Unified study of flow regimes and gas holdup in the presence of positive and negative surfactants in a non-uniformly aerated bubble column

In this paper, a study on the global gas holdup and hydrodynamic flow regimes developed in a partially aerated bubble column at variable air superficial velocities (U_G) in the presence of positive and negative surfactants is presented. According to the results obtained, despite the different liquid phase properties variation caused by the presence of positive (alcohols) and negative (electrolytes) surfactants, both reduce coalescence and the effect in the gas holdup (ε_G) is equivalent: it increases with the surfactant concentration (C) but only when the (C/C_t) ratio is clearly above 1, being C_t the transition concentration. Contrary to the results obtained for totally aerated bubble columns, for lower values of the (C/C_t) ratio, the holdup remains practically invariable. Considering the crucial role that C and C_t play in the resulting ε_G, a new prediction equation for ε_G accounting for the ratio (C/C_t) and U_G is presented and its performance for both types of surfactants validated. Additionally, visual and wall pressure fluctuations studies reveal that the vortical flow (VF), characterized by an oscillating bubble plume, prevails in ultrapure water (UPW) but results destabilized in the presence of surfactants. This destabilization results in an evolution to a pseudo-steady flow regime, the double cell turbulent flow regime (DCTF), characterized by a quasi-static bubble jet, located at the column centerline that determines the appearance of two static symmetrical vortices     

Experimental determination of the drag coefficient in a swarm of bubbles

Simultaneous measurements of liquid velocity by laser Doppler velocimetry and bubble velocity, diameter, and void fraction by a double optical probe are performed in a bubble column to study the influence of the void fraction on the relative velocity of a swarm of gas bubbles. Bubble diameters d_b vary from 2 to 10 mm and local void fractions α_loc can reach 35%. It is found that, for α_loc<15%, the relative bubble velocity is determined by the hindrance effect and consequently decreases with the void fraction. Beyond this critical value, the aspiration of bubbles in the wake of the leading ones dominates the hindrance effect and the relative velocity thus increases suddenly. The contribution of the bubble diameters to this evolution is also determined. Finally, a drag correlation, valid for the whole range of void fraction and for pure water-air systems, is proposed.     

Effect of bubble contamination on rise velocity and mass transfer

An apparatus where individual bubbles are kept stationary in a downward liquid flow was adapted to simultaneously (i) follow mass transfer to/from a single bubble as it inevitably gets contaminated; (ii) follow its shape; and (iii) periodically measure its terminal velocity. This apparatus allows bubbles to be monitored for much longer periods of time than does the monitoring of rising bubbles. Thus, the effect of trace contaminants on bubbles of low solubility gases, like air, may be studied.Experiments were done with air bubbles of 1-5 mm initial equivalent diameter in a water stream. The partial pressure of air in the liquid could be manipulated, allowing bubbles to be either dissolving or kept at an approximately constant diameter.Both drag coefficient and gas-liquid mass transfer results were interpreted in terms of bubble contamination kinetics using a simplified stagnant cap model. Drag coefficient was calculated from stagnant cap size using an adaptation of Sadhal and Johnson's model (J. Fluid Mech. 126 (1983) 237).Gas-liquid mass transfer modelling assumed two mass transfer coefficients, one for the clean front of the bubble, the other for the stagnant cap. Adjusted values of these coefficients are consistent with theoretical predictions from Higbie's and Frössling's equations, respectively.     

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.     

Lift force in bubbly suspensions

Closure relations are presented for the lift coefficient for ordered arrays of 2-D and 3-D bubbles at various bubble volume fractions. These were determined via lattice Boltzmann simulations of bubble rise in periodic boxes, where the bubbles were also subjected to shear. The single-bubble lift coefficient, determined by low-shear computational experiments, varies in a systematic manner with the aspect ratio of the bubbles. At high shear rates the lift coefficient manifested a noticeable shear rate-dependence and it could even become negative. Through a linear stability analysis of the uniformly bubbling state, it is demonstrated that the lift force can destabilize a uniformly rising array of highly distorted bubbles and give way to columnar structures.     

