Bouncing of a bubble at a liquid–liquid interface

Significant industrial relevance of gas–liquid–liquid flows calls for understanding of their various aspects. This study focusing on one of the aspects, i.e., interaction of a single bubble with a liquid–liquid interface, is aimed at providing the experimental evidence of a hitherto unreported phenomenon of conditional bouncing of a bubble at the interface between two immiscible, initially quiescent liquids. Bouncing of the bubble is observed for two of the six pairs of the immiscible liquids used in the experiments. The data, obtained by conducting experiments with different pairs of the lighter and heavier liquid bubble diameters and rise heights, suggest that a bubble crossing a liquid–liquid interface is expected to bounce when its average velocity is less than a threshold value that depends on the interfacial tension between the two liquids and the viscosity of the heavier liquid. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3150–3157, 2017     

A model to predict liquid bridge formation between wet particles based on direct numerical simulations

We study dynamic liquid bridge formation, which is relevant for wet granular flows involving highly viscous liquids and short collisions. Specifically, the drainage process of liquid adhering to two identical, non‐porous wet particles with different initial film heights is simulated using Direct Numerical Simulations (DNS). We extract the position of the interface, and define the liquid bridge and its volume by detecting a characteristic neck position. This allows us building a dynamic model for predicting bridge volume, and the liquid remaining on the particle surface. Our model is based on two dimensionless mobility parameters, as well as a dimensionless time scale to describe the filling process. In the present work model parameters were calibrated with DNS data. We find that the proposed model structure is sufficient to collapse all our simulation data, indicating that our model is general enough to describe liquid bridge formation between equally sized particles. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1877–1897, 2016     

Fast liquid mixing by cross-flow impingement in millimeter channels

A fast liquid mixing process was implemented by the cross-flow impingement of thin liquid sheets in the confined mixing channels with the width of millimeter(s). The species transport between the two liquids was studied by visualizing the 2-D concentration field of Rhodamine dye with the planar laser induced fluorescence (PLIF) technique, on which the intensity of segregation (IOS) and the 95% mixing time (τ₉₅) were calculated to evaluate the mixing quality. Due to the reduced spatial scale of liquid mixing and the high energy dissipation rate of ∼1000 to produced by the strong impingement between the liquid sheets, fast mixing of liquids was achieved at a time scale of milliseconds. The effects of operating conditions and the mixer geometry on the mixing behavior were investigated comprehensively by both experiments and computational fluid dynamics (CFD) simulations. Good agreement of the CFD predictions with the experimental data was obtained by the k-? model with species transport, where dependence of the CFD predictions on the turbulent Schmidt number (i.e. Sc_t) was discussed in detail. The results show that for this turbulence-induced mixing procedure the momentum ratio and the cross-flow angle between the two liquids play significant roles in the mixing efficiency. The absolute liquid velocity has little effect on the species transport in space, i.e. the mixing distance to reach IOS of 5%. Nevertheless, the mixing time is shortened at higher velocity conditions. The fluctuation of the transient concentration signals shows stronger interaction at the interface between the two liquid sheets. And the local concentration fluctuations can be well described by the β-PDF (probability density function) model.     

On the effect of liquid temperature upon bubble coalescence

An experimental study concerning the influence of liquid temperature on bubble coalescence is presented. Bubble collisions in two different liquids (water and ethanol) were analysed at four distinct temperatures , using air as the dispersed phase in all cases. A quantitative criterion was developed to compute the critical velocity for bubble coalescence based on the relative velocities and the outcome (coalescence or bouncing) of the recorded collisions. The critical velocity, and consequently bubble coalescence, was shown to increase as the liquid temperature was raised, an effect whose intensity depended on the kind of liquid employed. Using some simplifying assumptions, a comparison between the experimentally observed trends and the predictions of literature models for the film drainage was drawn. The experimental data were used together with available literature data in the development of a dimensionless correlation for predicting the critical velocity as a function of the liquid properties.     

