Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.     

THE BULK AND SURFACE STRUCTURE OF γ-ALUMINA

This paper presents the real-time application of the learning control theory to the control of a chemical pilot plant: a pulsed liquid-liquid extraction column.

The behaviour of an agitated liquid-liquid extraction column can be related to random mechanisms such as the phenomena of droplets breakage and coalescence. Previous studies on hydrodynamic and mass transfer aspects showed that a pulsed liquid-liquid extraction column had an optimal behaviour for operating conditions close to flooding. These results led to choose the following strategy to control the column in its optimal behaviour zone:

- the measure of the conductivity of the liquid medium below the distributor which gives a good information about flooding, is the controlled variable

-the pulse frequency is the control action.

The learning control algorithm is based on a multilevel system of automata which operates in a random environment. By means of an evaluation unit of the performances of the column which generates either penalty (inaction) or reward on the basis of heuristic rules, the automaton chooses a value of the pulse frequency. This approach is essentially connected to artificial intelligence in so far as human knowledge on the plant is included in these rules.

This algorithm has been implemented on a microcomputer for control purposes. The experimental results presented show the good performances of the approach.     

CONTROL OF A PULSED LIQUID-LIQUID EXTRACTION COLUMN BASED ON A MULTILEVEL SYSTEM OF AUTOMATA

This paper presents the real-time application of the learning control theory to the control of a chemical pilot plant: a pulsed liquid-liquid extraction column.

The behaviour of an agitated liquid-liquid extraction column can be related to random mechanisms such as the phenomena of droplets breakage and coalescence. Previous studies on hydrodynamic and mass transfer aspects showed that a pulsed liquid-liquid extraction column had an optimal behaviour for operating conditions close to flooding. These results led to choose the following strategy to control the column in its optimal behaviour zone:

- the measure of the conductivity of the liquid medium below the distributor which gives a good information about flooding, is the controlled variable

-the pulse frequency is the control action.

The learning control algorithm is based on a multilevel system of automata which operates in a random environment. By means of an evaluation unit of the performances of the column which generates either penalty (inaction) or reward on the basis of heuristic rules, the automaton chooses a value of the pulse frequency. This approach is essentially connected to artificial intelligence in so far as human knowledge on the plant is included in these rules.

This algorithm has been implemented on a microcomputer for control purposes. The experimental results presented show the good performances of the approach.     

A Critical Review of the Application of Drop-Population Balances for the Design of Solvent Extraction Columns: I. Concept of Solving Drop-Population Balances and Modelling Breakage and Coalescence

Population-balances are a powerful method to predict the population behavior of drops in chemical-engineering equipment such as solvent extraction columns. In such columns a complex interaction of different phenomena, namely drop sedimentation, mass transfer, drop breakage and coalescence as well as axial dispersion occurs. In this article the concept of drop-population balances is discussed in detail as well as possible solution methods. Also, a critical review of existing models accounting for breakage and coalescence taking place in extraction columns is presented. Future parts of this series will be devoted to modelling mass-transfer and sedimentation as well as on application of single-drop based modelling.     

萃取塔数学模型及过程强化的若干研究进展

萃取塔因生产能力大、占地面积小、密闭性好等优点,在石油、化工、生物、医药和环境工程等多领域被广泛应用。本文从以下几个方面介绍了萃取塔近些年的研究进展：综述了传统萃取塔（脉冲萃取塔、转盘塔与Kühni塔等）的水力学、轴向扩散与传质模型的发展,分析比较了表面张力、传质方向、放大效应等因素对模型的影响;介绍了计算流体动力学（CFD）在萃取塔中单液滴、单相流模拟、液-液两相流模拟、外加能量模拟、与群体平衡模型（PBM）耦合模拟中的应用进展;介绍了国内外设计开发的新型萃取塔,包括改变传统塔的内构件和引入多种外场能量等方式来强化相间传质。研究表明,将先进实验研究方法、准确经验模型和可靠理论计算相结合,将会是萃取塔研究的重要手段和方向。     

Modelling of liquid-liquid extraction columns: Use of published model correlations in design