Hydrodynamic stability of a bubble column with a bottom-mounted point air source

Bubble column is widely used in both industrial and environmental applications. In this study, we examine the flow dynamics and stability of a bubble column driven by a point air source centrally mounted at the bottom using Phase Doppler anemometry (PDA). The model cylindrical bubble column had an inner diameter of 152 mm and was filled with the liquid to about 1 m height, above the point air source, which was made of a 30-mm diameter perforated air stone. The bubble diameters were within the range of 400–1300 μm. A customized setup was developed for accurate PDA measurements of the two phases, and detailed turbulent characteristics of the liquid phase velocity, bubble diameter, bubble velocity and the slip velocity were collected throughout the column. The comprehensiveness of the data set enabled a close examination of the hydrodynamic stability inside the column. Measurements were taken at three different air rates, namely 0.13, 0.25 and 0.38 L/min (corresponding to average gas volume fractions of 0.0065, 0.0138 and 0.0197, respectively). The results illustrated a large-scale coherent liquid circulation pattern inside the column. The circulation pattern in the upper column was relatively steady, while the pattern in the lower column was strongly unsteady with the probability density functions (pdf) for both the liquid and bubble velocities showing distinct twin peaks. An analysis based on the determination of the bubble drag forces and transversal lift forces is performed by decomposing the twin-peaked pdfs into two separated Gaussian distributions, one for the upward flow due to the bubble rises and the other for the downward flow due to circulation. Through the decomposition, a stability criterion can then be established by choosing the local bubble size as the representative length scale for the turbulent eddies inside the column. The analysis with the criterion illustrates why a steady circulation pattern was achieved in the upper column, and at the same time shows that the instability at the bottom column was induced by the low frequency meandering of the bubble swarm.     

A new approach for scale-up of bubble column reactors

The reactor of choice for the Fischer-Tropsch synthesis is a slurry bubble column. One of the few disadvantages of bubble columns is the difficulties associated with their scale-up. The latter is due to complex phases’ interactions and significant back-mixing.     

Shape oscillations and path transition of bubbles rising in a model bubble column

We investigate experimentally the occurrence of shape oscillations accompanied by path transition of periodically produced air bubbles rising in water. Within the period of bubble formation, the induced velocity is measured to examine bubble-liquid and bubble-bubble interactions. The flow is produced in a small-scale bubble column with square-shaped cross section. A capillary aerator produces bubbles of size 3.4 mm at a frequency of 5 Hz. Measuring techniques employed are high-speed imaging to capture bubble shape oscillations and path geometry, and laser-Doppler anemometry (LDA) to measure the velocity in the liquid near the rising bubbles. The experimentally obtained bubble shape data are expanded in Legendre polynomials. The results show the occurrence of oscillations by the periodicity of the expansion coefficients in space. Significant shape oscillations accompanied by path transition are observed as the second-mode oscillation frequency converges to the frequency of the initial shape oscillations. The mean velocity field in the water obtained by LDA agrees well with potential theory. An analysis of the decay of the induced flow shows that there is no interaction between the flow fields of two succeeding 3.4 mm bubbles in the rectilinear path when the bubble production frequency is lower than 7.4 Hz.     

Effect of electrolytes in aqueous solutions on oxygen transfer in gas–liquid bubble columns