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     

CFD Modeling of Single-Drop Hydrodynamics at Submerged Nozzles: Validation with TBP-Dodecane and Nitric Acid System and Parametric Analysis

ABSTRACT

Solvent extraction is an important separation process having many applications in chemical process industry, wastewater treatment, and separation of nuclear materials in the front-end and back-end of the closed nuclear fuel cycle. It is essentially based on dispersion of one liquid phase into another immiscible liquid phase in the form of drops. This study, which is relevant to solvent extraction, is focused on computational fluid dynamics simulations of one of the mechanisms to generate dispersion in which drops are generated by flowing a liquid through a nozzle submerged in another immiscible liquid. Two different orientations of nozzles, vertically upward and vertically downward, are considered. Transient simulations are carried out using the phase-field method for tracking the interface between the two immiscible liquids. Validation has been done with the experimental data of 30%TBP-dodecane and nitric acid system. The validated model is used to perform parametric analysis to get insights into the effects of physical properties (interfacial tension, contact angle, and density difference) on drop formation phenomenon. The results from parametric analysis are used to obtain correlations to estimate drop diameter at upward-oriented and downward-oriented nozzles.     

Motion of a two-phase bubble through a quiescent liquid

The motion of a two-phase bubble in immiscible liquids is associated with the development of three-phase heat exchangers applicable for heat transfer at low driving forces. An analytical expression for the instantaneous velocity of a two-phase bubble moving through a quiescent, less viscous, immiscible liquid has been developed. This expression predicts, very well, the available experimental data over the whole operational range of temperature and initial drop diameter.     

Interaction of two in-line bubbles of equal size rising in viscous liquid

The interaction of bubbles is the key to understand gas–liquid bubbling flow. Two-dimensional axis-symmetry computational fluid dynamics simulations on the interactive bubbles were performed with VOF method,which was validated by experimental work. It is testified that several different bubble interactive behaviors could be acquired under different conditions. Firstly, for large bubbles(d: 4, 6, 8, 10 mm), the trailing bubble rising velocity and aspect ratio have negative correlations with liquid viscosity and surface tension. The influences of viscosity and surface tension on leading bubble are negligible. Secondly, for smaller bubbles(d: 1, 2 mm), the results are complicated. The two bubbles tend to move together due to the attractive force by the wake and the potential repulsive force. Especially for high viscous or high surface tension liquid, the bubble pairs undergo several times acceleration and deceleration. In addition, bubble deformation plays an important role during bubble interaction which cannot be neglected.     

In-line interaction of a pair of bubbles in a viscous liquid

The axial velocity behind a single bubble rising in a viscous liquid has been measured. It is lower than the asymptotic wake velocity even 30 diameters behind the bubble. The inline interaction of two bubbles can be described by a superposition approximation in which the trailing bubble rises at a velocity equal to its terminal velocity plus the wake velocity behind the leading bubble and the leading bubble is unaffected by the trailing bubble. A wake velocity correlation and the critical conditions for coalescence are provided for 10<Re<100 and M > 4 × 10^?3.     

A CFD-based approach to the interfacial mass transfer at free gas–liquid interfaces

A novel computational fluid dynamics (CFD) based approach is suggested, which incorporates interfacial mass transfer at moving interfaces. This approach is general and able to govern multicomponent systems as well as interfacial boundary conditions in an arbitrary form. This is important in order to properly handle the typical concentration jump at the phase interface and to avoid an assumption of a constant distribution coefficient, which is seldom met in real processes. A test case study is carried out for a gas bubble rising in a stagnant liquid phase, whereas two different liquids, namely water and water–carboxymethylcellulose solution, are used. The gas bubble contains 99% of oxygen diffusing into continuous phase. The movement of the bubble is simulated using the level set method. Both velocity vectors and concentration contours are demonstrated and analysed.     