Design of several liquid-liquid extraction columns — packed, pulsed-packed, pulsed-plate, Oldshue-Rushton columns and the rotating disc contactor — was attempted utilizing available correlations for drop size, holdup of dispersed phase, flooding velocities, mass transfer coefficients and axial mixing coefficients. Correlations in many cases were vaguely defined and often based on very limited data. Results indicated that for given flow rates and extraction efficiency, the height of a packed or Oldshue-Rushton column must be considerably greater than the predicted minimum heights of the other three columns, which were comparable considering the limited data utilized in the developed correlations. A critical evaluation of the correlations should be carried out to guide the further experimental effort required to confirm the utility of the axial dispersion model in liquid-liquid extraction column design. Extension of the theory to include drop size variation is highly desirable.     

萃取柱内液-液两相流CFD-PBM模拟研究进展

对萃取柱内CFD-PBM模拟研究进行了较详细的综述,包括其基本理论、不同的求解方法及模拟研究现状等. CFD-PBM模拟的基本方程包括流动方程和群体平衡方程,其相互耦合,群体平衡方程涉及破碎与聚并2个关键模型. 群体平衡模型的求解方法包括直接离散化方法、矩量法、正交矩量法、直接正交矩量法、分段正交矩量法等,对这些方法的原理、优点和缺点进行了综述. 目前国际上关于萃取柱内CFD模拟采用较多的是简单的欧拉-欧拉两相流模拟,考虑液滴尺寸分布和进一步的浓度分布的群体平衡模型应用较少. 完善伴随传质的液-液分散体系的群体平衡模型,并将其应用于不同类型的萃取柱中,是萃取分离学科的重要任务.     

GRAVITY SETTLING OF DISPERSED PHASE DROP SWARMS IN EXTRACTION COLUMNS IN ABSENCE OF MASS TRANSFER

Taking into account the effect of velocity profiles of the continuous phase in interstices of drops,dragcoefficient and relative motion correlations for dispersed liquid-liquid two-phase flow in absence of mass transferwere developed in terms of the pseudo-fluid concept based on the simple similarity criteria and the mixtureviscosity model suggested by Ishii and Zuber.The present model was compared with the experimental data fromfive(different sources and also with seven other pertinent correlations available in literature.Fairly goodpredictions were obtained under wide ranges of the dispersed phase holdup and Reynolds number.The validity ofthe present model has also been checked against the experimental slip velocity data and holdup data obtained ina Karr reciprocating plate extraction column by the author of the present paper and satisfactory agreement isachieved、The results show that the equations of the motion of a multi-droplet system can be formulated in aform identical with those for a single dr     

Modelling of mass transfer in extraction columns with drop forward-mixing and coalescence-redispersion

The objective of this work is to model the effect of simultaneous drop forward-mixing and coalescence-redispersion on the hydrodynamics and mass transfer efficiency of a two phase countercurrent extraction process. Based on the flow mechanism and drop size distribution in extraction columns, a novel model with a simplified sequential algorithm is developed. It is much easier to use, and computationally less expensive, than a direct simulation technique which would typically be a tedious boundary-value iteration method. A new concept of Effective Mass Transfer Coefficient is presented, from which the effect of drop forward-mixing and coalescence-dispersion on extraction performance is directly evaluated from an analytical expression. The results calculated from the model are satisfactorily compared to experimental results obtained from three actual extraction system in two pulsed sieve-plate extraction columns. The relationship between the present model and the diffusion model is discussed and a parameter transformation equation for the two models is given.     

振动筛板槽中液滴分散动力学的研究(Ⅰ)实验研究及理论分析

本文通过实验观察发现,液滴的破碎只有在液滴与振动筛板孔口发生碰撞时才发生.基于这个实验现象,建立了振动筛板槽内液滴破碎的新模型.把筛板孔口附近的剪应力作为破碎力,破碎速率可表示为:G(d)=C_12Af/H(?)~n_4(d/d_h)~n_5[1-(d_(cr)/d)~(2n_1+1)]~0.5n(d)液滴的凝聚可以按气体分子碰撞过程来处理.凝聚速率可以用下式表示:ω(d_1,d_2)=C_Ⅱ(d_1+d_2)~(7/3)∈~（1/3)[β_d∈~(2/3)d_1+d_2/σ(d_1+d_2）~（1/3）]~n_6n(d_1)n(d_2)     

