Drop size distribution and mean drop size in a pulsed packed extraction column

Drop size distribution and mean drop size are used for calculation of interfacial area available for mass transfer. In this study, the drop size distribution and Sauter mean drop diameter (d₃₂) have been investigated using three different liquid systems in the absence of mass transfer in a pilot plant pulsed packed column. The drop size was measured at four different points along the active column height. Three operating variables have been studied including the pulse intensity (af) and flow rates of both liquid phases. The effect of liquid properties and height of the active column were also investigated. A combination of the pulse intensity and interfacial tension had the largest effect on the drop size distribution while none of the flow rates were of significance. The height of the column played an important role at the bottom of the active column, but the associated effect was reduced with increase of the height. Finally, a normal probability function of number density was proposed for prediction of the drop size distribution with an Average Absolute Relative Error (AARE) of 8.8% for their optimized constant. Furthermore, two correlations were presented involving height or flow rates of the two phases along with operating variables and physical properties of the liquids. These correlations had AARE values of about 8.5 and 7.8%, respectively.     

Dispersed phase holdup and drop size distribution in pulsed plate columns

Dispersed phase holdup was measured in a pulsed plate column for the kerosene-water system under binary conditions and under solute transfer from dispersed to continuous and continuous to dispersed phases. The experimental data were satisfactorily modelled through a recirculation regime model. The drop size distribution, measured by a photographic technique, exhibited a multinodal character at low agitation rates and high dispersed phase flow rate. Sauter mean drop diameter was found to depend on the agitation rate, the dispersed phase flow rate, the mass transfer direction and the plate free area. Correlations for d₃₂ and the interfacial area were presented using Kolmogoroff's isotropic turbulence model.     

Drop size correlation and population balance model for an agitated-pulsed solvent extraction column

Agitated-pulsed column (APC) is a newly designed extraction column with excellent mass transfer performance. In this work, Sauter mean drop diameter d₃₂ and drop size distribution was investigated under different operation conditions in a 25 mm diameter APC. The results show that with an increase in pulsation intensity and agitation speed the drop size distribution is narrowed and d₃₂ is decreased significantly. With increasing dispersed-phase velocity, d₃₂ increased and drop size distribution become narrow, while there was no noticeable change with continuous velocity. The cumulative size distribution was found to be predicted well using the Inverse Gaussian function. A new correlation was proposed to predict the experimental d₃₂ data of the APC column used in this study. Furthermore, population balance model was applied to predict the drop size distribution with refitted parameters in the breakage, coalescence kernels functions.     

Study of mass transfer and determination of drop size distribution in a pulsed extraction column

A better understanding of pulsed liquid-liquid extraction columns was obtained by using an online digital image analysis system to characterize emulsion drop. The mass transfer of acetic acid from dispersed phase (ethyl acetate) to continuous phase (water) was studied under standard conditions. The system enabled drop size distribution (DSD) to be measured as a function of physical and thermodynamic parameters. The surface tension was investigated by static contact angle measurement. Mass transfer and energy transfer, characterized by the surface/volume ratio of the droplets were compared with the working parameters in order to interpret restrictive phenomena such as hold up and column efficiency. The experimental values of Sauter diameter (d₃₂) and those predicted by a correlation proposed in the literature are in good agreement. However, the adhesion work between liquid and PTFE plate surface indicates that interface property variations, as a function of solute concentration, must be taken into account in the theoretical correlations. It was found that hold up and separation efficiency depend mainly on the stirring rate. These results show that online image analysis can be used as a process control of a liquid-liquid extraction column in order to optimize the mixing phenomena and the DSD, the key parameter of extraction efficiency.     

Flooding and drop size in a pulsed disc and doughnut extraction column

The hydrodynamic behavior of a pulsed disc and doughnut column has been investigated using three different systems in the absence of mass transfer. Sauter-mean drop diameter (d₃₂), flooding velocity and holdup at flooding have been measured at different operating conditions. The following operating variables have been studied: pulsation intensity and flow rate of both liquid phases. As expected, smaller mean drop sizes are obtained with the increase of pulsation intensity. The results also show no significant effect of continuous phase flow rate on mean drop size, which increases with increase of dispersed phase flow rate for the operating conditions investigated. A single correlation for the prediction of d₃₂ in the mixer-settler, transition and emulsion regimes of operation is proposed with a mean deviation of 7.32%. The maximum throughput is influenced mainly by pulsation intensity and interfacial tension. Two precise correlations are proposed for predicting flooding velocities in this column. The first is based on operating variables, column geometry, and system physical properties. The second one considers the same variables, except column geometry. Good agreement between prediction and experiments is found for all operating conditions investigated.     

