slightly the bubble formation times. The calculation of the various forces acting on the bubble in the vertical direction indicates that the real forces governing the bubble growth are the buoyancy force, the surface tension force, and near detachment the inertial force.     

Influence of liquid surface tension (surfactants) on bubble formation at rigid and flexible orifices

The influence of liquid surface tension on the bubble formation from both rigid and flexible orifice has been investigated. The liquid phases under test are aqueous solutions with butanol or surfactants (cationic, non-ionic and anionic); static and dynamic measurements of liquid surface tension have been performed to characterise them. This study shows that the effect of surface tension on the bubbles generated cannot be analysed only in terms of the static surface tension, but also depends on whether the bubbles are generated from a rigid orifice or from a flexible orifice. The kinetics of adsorption and diffusion of the solute molecules towards the bubble interface have to be taken into account insofar as their time scales are comparable to those of the bubble formation phenomenon.     

Effect of the physical properties of gas on the volume of bubble formed from a submerged single orifice

The effects of the gas properties on the volume of a bubble formed from a submerged single orifice in the presence of pressure fluctuations in the gas chamber are investigated experimentally. The bubble volumes are affected by the specific heat ratio of gas and/or the gas density depending on the dimensionless capacitance number N_c. An extended two stage bubble formation model is proposed by considering the physical properties of gas. The bubble volumes calculated by the present model compare reasonably well with the experimental results.     

Effects of Orifice Orientation and Gas-Liquid Flow Pattern on Initial Bubble Size

In many gasliquid processes, the initial bubble size is determined by a series of operation parameters along with the sparger design and gasliquid flow pattern. Bubble formation models for variant gasliquid flow pat terns have been developed based on force balance. The effects of the orientation of gasliquid flow, gas velocity, liquid velocity and orifice diameter on the initial bubble size have been clarified. In ambient airwater system, thesultable gasllquid flow pattern is important to obtain smaller bubbles under the low velocity liquid crossflow con ditions with stainless steel spargers. Among the four types of gasliquid flow patterns discussed, the horizontal orifice in a vertically upward liquid flow produces the smallest initial bubbles. However the orientation effects of gas and liquid flow are found tobe insgnifican whenliq.uid velocity is.higher than. 3.2 m;sa or theorifice diameter is small enough.     

Bubble Volume and Aspect Ratio Generated in Non‐Newtonian Fluids

Bubble formation from an orifice submerged in quiescent polyacrylamide aqueous solution was investigated numerically with a sharp‐interface coupled level‐set/volume‐of‐fluid method based on the rheological characteristics of the fluid. In both non‐Newtonian fluids and Newtonian fluids, the numerical approach was able to capture accurately the deformation of the bubble surface, validated by comparison with experimental results. The effects of orifice diameter, solution mass concentration, and gas flow rate on bubble volume and aspect ratio were evaluated. Both the instantaneous and detached volume decrease with the orifice diameter but increase with mass concentration and gas flow rate. The aspect ratio at the departing point tends to rise with the orifice diameter and mass concentration and falls with the gas flow rate.     

On the possibility of diffusionally driven oscillations in two component gas bubbles in fluids

The problem of an isolated, stationary, two-component gas bubble in a fluid is analysed. The appropriate governing equations, and an approximate version of these equations, for this model system are reviewed. The qualitative differences in bubble dissolution behaviour between single- and two-component gas bubbles are elucidated. In particular, it is demonstrated that in the latter case the gas bubble radius may exhibit extrema as a function of time for certain values of the controlling parameters. The conditions under which these extrema may occur, and the maximum number of extrema which are permitted are elucidated.     

A model for non-spherical bubble growth at a single orifice

A model for predicting bubble growth and detachment at a single submerged orifice using an interfacial element approach is presented. The theoretical development of the model takes into account the gas kinetic energy and liquid circulation around the bubble as well as the effect of necking of the bubble surface. The calculated values of bubble volume and gas chamber pressure with time are compared with a wide range of experimental data in the literature. The results are in good agreement for single bubbling.     

Effect of Orifice Submergence on Bubble Formation

The effect of orifice submergence on bubble formation was experimentally studied. Four orifices were used of a diameter equal to 0.115, 0.210, 0.325 and 0.435 cm. Air was used as the gas phase and water as the liquid phase. Experiments were conducted in the range of gas flow rates 0.75–56.7 cm³/s, chamber volumes 150–7000 cm³ and orifice submergence 10–150 cm. Results show that in the region of single bubble formation the bubble size increases with the orifice submergence. In the region of group formation of bubbles the individual bubble size is independent of the orifice submergence, ranging from 0.1 to 0.5 cm³ for the smallest orifice and from 0.2 to 1 cm³ for the other ones. No effect of orifice submergence was observed on weeping.