Simultaneous Transport and Separation of Cu(II) and Zn(II) in Cu-Zn-Co Sulfate Solution by Double Strip Dispersion Hybrid Liquid Membrane (SDHLM)

A double strip dispersion hybrid liquid membrane (SDHLM) was successfully used in the simultaneous extraction and separation of Cu(II), Zn(II), and Co(II) from Cu-Zn-Co dilute feed phase. In the double SDHLM system, Acorga M5640-loaded membrane was placed between the 1st and the 2nd compartment, whereas the mono(2-ethylhexyl) 2-ethylhexyl phosphonate [HEH(EHP)]-loaded membrane was placed between the 1st and the 3rd compartment of the transport cell. The feed solution was filled in the central feed compartment(1st compartment) of the transport cell. The effect of the different experimental variables on separation was examined. The optimum separation conditions were summarized.

An analysis of mass transfer resistances in the double SDHLM system shows that the mass transfer resistance for the diffusion of Zn(II) ions in the microporous membrane phase is dominant and the mass transfer resistances for the diffusion of copper (II) ions in the aqueous boundary layer and in the microporous membrane phase are dominant in comparison with the overall mass transfer resistance. The experiments verify that the double strip dispersion hybrid liquid membrane (SDHLM) possesses the nonequlibrium mass transfer characteristic.     

The transport equations for multi-phase systems

A rigorous theoretical treatment of the transport equations is presented for multi-phase systems. The results have application in the analysis of a variety of processes including liquid—liquid extraction, gas—liquid mass transfer, and chemical reaction and dispersion in multi-phase systems. The case of mass transfer is examined in detail.     

Gas-Liquid mass transfer in fixed beds with two-phase cocurrent downflow: Gas/newtonian and non-newtonian liquid systems

New data of gas-liquid mass transfer for cocurrent downflow through packed beds of porous and non-porous particles are presented. Mass transfer parameters for air/carbon dioxide/water, air/carbon dioxide/carboxymethylcellulose solution and air/carbon dioxide/sodium hydroxide systems were evaluated by least square fit of the calculated CO₂ concentration profiles in gas phase to the experimental values. The volumetric liquid-side mass transfer coefficient increases with the increase of the flow consistency index of the liquid. A comparison of the volumetric liquid-side mass transfer coefficient values evaluated with and without taking into account the axial dispersion shows that the influence of the liquid axial dispersion is significant at low liquid velocity and high CMC concentrations, and the influence of the gas axial dispersion is insignificant.     

Simulation of true moving bed adsorptive reactor: Detailed particle model and linear driving force approximations

A new true moving bed (TMB) adsorptive reactor model with a detailed particle approach is presented introducing the formulation of the mass balance for the solid phase in counter-current moving systems. The system studied here is the enzymatic inversion of sucrose into fructose and glucose and subsequent separation of glucose/fructose; the reaction occurs both in the outer fluid phase and inside particles. Model equations include film mass transfer, intra-particle diffusion resistance, axial dispersion for the outer fluid phase, plug flow of the solid phase and linear adsorption equilibrium of glucose/fructose. This new model is compared with previous LDF-type approximations for reactive systems and applied to pure separative TMB process. The numerical solution of model equations is obtained for transient and steady state with commercial and public domain packages (gPROMS and COLNEW). The influence of the particle size and reaction rate constant is analyzed in the (γ₂×γ₃) reactive/separation region.     

Shock layer in two solute chromatography: effect of axial dispersion and mass transfer

A theoretical study for two solute chromatography when axial dispersion or interphase mass transfer is significant is presented. With a Langmuir isotherm the mathematical theory of the shock layer plays a key role in generating asymptotic solutions, from which one can deduce the effect of axial dispersion or mass transfer resistance. A full discussion is given for the existence and uniqueness of the asymptotic solution. If a shock layer exists, the end states satisfy the compatibility condition and it propagates at the same speed as the corresponding shock. Analytic expressions are developed for the case of equal Peclet numbers (or equal Stanton numbers) whereas for other cases the shock layer profiles are determined numerically. Comparison between transient solutions and shock layers demonstrates the validity and usefulness of the present study.     