旋流压力式喷嘴低压喷淋液滴粒径的实验研究

以自来水为喷淋介质,对旋流压力式喷嘴低压喷淋液滴粒径进行了测试,分析了压力、喷孔直径和喷嘴流量对液滴索特平均直径(d_(SMD))的影响规律,研究了旋流压力式喷嘴液滴尺寸的分布规律。采用跨径(K)和均匀度指数(N)来揭示喷嘴低压喷淋质量。实验结果表明,d_(SMD)较大,超过250μm；d_(SMD)随喷孔直径增大而增大,随压力和喷嘴流量增大而减小；喷淋液滴尺寸分布均匀性较好,K小于0．65,N大于4。实验结果可以为旋流压力式喷嘴设计和改进提供重要的实验依据。     

Study of droplet behaviour along a pulsed liquid–liquid extraction column in the presence of nanoparticles

In this article, droplet size and its distribution along a pulsed liquid–liquid extraction column, is studied where SiO₂ nanoparticles with concentrations of 0.01, 0.05 and 0.1 vol.% and different hydrophobicities are applied to the dispersed phase. Using ultrasonication, nanoparticles were dispersed in kerosene as the base fluid. Nanofluids' stability was ensured using a UV–vis spectrophotometer. Some 22,000 droplets were measured by photographic technique and results were compared with systems containing no‐nanoparticles (Water–Acetic acid–Kerosene). Addition of nanoparticles changed the droplet shape from ellipsoidal to spherical. Also, there was a marked influence on droplet breakage and droplet coalescence at 0.01 vol.%, and 0.05 vol.% or higher volume fractions, respectively. © 2012 Canadian Society for Chemical Engineering     

Drop size distribution in a liquid-liquid spray column via a photographic technique

A photographic technique was devised for obtaining drop size distribution in a liquid-liquid (kerosene-water) spray column. Drop sizes were determined with the aid of a reference ball, using a double-flash technique with side lighting. Experimentally analyzed Sauter mean diameters were in good agreement with those predicted by the Kumar and Hartland correlations. The technique was applied up to a holdup of about 6% in this countercurrent flow study     

脉冲筛板萃取柱中连续相的轴向混合

通过示踪剂实验方法对38mm脉冲筛板萃取柱中连续相的轴向混合进行了研究。分别采用亚甲基蓝溶液和氯化钾溶液为示踪剂。实验过程中,首先采用"扰动-响应"技术实测了示踪剂的停留时间分布(RTD)曲线,然后依照轴向扩散模型(ADM)应用最小二乘法拟合求出连续相的轴向混合系数Ec,并分析了连续相表观流速、分散相表观流速、脉冲强度对于Ec的影响。实验结果表明,示踪剂浓度、径向取样位置和轴向取样位置对轴向混合系数Ec值的影响可以忽略,轴向混合系数Ec随着脉冲强度和两相表观流速的增加而增大。最后在本实验参数范围内,拟合出了连续相的轴向混合系数随操作参数变化的经验关系式,与实验结果对比,相对偏差在±20%以内。     

Lightnin静态混合器内气泡分散流体动力学特性实验研究

以Lightnin静态混合器（LSM）内水-空气气液两相体系为研究对象,在连续相水表观速度U_L=0.071~0.127 m/s和离散相空气表观速度U_G=0.007~0.042 m/s的条件下,研究内径100 mm的LSM内气液两相湍流流动阻力与气泡分散水动力学行为。使用分辨率为1920×1080的高速相机Revealer-2F04M采集混合器内不同轴向窗口的气泡群演化过程。结果表明：当U_L<0.085 m/s和U_G=0.025~0.042 m/s时,LSM内的流型为泡状流。随着气泡群流经混合元件数的增加,气泡群的Sauter平均直径d₃₂逐渐减小。当液体表观速度U_L≤0.085 m/s时,Sauter平均直径d₃₂随气体表观速度的增加先减小后增大;U_G =0.028 m/s时d₃₂达到局部最小值,53%的气泡直径d_B/D₀在0.02~0.05范围内。Sauter平均直径、内径与无量纲停留时间τ之间的关系满足d₃₂/D₀=0.031τ^-0.14We^-0.41。平均气含率α的增大显著增加了单位体积内气泡数量密度,加剧气泡与元件表面碰撞频率,增大旋涡二次流强度,导致摩擦系数显著降低;采用Lockhart-Martinelli方法对实验数据回归,得到气液两相流压降预测常数C的关联式：C=5.26×10⁵U_G^-0.91/Re^0.74。     