The effects of inorganic electrolytes (NaCl, MgCl₂, CaCl₂) in aqueous solutions on oxygen transfer in a bubble column were studied. Electrolyte concentrations (c) below and above the critical concentrations for bubble coalescence (c_tc), and six superficial gas velocities (v_sg), were evaluated. The volumetric mass transfer (k_La) and the mass transfer (k_L) coefficients were experimentally determined. It was found that the concentration of electrolytes reduced the k_L, but the interfacial area (a) increased enough to result in a net increase of k_La. Using as independent variable a normalizing variable (c_r = c/c_tc), and maintaining fixed v_sg, similar values of k_La were observed regardless the kind of electrolyte; the same happened for k_L. This suggests that c_r quantifies the structural effects that these solutes exert on mass transfer. Also, once c_r = 1 was reached, no significant variations were found in k_La and k_L for constant v_sg. It is concluded that the gradual inhibition of bubble coalescence (c_r < 1) governs the significant changes in hydrodynamics and mass transfer via the reduction of bubble size and the consequent increment of a and gas holdup (?_g). Finally, regarding the effects of v_sg on mass transfer, transition behaviors between those expected for isolated bubbles and bubble swarms were observed.     

A bubble-based EMMS model for gas–solid bubbling fluidization

An EMMS/bubbling model for gas–solid bubbling fluidized bed was proposed based on the energy-minimization multi-scale (EMMS) method (Li and Kwauk, 1994). In this new model, the meso-scale structure was characterized with bubbles in place of clusters of the original EMMS method. Accordingly, the bubbling fluidized bed was resolved into the suspending and the energy-dissipation sub-systems over three sub-phases, i.e., the emulsion phase, the bubble phase and their inter-phase in-between. A stability condition of minimization of the energy consumption for suspending particles (N_s→min) was proposed, to close the hydrodynamic equations on these sub-phases. This bubble-based EMMS model has been validated and found in agreement with experimental data available in literature. Further, the unsteady-state version of the model was used to calculate the drag coefficient for two-fluid model (TFM). It was found that TFM simulation with EMMS/bubbling drag coefficient allows using coarser grid than that with homogeneous drag coefficient, resulting in both good predictability and scalability.     

Lift force on bubbles in a bubble column reactor: Experimental analysis

The lift force acting on bubbles in a swarm has been estimated by analyzing the instantaneous velocity-time data obtained using LDA in a cylindrical bubble column. Phase distinction was achieved through the multiresolution analysis of the velocity-time data. Several important issues related to the transverse motion of bubbles subjected to a shear field have been discussed quantitatively. The actually measured bubble sizes, the respective slip velocity values in transverse and axial directions and the local shear rates (γ) enabled the verification of known formulations for the lift coefficient (C_L) for bubbles. At many locations in the column the radial flux of the gas phase by turbulent dispersion and the radial slip were estimated. The radially inward movement of bubbles from low to high axial velocity (from column wall to center, i.e., C_L<0) was observed at most of the measurement locations. The local lift coefficient was estimated using the transverse drag force and the values support the results from the material balance approach. The estimated C_L values showed a wide variation over the column cross-section.     

Analysis of local heat transfer and hydrodynamics in a bubble column using fast response probes

A fast response probe is used to measure local heat transfer in a bubble column. It captured the variations in local heat transfer coefficients due to changes in local hydrodynamic conditions in radial and axial directions. These measurements have been used to identify flow regime transitions, variations in flow patterns and local hydrodynamic structure as obtained with different gas distributors and varying gas velocity. Standard deviations of pressure measurements obtained with a fast response probe have been compared with heat transfer coefficient fluctuations for the first time and the similarities and differences have been pointed out. Variations in average heat transfer coefficients and standard deviations in radial and axial directions point to different hydrodynamic conditions and are compared with literature studies. Relationships between local heat transfer measurements and hydrodynamic conditions are shown.     

Bubble coalescence at sieve plates: II. Effect of coalescence on mass transfer. Superficial area versus bubble oscillations

Bubble columns are among the most used equipments for gas-liquid mass transfer processes. This equipment's aim is to generate gas dispersions into a liquid phase in order to improve the contact between phases. Bubble coalescence has always been one of their greatest problems, since it reduces the superficial gas-liquid contact area. However, bigger bubbles can oscillate, and these oscillations increase the mass transfer rate by means of modifying the contact time as well as the concentration profiles surrounding the bubble. In the present work, the coupled effect has been studied by means of two-holed sieve plates with diameters of 1.5, 2 and 2.5 mm each, close enough to allow the coalescence and separated enough to avoid it. The results show that although coalescence decreases mass transfer rate from bubbles the deformable bubble generated can, in certain cases, balance the decrease in mass transfer rate due to the reduction in superficial area. This fact can then be used to avoid the harmful effect of coalescence on the mass transfer rate. Empirical and theoretical equations have also been used to explain the phenomena.     