小液滴在水平液液界面上的聚并

对纯净系统中的小液滴在水平液液界面上聚并时的薄液膜排液过程进行了理论分析，研究两相物理性质、范德华力、界面切向运动对聚并速率的影响，得到了计算聚并时间的公式．理论预测与实验结果符合良好．     

Drop breakage in counter current flow liquid-liquid extraction columns

A mathematical model of the drop breakage process is applied to countercurrent flow liquid-liquid extraction columns. The resulting drop population balance equations have been solved to predict rates of drop breakage and ensuing local drop size distribution changes with height. Predictions have been compared with data obtained from a Rotating Disc Contactor.     

Drop size distribution and holdup in a rotating impeller extraction column

A stagewise hydrodynamic model, applying drop population balance equations derived from models for breakage and coalescence of drops in a countercurrent liquid-liquid extraction system, was developed to predict the drop size distribution and the holdup of the dispersed phase in a rotating impeller extraction column. The drop size distributions were obtained by taking the photographs of the dispersions at the same locations through the rectangular shaped glass box filled with distilled water. The experimental variables were the impeller speed and flow rates of the continuous and dispersed phases. The solutions of the model equations were obtained by performing the computer simulation and the optimum parameter values were determined. The results predicted by the model were in good agreement with the experimental results obtained from the present rotating impeller extraction column.     

Kennlinienfelder zur Interpretation des Stoffwerteeinflusses auf das Betriebsverhalten einer gerührten Extraktionskolonne

Mass Transfer Characteristics of an Agitated Extraction Column Depending on Material Properties For several studied test systems separation efficiency of agitated and pulsed counter-current extraction columns is found to rise continuously with increasing throughput. Test runs with n-butylacetate, aceton, water, however, show, that separation efficiency atypically runs through different typical maxima, if loading is increased up to flooding point. Series of exemplary experiments were carried out with mentioned test system at a Kühni-column DN 150 to analyse this influence, which obviously only depends on material properties, but not on the apparatus. Under variation of geometrical and experimental parameters for all test runs there were measured simultaneously: drop size distribution, holdup of dispersed phase, dispersion coefficients of both phases and concentration profiles along the extractor height. This way the mentioned atypical dependence between separation efficiency and loading bases on drop-drop-coalescence. So the basis for calculation of mass transfer process in an extractor is the deep knowledge of its fluid dynamics. Well known dispersion model or backflow-model is able to predict concentration profiles correctly, if coalescence behaviour of drop swarms is considered, so that calculation errors of drop sizes are less than +/?10%. This work reports experiments, experimental results and basic modelling.     

RAPID COALESCENCE OF MERCURY DROPS AT PLANAR MERCURY-LIQUID INTERFACES

Two modes of coalescence were observed following impact of a mercury drop with a planar mercury interface in immiscible liquid-liquid systems. At low impact velocities slow stagewise coalescence occurred in the manner observed in many previous studies, while at high velocities coalescence occurred rapidly, within 0.05 seconds following impact. The probability of rapid coalescence increased from zero to one over a narrow velocity range. The critical velocity at which the rapid coalescence probability became 0.5 decreased with increasing drop diameter and decreasing continuous phase viscosity and was affected by drop oscillation for the largest viscosity continuous phase liquid studied.     

RAPID COALESCENCE OF MERCURY DROPS AT PLANAR MERCURY-LIQUID INTERFACES

Two modes of coalescence were observed following impact of a mercury drop with a planar mercury interface in immiscible liquid-liquid systems. At low impact velocities slow stagewise coalescence occurred in the manner observed in many previous studies, while at high velocities coalescence occurred rapidly, within 0.05 seconds following impact. The probability of rapid coalescence increased from zero to one over a narrow velocity range. The critical velocity at which the rapid coalescence probability became 0.5 decreased with increasing drop diameter and decreasing continuous phase viscosity and was affected by drop oscillation for the largest viscosity continuous phase liquid studied.