Plate wettability and droplet diameter in a pulsed perforated-plate extraction column

The liquid-liquid-plate contact angles of several plate materials were measured using a “preferential wetting method” proposed by the authors. The adhesional work (I_SL), calculated on the basis of contact angles was utilized to evaluate plate wettability. The experimental results indicate that different plate materials affect differently plate wettability. The plate wettability of stainless steel in an aqueous phase was observed to be different from that in an organic phase. The droplet diameter in the mixer-settler region of operation of a pulsed perforated-plate extraction column using several different plate materials, was measured. An empirical correlation of mean droplet diameter: d_p = 0.222(a_f/l_SL^1/3)^?0.13 is proposed except for alumina plates with dispersed aqueous phase operation.     

Lightnin静态混合器内气泡分散流体动力学特性实验研究

以Lightnin静态混合器（LSM）内水-空气气液两相体系为研究对象,在连续相水表观速度U_L=0.071~0.127 m/s和离散相空气表观速度U_G=0.007~0.042 m/s的条件下,研究内径100 mm的LSM内气液两相湍流流动阻力与气泡分散水动力学行为。使用分辨率为1920×1080的高速相机Revealer-2F04M采集混合器内不同轴向窗口的气泡群演化过程。结果表明：当U_L<0.085 m/s和U_G=0.025~0.042 m/s时,LSM内的流型为泡状流。随着气泡群流经混合元件数的增加,气泡群的Sauter平均直径d₃₂逐渐减小。当液体表观速度U_L≤0.085 m/s时,Sauter平均直径d₃₂随气体表观速度的增加先减小后增大;U_G =0.028 m/s时d₃₂达到局部最小值,53%的气泡直径d_B/D₀在0.02~0.05范围内。Sauter平均直径、内径与无量纲停留时间τ之间的关系满足d₃₂/D₀=0.031τ^-0.14We^-0.41。平均气含率α的增大显著增加了单位体积内气泡数量密度,加剧气泡与元件表面碰撞频率,增大旋涡二次流强度,导致摩擦系数显著降低;采用Lockhart-Martinelli方法对实验数据回归,得到气液两相流压降预测常数C的关联式：C=5.26×10⁵U_G^-0.91/Re^0.74。     

Probability density functions for bubble size distribution in air–water systems in stirred tanks

Bubble size distribution (BSD) is relevant to the design of gas–liquid systems, as it determines the interfacial area available in heat and mass transfer processes. Although data on BSD in stirred aerated tanks are available, a systematic comparison of alternative modeling functions for these data is lacking. In this work, BSDs obtained in air–water dispersions in a stirred aerated tank with a Rushton turbine and BSDs available in the literature for similar systems were modeled by 14 empirical probability density functions (PDFs). It was found that both the distribution of Nukiyama–Tanasawa with three adjustable parameters and the Rosin–Rammler distribution with two adjustable parameters reasonably fit original and literature BSDs. It is also concluded that it is possible to correlate the PDF parameters with the power dissipated by the agitator in the liquid phase, allowing the BSD to be modeled with only two parameters in a range of dissipated power from 0.5 to 2.3?kW/m³. BSDs thus modeled provide good predictions of average bubble size.     

鼓泡塔中气泡尺寸分布和局部气含率研究

在内径为0.38 m的鼓泡塔中采用双电导探针法对不同通气速率下的气泡尺寸分布和局部气含率进行了实验研究,分析了气泡尺寸的概率密度分布。结果表明:气泡尺寸随轴向高度的增加而增大,随径向距离增加而减小;鼓泡塔中气液流动可分为过渡流域和充分发展流域,在过渡流域气含率随轴向高度增加而增大,在充分发展流域气含率趋于均值,径向局部气含率分布呈抛物线型下降。高气速下气泡尺寸概率密度分布比低气速下宽,且随轴向高度的增加分布变宽。     

具有冲击平板的雾化喷雾流中汽液流动的模拟

A comprehensive three-dimensional model of droplet-gas flow was presented to study the evolution of spray in the effervescent atomization spray with an impinging plate.For gas phase,the N-S equation with the k-ε turbulence model was solved,considering two-way coupling interaction between droplets and gas phase.Dispersed droplet phase is modeled as Lagrangian entities,accounting for the physics of droplet generation from primary and secondary breakup,droplet collision and coalescence,droplet momentum and heat transfer.The mean size and statistical distribution of atomized droplets at various nozzle-to-plate distances were calculated.Some simulation results were compared well with experimental data.The results show that the existence of the impinging plate has a pronounced influence on the droplet mean size,size distribution and the droplet spatial distribution.The air-to-liquid ratio has obvious effects on the droplet size and distribution.     