THEORETICAL PREDICTION OF GAS HOLDUP IN BUBBLE COLUMNS WITH NEWTONIAN AND NON-NEWTONIAN LIQUIDS

A simple model based on an energy balance which takes into account the friction losses at the gas-liquid interface and the slip velocity of single bubble is used to simulate the gas holdup in bubble columns containing Newtonian and non-Newtonian liquids which circulate in both laminar and turbulent flows. Experimental data available from the literature for bubble columns up to 7 m height and 1 m diameter with water and glycerol as Newtonian liquids and different solutions of CMC in a wide range of concentrations as non-Newtonian liquids are simulated with good agreement despite the simplifications made to describe the gas liquid flow regimes. Most of the differences between experimental and calculated gas holdup are justified on the basis of the simplifying assumptions.     

Mathematical modeling of gas-liquid mass transfer rate in bubble columns operated in the heterogeneous regime

In this paper, a multi-scale approach is followed to study gas-liquid mass transfer in bubble columns. First, a single bubble of equivalent diameter d is considered. Its morphology and its gas to liquid relative velocity are related to the bubble diameter through the use of known correlations. Then, the gas-liquid mass transfer between the bubble and the surrounding liquid is studied theoretically. An equation describing the transport of the transferred species in the viscous boundary layer around the bubble is solved. In a second step, a bubble column of 6-10 m height is studied experimentally. The gas phase in the column is characterized experimentally by means of a gammametric technique. Finally, the two studies are linked, yielding a 1D mathematical model able to predict the gas-liquid mass transfer rate in a bubble column operated in the heterogeneous regime.     

重力场对管内液液间传质影响的数值模拟

针对管内液液传质现象,建立速度场、重力场及湍流涡旋影响下的质量传递非稳态数学模型。利用PHOE-NICS 3.6软件数值求解,分析了在不同工况下管内柴油与汽油顺序输送界面处的体积分数分布情况。结果表明,在紊流输送下,密度差影响体积分数分布曲线的位置,管道倾角影响体积分数曲线的斜率,重力场对管内液液间传质总体影响较小;在停输下,较重液体处在势能高处时,则产生自然对流,对传质影响很大,且随时间延长持续下去;对较重液体处在势能较低处时,随时间延长,自然对流传质被抑制,二液体分子扩散起主导作用,且产生明显的分层。因此,依据此研究方法所得结果比试验测定提供了更为丰富的体积分数场分布信息。     

Local hydrodynamics modeling of a gas–liquid–solid three-phase bubble column

A three-dimensional (3D) transient model was developed to simulate the local hydrodynamics of a gas–liquid–solid three-phase bubble column using the computational fluid dynamic method, where the multiple size group model was adopted to determine the size distribution of the gas bubbles. Model simulation results, such as the local time-averaged gas holdups and axial liquid velocities, were validated by experimental measurements under varied operating conditions, e.g., superficial gas velocities and initial solid loadings at different locations in the three-phase bubble column. Furthermore, the local transient hydrodynamic characteristics, such as gas holdups, liquid velocities, and solid holdups, as well as gas bubble size distribution were predicted reasonably by the developed model for the dynamic behaviors of the three-phase bubble column. © 2007 American Institute of Chemical Engineers AIChE J, 2007     

Numerical Simulation of Single‐Bubble Dynamics in High‐Viscosity Ionic Liquids Using the Level‐Set Method

Two numerical models for studying the dynamics of formation and rise of single bubbles in high‐viscosity ionic liquids were implemented using the level‐set method. The models describe two stages of bubble dynamics: bubble formation at the inlet nozzle and bubble displacement across the column. The models were experimentally validated through a laboratory‐scale bubble column using water‐glycerol mixtures and two imidazolium‐type ionic liquids. The models were consistent with the experimental tests for Reynolds numbers < 5. Outside this range, the models tend to underestimate the bubble terminal velocity, which can be explained by the effect of the high velocity and pressure gradients close to the gas‐liquid interface. The models also predicted the velocity and pressure fields near the bubble surface before and after detachment.     