Studies on frictional pressure drop of gas-non-Newtonian two-phase flow in a cocurrent downflow bubble column

An exclusive study has been done on experimental investigation of the two-phase frictional pressure drop with air-non-Newtonian liquid (CMC solutions) system in cocurrent downflow bubble column. The effects of gas and liquid flowrate on two-phase frictional pressure drop have been illustrated. An attempt has been made to fit the experimental two-phase frictional pressure drop data by modified Lockhart and Martinelli correlation and Aoki correlation. In another approach, friction factor method was adopted to correlate the experimental results in terms of dimensionless groups of the operating and system variables and the predicted values were found to be in good agreement with the experimental result. The experiments were performed in the bubbly flow regime because of its stability and uniformity.     

A two-dimensional hydrodynamic model of a slurry system with immersed filters

A model describing hydrodynamics of a filtering slurry system is presented, incorporating axial effects in the entire slurry volume as well as radial effects at the axial positions where a filter is present. It is demonstrated that the model is capable of handling all different types of hydrodynamic steady states that may occur.Model predictions with respect to build-up of filter cake are compared to previously reported results of experiments and calculations using a model neglecting axial variations at the positions where a filter is present. In the experimental range of interest quantitative results (especially for the surface renewal model) are slightly altered when taking axial variations in the filter zone into account. However, after fitting the unknown model constants to experiments, the relevant trends remain unchanged as compared to previous results.The physical meaning of dimensionless numbers derived from the model equations is discussed as well as the implications different values for these numbers (not limited to the experimental range) have on model results. It is also demonstrated that when applying the force balance model to describe radial hydrodynamics, a relatively uniform cake distribution is observed as compared to applying the surface renewal model. A physical explanation is offered for the existence of a maximum allowable filter length as mentioned in literature for systems free of filter cake. Implications of model results for design of filtering slurry systems are given.     

Effect of gas expansion on the velocity of individual Taylor bubbles rising in vertical columns with water: Experimental studies at atmospheric pressure and under vacuum

This study was designed to determine the effect of gas expansion on the velocity of Taylor bubbles rising individually in a vertical column of water. This experimental study was conducted at atmospheric pressure or under vacuum (33.3 and ) using three different acrylic columns with internal diameters of 0.022, 0.032, and 0.052 m, and more than 4.0 m high. A non-intrusive optical method was used to measure velocity and length of Taylor bubbles at five different locations along the columns. The operating conditions used correspond to inertial controlled regime.In experiments performed under vacuum, there is considerable gas expansion during the rise of Taylor bubbles, particularly when they approach the liquid free surface where the pressure drop (due to the hydrostatic pressure) is of the order of magnitude of the absolute pressure. The liquid ahead of the bubble is displaced upward by an amount proportional to the gas expansion resulting in increased bubble velocity. The calculated Reynolds number suggests a laminar regime in the liquid ahead of the bubble. However, the experimentally determined velocity coefficient C for each column was much smaller than 2, which would be expected for laminar flow. The value of C obtained ranges from 1.13±0.09, for the narrowest column, to 1.40±0.24, for the widest column. This suggests that a fully developed laminar flow in the liquid ahead of the bubble is never achieved due to continuous bubble expansion at a variable rate, regardless of column height.The velocity coefficient C can be used to calculate the contribution of liquid motion to bubble velocity. Subtracting this contribution from the measured bubble velocity defines a constant value which is nearly identical to the bubble rise velocity measured in the same column operated as a constant volume system (two ends closed) where gas expansion is absent.