Design aspect of a novel L-shaped pulsed column for liquid–liquid extraction applications: Energy consumption and the characteristics velocity concept

This article deals with the evaluation of the consumption of energy for a steady state solvent extraction in a novel L-shaped pulsed sieve-plate column,which is highly required for design and optimization of the periodic flow processes for industrial applications.In this regard,a comprehensive evaluation on the energy consumption in case of a pulsed flow for three different chemical systems is conducted and besides the influence of pulsation intensity,the effect of geometrical parameters including the plate spacing and the plate free area is investigated as well.Moreover,the concept ofcharacteristic velocity models at flooding points is evaluated with respect to the variation of pressure drop along the column at different operational conditions.     

The effect of sodium dodecyl sulfate on mean drop size in a horizontal mixer–settler extractor

The effects of surfactant concentration, impeller speed, and holdup on mean drop diameter, D₃₂, during emulsification have been studied in a mixer–settler. Two well‐defined regions for the dependence of D₃₂ on surfactant concentration were observed. At low surfactant concentrations, D₃₂ decreased significantly with an increase in surfactant concentration, whereas D₃₂ did not depend on surfactant concentration at high surfactant concentrations. The decreasing rate of change of D₃₂ with impeller speed and the increasing rate of change of D₃₂ with holdup both decreased when a surfactant was added to the system. Moreover, an empirical correlation has been derived to predict D₃₂.     

Estimate of confidence intervals for geometric mean diameter and geometric standard deviation of lognormal size distribution

Confidence of particle size distribution, which is the size distribution of sample particles selected from a large population with lognormal size distribution, has been studied theoretically. Theoretical equations were derived from the basic formulas commonly used in statistics to estimate confidence intervals for geometric mean diameter and geometric standard deviation. Computer simulation has provided size distribution of sample particles by random sampling in order to confirm the theoretical equations. For both geometric mean diameter and geometric standard deviation, the confidence intervals were calculated so that both values of population were placed approximately in the middle of the intervals. The tendencies for the intervals to decrease with an increase in sample particle number and/or significance level, and with a decrease in geometric standard deviation, were reasonable in statistics. The proposed theoretical equations should be useful for estimating confidence of lognormal size distribution.     

二维鼓泡床内气泡尺寸分布的实验与CFD模拟

在有机玻璃制成的二维鼓泡床(0.20m×0.02m×2.00m)内,采用摄像法对空气－自来水的气液两相体系的气泡尺寸分布进行了考察。以商业计算流体力学软件ANSYS CFX 10.0为平台,在双流体模型的基础上,采用k-ε湍流模型和GRACE曳力模型对气液鼓泡床内流体动力学行为进行了多相流CFD数值模拟。结果表明 MUSIG(Multiple Size Group)模型实现了对多气泡体系内气泡尺寸分布特性的考察,气泡尺寸分布的模拟结果与实验结果吻合得较好,从而说明了考虑了气泡聚并破碎的MUSIG模型能很好地反映出鼓泡床内气泡尺寸分布特性。     

Direct measurement of droplet breakage in a pulsed disc and doughnut column

The lack of experimental data for the droplet breakup has been one of the limitations for the application of population balance model (PBM). In this work, a high‐speed camera was used to directly measure the droplet breakup frequency and daughter size distribution in a pulsed disc and doughnut column. It was found from the captured video that multiple breakup events were more frequently observed than binary breakup. The multiple breakup was treated as an original breakup and several intermediate breakups to characterize the process quantitatively. The effects of pulsation intensity, dispersed phase flow rates, and the spatial locations were investigated in detail. Empirical correlations were finally established for both the breakup frequency function and the daughter droplet size distribution function and fitted well with the experimental data. The correlation equations were then used in a simplified PBM to calculate the droplet number density, which further proved the feasibility of the correlations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4188–4200, 2017