Analyses of mass transfer in hemodialyzers for laminar blood flow and homogeneous dialysate

Theoretical analyses of mass transfer in hemodialyzers which contain flowing blood and dialysate streams separated by a semi-permeable membrane are presented. Semi-infinite parallel-plate and cylindrical tube geometries are considered. Solutions are obtained in terms of well-known functions, a method which avoids difficulties associated with computing the higher eigenvalues encountered in previous analyses. Applications of the mathematical model to systems used in clinical practice are discussed.     

Adsorption fixed beds modeling revisited: Generalized solutions for S-shaped isotherms

Adsorption fixed bed models are of paramount importance in chemical and environmental engineering research. Although the related literature is rich, the vast majority of models employed are either phenomenological, based on chemical reaction kinetics, or limited to systems that obey simple equilibrium isotherms (favorable, unfavorable, linear, and rectangular) combined to linear driving force (LDF) for the solid-phase mass transfer kinetics and ideal plug flow. This paper complements the existing studies by presenting and analyzing a versatile nondimensional fixed bed model equipped with diffusion-based mass transfer kinetics and nonideal flow terms and adapted to deal with S-shaped (sigmoidal) isotherms. A discussion is conducted on the rather unusual fixed bed dynamics produced by systems that follow S-shaped isotherms, a subject which has been rarely and nonsystematically discussed in the related literature. Thus, this study aims at providing better understanding of the interactions of S-shaped isotherms, mass transfer, and axial dispersion on the shape of adsorption fixed bed breakthrough curves and comes to clarify and complement previously published results, especially on the unexplored effects of the isotherms’ inflection point on the breakthrough curves.     

开式涡轮转盘塔用于液液固体系的性能研究

由转盘塔改型的开式涡轮转盘塔是一种新型的搅拌萃取塔,它适用于固含量较高的体系.其特点是每个转盘下方有3条叶片.选用水-煤油-石英砂体系,以丁酸为溶质,在内径52mm的塔中作流体力学和传质实验.结果表明,传质方向对液体分散相滞留率、固相滞留率和体积传质系数都有一定影响.固体颗粒的存在可降低扩散单元高度,但对传质并不总是有利.     

An agent-based solution of Lagrange equations for adsorption processes

A simple numerical method for solving the rate equation of adsorption processes is presented. The method starts with the mass balance for the fluid phase in its lagrangian form and the corresponding equation for the solid phase; these equations are then used to specify the governing interaction rules of discrete elements, dubbed agents. In the calculation code, ALEAP, the calculation is carried out as a series of cycles in which the agents, representing the adsorption process, interact according to these rules. In this paper we present the results obtained for linear isotherms from no transfer to high transfer rate. The method is surprisingly efficient for finding the right solution for the problem of dispersion with no adsorption and superior, in terms of computer processing time, to other methods for the simulation of the adsorption process with linear or non-linear isotherms.     

Modeling breakthrough and elution curves in fixed bed of inert core adsorbents: analytical and approximate solutions

A mathematical model is developed for fixed-beds packed with inert core adsorbents. New analytical solutions to predict breakthrough and elution curves are derived for linear adsorption systems coupled with axial dispersion, film mass transfer and intraparticle mass transfer. New approximate solutions are also obtained based on the assumptions of parabolic concentration profile in the adsorbent shell and the quasi-lognormal distribution for the impulse response in order to predict breakthrough and elution curves. The applicability of these approximate solutions is suggested by comparison with the new analytical solutions. The effects of the size of inert core, sample input mode, axial dispersion, film mass transfer resistance and intraparticle diffusion resistance, on the breakthrough and elution curves are discussed. The decrease of the intraparticle mass transfer resistance by using inert core adsorbents is quantitatively analyzed by introducing the parameter 1/Θ. Furthermore, an analytical expression for the resolution of two components is derived based on the quasi-lognormal distribution approximate solution; the resolution of two components is improved with the inert core adsorbent when compared with the conventional adsorbent, especially for biomacromolecules where the intraparticle diffusion rate is slow.     