Numerical Simulation of Absorbing CO2 with Ionic Liquids

Although separating CO₂ from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of CO₂ absorption in these solvents have not been researched. In this paper, a coupled computational fluid dynamic (CFD) model and population balance model (PBM) was applied to study the mass transfer properties for capturing CO₂ with ionic liquids solvents. The numerical simulation was performed using the Fluent code. Considering the unique properties of ionic liquids, the Eulerian‐Eulerian two‐flow model with a new drag coefficient correlation was employed for the gas‐liquid fluid dynamic simulation. The gas holdup, interfacial area, and bubble size distribution in the bubble column reactor were predicted. The mass transfer coefficients were estimated with Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor were also predicted in this paper.     

Bubble size effect on low liquid input drift-flux parameters

We investigated the effect of bubble size on the drift-flux parameters at low liquid flow conditions by measuring the radial profiles of void fraction and phase velocities in a vertical bubbly pipe flow of diameter and height . To study the effect of the bubble size we used two different types of bubble inlets. We measured the local bubble fraction and velocity U_g by using single and four-point-optical fibre probes, and we used Laser Doppler Anemometry to determine the liquid velocity U_l. The distribution parameter C₀ and the weighted mean drift velocity |U_drift| were directly computed from the local measurements at a height on our experimental set-up. Both parameters were influenced by the bubble size. Provided no liquid flow reversal occurred at the near wall region, the distribution parameter reached a below unity minimum plateau value of C₀=0.95 for wall peaking void fraction profiles. At low liquid input conditions both the liquid input and bubble size had an influence on the distribution parameter. Extreme values such as C₀>2 were measured. From these measurements we developed models for the drift-flux parameters to take into account the effect of bubble size and input-flow conditions for our intermediate pipe diameter value. These models were tested and validated with separately collected experimental data.     

Hydrodynamics and simulation of air–water homogeneous bubble column under elevated pressure

A gas–liquid Eulerian computational fluid dynamics (CFD) model coupled with a population balance equation (PBE) was presented to investigate hydrodynamics of an air–water bubble column (1.8 m in height and 0.1 m in inner diameter) under elevated pressure in terms of pressure drop, gas holdup, mean bubble size, and bubble surface area. The CFD-PBE model was modified with three pressure correction factors to predict both the total gas holdup and the mean bubble size in the homogeneous bubbly flow regime. The three correction factors were optimized compared to experimental data. Increasing the pressure led to increasing the density, reducing the bubble size, and increasing the gas holdup. The bubble size distribution moved toward a smaller bubble size, as the pressure increased. The modified CFD-PBE model validated with experimental data and empirical models represented well hydrodynamics of the bubble column at P = 0.1, 1.5, and 3.5 MPa.     

Liquid phase axial mixing in a bubble column with viscous non-newtonian liquids

This paper presents some new data for the liquid phase axial dispersion coefficient in a bubble column with highly viscous non-Newtonian liquids (μ_L > 0.03 Pa · s). The data were obtained in a 0.15 m diameter column operating in the slug flow regime, and the dispersion measurements were conducted using heat aas a tracer. The experimental results show that the dispersion coefficients increase with both gas and liquid velocities and quantitatively they are about three times higher than those obtained for the air-water system. The results are explained based on a known hydrodynamic model of vertical gas-liquid slug flow.     

Assessment of a subgrid-scale model for convection-dominated mass transfer for initial transient rise of a bubble

The mass transfer between a rising bubble and the surrounding liquid is mainly determined by an extremely thin layer of dissolved gas near the bubble interface. Resolving this concentration boundary layer in numerical simulations is computationally expensive and limited to low Péclet numbers. Subgrid-scale (SGS) models mitigate the resolution requirements by approximating the mass transfer near the interface. In this contribution, we validate an improved SGS model with a single-phase simulation approach, which solves only the liquid phase at a highly resolved mesh. The mass transfer during the initial transient rise of moderately deformed bubbles in the range Re = 72–569 and Sc = 10²–10⁴ is carefully validated. The single-phase approach is able to mirror the two-phase flow field. The time-dependent local and global mass transfer of both approaches agree well. The difference in the global Sherwood number is below than 2.5%. The improved SGS model predicts the mass transfer accurately and shows marginal mesh dependency.