多通道流动电泳的计算流体力学模拟与实验研究（Ⅰ）离子分布模型

多通道流动电泳（MFE）是一种制备型流动电泳技术,采用计算流体力学方法描述MFE设备中的流体流动特性,以指导分离过程和分离设备设计.基于MFE分离过程中离子迁移方程、电解质解离方程和电中性方程建立描述各腔室pH值及离子分布的模型,并通过实验进行了验证.为后续计算流体力学模拟各腔室流场分布提供了基础.     

PREDICTION OF DROP SIZE IN PULSED PERFORATED-PLATE EXTRACTION COLUMNS

A single expression for the prediction of drop size in the mixer-settler, transition and emulsion regimes of operation in pulsed perforated-plate liquid/liquid extraction columns is presented. Analysis of 326 published drop size measurements both with and without mass transfer for 16 liquid/liquid systems from 12 different data sources show that the Sauter mean drop diameter, d ₃₂, in the dispersion is given in terms of column geometry, operating conditions and physical properties of the phases by:

in which ρ_* and σ _* are the density and surface tension of water at 20°C and α and 1 are the fractional plate free area and compartment height respectively. This equation predicts the drop diameter with an average deviation of 11·3% which is much better than the average errors obtained using other available correlations.     

用单纯形法同时确定轴向混合系数与传质系数

在内径5cm的梯形波空气脉冲柱内,测定了30%TBP(煤油)-Th(NO_3)_4-HNO_3(H_2O)体系在两种板段结构条件下钍的浓度剖面.用扩散模型描述萃取过程,用单纯形法直接由浓度剖面同时确定轴向混合系数、传质系数与真实传质单元高度.由此获得的计算的浓度剖面与实验测定的浓度剖面比较符合.结果表明:梯形波脉冲柱的轴向混合系数较小,用于补偿轴向混合的柱高约占表观传质单元高度的32—44%;用单纯形法寻优,对原始微分方程采用差分近似得两组线性代数方程组,对每组线性代数方程组用追赶法直接解,两组方程之间用迭代法,程序简单,收敛较快.在PDP11/23小型计算机上,约1分钟即算得一组结果.     

Detailed Mathematical Analysis of Solute Transport in Armfield's Liquid Diffusion Apparatus

A solute's diffusivity is a key property in the design and analysis of mass transfer systems. A simple method to determine such coefficients in aqueous media is Armfield's diffusion apparatus, in which reservoir (donor) and bath (receiver) compartments are separated by a honeycomb array of liquid‐filled cylindrical pores. The solute of interest, i.e., NaCl, diffuses from the reservoir and pores into the bath. The electrical conductivity of the bath solution, which is proportional to the NaCl molarity, is tracked as a function of time at constant temperature. A comprehensive mathematical model is presented which combines simultaneous solute transport in the three compartments, allowing estimation of the aqueous NaCl diffusivity from experimental data. The model improves existing theoretical analyses of such data and can be adapted to study other challenging systems.     

Modelling of interactive populations of disperse systems

The paper presents a general mathematical model for disperse systems in which direct interactions between particles are taken into consideration. The model is formulated in terms of transition measures, introduced on the basis of conditional Markov processes. The population balance equation, describing the behaviour of interactive populations, is developed in a general form of continuous and discontinuous terms. Moment equations are presented and analysed for the axial dispersion model with interparticle exchange processes of heat and mass. The applicability of the model is illustrated by applying it for describing a process of heating particles by gas with interparticle heat transfer, and a mass exchange process between fluid particles.     

Dynamics of liquid-liquid systems based on linear thermodynamics of irreversible processes

The use of non-equilibrium models for integrated processes involving liquid-liquid systems has increased in recent years. These processes often exhibit complex dynamic behavior. These dynamical systems still pose many open questions, e.g. with regard to the sources of multiple steady states (MSS). This article analyzes the effect of mass transfer on the MSS of these systems. A generalized non-equilibrium modeling approach based on linear thermodynamics of irreversible processes (LTIP) is presented, and the dynamics of the system is studied systematically. It is shown that the non-linearity present in even the simplest non-ideal activity model acts as a source for MSS. The parameters that affect the solubility, e.g. temperature, can play a critical role on the existence of MSS in the system. A geometrical visualization of the MSS is also illustrated.     

Gas recirculation rate and its influences on mass transfer in multiple impeller systems with various impeller combinations

Both the numerical and experimental approaches were used to study the effects of the gas recirculation and non‐uniform gas loading on the mass transfer rate for each impeller in a multiple impeller system. By combining the calculated gas velocity and local gas holdup, the gas recirculation rate around each impeller was estimated. The local mass transfer coefficients for systems equipped with various combinations of the Rushton turbine impeller (R) and pitched blade impeller (P) were determined by using the dynamic gassing out method. It is found that the Rushton turbine impeller has to be served as the lowest impeller in order to have a better gas dispersion and to give a higher overall K_La for a multiple impeller gas‐liquid contactor. The upper pitched blade impeller always enforces the circulating flow around the Rushton turbine impeller just beneath it and gives a higher overall average mass transfer rate. However, the system equipped with only the pitched blade impellers results in a much lower mass transfer rate than the other systems owing to the poor gas dispersion performance of the pitched blade impeller.     

ON EXACT SOLUTIONS OF THE MAXWELL-STEFAN EQUATIONS FOR THE MULTICOMPONENT FILM MODEL

A general solution of the Maxwell-Stefan equations for mass transfer in multicomponent mixtures is obtained in terms of the characteristic roots (or eigenvalues) of these equations. The linear dependence among the composition gradients means that only n-1 of the eigenvalues are independent; the additional eigenvalue is always zero. A number of previously published exact solutions of the Maxwell-Stefan equations (obtained by a variety of mathematical methods) are shown to be essentially equivalent since they are special cases of the fundamental results described here. The general solution of Krishna and Standart may also be obtained using the same method. For the commonly encountered delerminacy conditions of transfer through a stagnant component and of equimolar counter transfer at least one of the independent eigenvalues may be evaluated explicitly in advance of calculating the molar rates of transfer thus reducing the computational eigenvalue problem from one of order n-1 to one of order n-1.     

Methode zur Erfassung von Stofftransport an fluiden Phasengrenzflächen

A finite volume‐based approach to capture mass transfer phenomena at moving fluid interfaces is proposed. The approach is capable of describing two‐phase systems containing several transferred components. Two concentration fields are defined for each transferred component, while each field has physical meaning just in one phase. This two‐field approach allows formulation of space‐ and time‐dependent boundary conditions at the interface. The suggested approach is validated with three test cases describing a single droplet in a continuous liquid phase. Purely diffusive mass transfer is captured very well. The simulation results for the moving system are in good agreement with experimental data.     

Measurement of concentration profiles in a liquid-liquid extraction column

A novel experimental technique for withdrawing uncontaminated samples of each phase from a highly agitated two liquid phase system (primary dispersion) is presented. The technique has been applied in the study of the continuous and dispersed phase axial mixing characteristic of a mechanically agitated liquid Scheibel extraction column operating under different conditions treating the chemical system acetone-toluene-water. The column mixing compartments were separated by a mixed stainless steel-polypropylene knitted mesh packed bed which was completely ‘wetted’ by the organic dispersed phase. Several concentration profiles are presented and the non-ideal flow parameters as well as the mass transfer coefficients for the column and system under study are reported.