Liquid membrane system theoretical models

For emulsion liquid membrane systems, a model which contains six differential and algebraic equations is developed by Huang et al in Chapter 8. The model takes into account five steps in the transport process. For comparison with experiment, the arsenic concentration in the external phase versus time is measured for the removal of arsenic from water in an ELM system. Excellent correlation of the experimental data with the theoretical predictions is obtained. 

Transport Through a Bulk Liquid Membrane. All theoretical models concerning carrier-assisted transport through SLMs are based on the theoretical work for carrier-assisted transport through BLM systems reported by Reusch and Cussler (5). They described the transport of different alkali salt mediated by dibenzo-18-crown-6 through a BLM. 

Extensive theoretical and experimental work has previously been reported for supported liquid membrane systems (SLMS) as effective mimics of active transport of ions (Cussler et al., 1989 Kalachev et al., 1992 Thoresen and Fisher, i995 Stockton and Fisher, 1998). This was successfully demonstrated using di-(2-ethyl hexyl)-phosphoric acid as the mobile carrier dissolved in n-dodecane, supported in various inert hydrophobic microporous matrices (e.g., polypropylene), with copper and nickel ions as the transported species. The results showed that a pH differential between the aqueous feed and strip streams, separated by the SLMS, mimics the PMF required for the emulated active transport process that occurred. The model for transport in an SLMS is represented by a five-step resistance-in-series approach, as follows (1) diffusion of the ion through a hydrodynamic boundary layer (2) desolvation of the ion, where it expels the water molecules in its coordination sphere and enters the organic phase via ion exchange with the mobile carrier at the feed/membrane interface (3) diffusion of the ion-carrier complex across the SLMS to the strip/membrane interface (4) solvation of the ion as it enters... 

The application of mercury is widespread in agriculture, for example, as insecticide in seed treatment, and different types of industry [60]. A promising method for the removal and preconcentration of mercury from wastewater has been the application of liquid membranes containing calixarenes as carriers [61]. A three-phase system for the extraction of Hg from industrial wastewater has been reviewed by Ersoz [62]. Models and implication of theoretical conclusions are presented. 

Phase-transfer catalysis (PTC) is the most widely synthesized method for solving the problem of the mutual insolubility of nonpolar and ionic compounds. The liquid-solid-liquid phase-transfer catalysis (LSLPTC) can overcome the purification of product and the separation of reactant and catalyst in the liquid-liquid phase-transfer catalytic reaction. The main structure of LSLPTC discussed in this study was focused the quaternary ammonium poly(mcthylstyrene-resin system. The reaction mechanism, catalytic activity, characterization of catalyst, theoretical modeling, mass transfers of reactant and pnxluct. and reactor design of LSLPTC were investigated. 

The applications cover a wide range of problems, from tests of theoretical models for molecular mobility in simple liquids and investigations of ion-solvent interactions, to studies of complicated biological systems, such as those concerned with the mechanism of enzymatic reactions and the function of biological membranes. 

Liquid membrane separation systems possess great potential for performing cation separations. Many factors influence the effectiveness of a membrane separation system including complexation/ decomplexation kinetics, membrane thickness, complex diffusivity, anion type, solvent type, and the use of ionic additives. The role that each of these factors plays in determining cation selectivity and flux is discussed. In an effort to arrive at a more rational approach to liquid membrane design, the effect of varying each of these parameters is established both empirically and with theoretical models. Finally, several general liquid membrane types are reviewed, and a novel membrane type, the polymeric inclusion membrane, is discussed. 

The theoretical description of the kinetics of transmembrane transport through a liquid membrane should be based on the principles of solvent extraction kinetics. It should be determined by the processes at both water/membrane interphases and should also involve the intermediate step of diffusion in the membrane. Thus the existence of all these three steps makes the membrane system and its description much more complicated than the relatively simple water/organic phase. However, even the kinetics mechanism in simpler extraction systems is often based on the models dealing only with some limiting situations. As it was pointed out in the beginning of this paper, the kinetics of transmembrane transport is a fimction both of the kinetics of various chemical reactions occurring in the system and of diffusion of various species that participate in the process. The problem is that the system is not homogeneous, and concentrations of the substances at any point of the system depend on the distance from the membrane surface and are determined by both diffusion and reactions. The solution of a system of differential equations in this case can be a serious problem. 

Interfaces between two immiscible solutions with dissolved electrolytes, which are most interesting to workers in several disciplines, cover theoretical physical electrochemistry and analytical applications for sensor design. These interfaces are used in interpretation of processes that occur in biological membranes and in biological systems. The interface between two immiscible electrolyte solutions was studied for the first time at least 100 years ago by Nemst (I), who performed the experiments that provide the theoretical basis for current potentiometric and voltammetric studies of interfaces. In 1963, Blank and Feig (2) suggested that an interface between two immiscible liquids could be used as a model (at least as a crude approximation) for... 

In 1979, Baadenhuijsen and Seuren-Jacobs [2] were the first to report on a FI gas diffusion separation system with a semi-permeable dimethylsilicone rubber membrane, used for the determination of carbon dioxide in plasma. In the same year. Zagatto et al.[3] introduced an isothermal distillation FI system in which ammonia diffused from a flowing donor liquid film across an air-gap and absorbed by a flowing acceptor film on the opposite side of the gap. However, later developments on gas diffusion separations mainly followed the approach of Baadenhuijsen and Seuren-Jacobs, obviously due to its simpler design and higher versatility. The first theoretical study on an FI gas-diffusion separation system was attempted by van der Linden [4], who used a tank-in-series model for the mathematical evaluation of the separation process. 

The understanding of the surface properties of both fluid and more ordered membranes has recently attracted much experimental and theoretical attention. 21-29 to a large degree, this focus of attention stems from the inherent interest in elucidating the statistical physics of two-dimensional random surfaces. More generally, multilayered membranes which are lyotropic liquid crystals, are of high scientific interest because they are prototype models for elucidating the nature of phases and their phase transitions in two-dimensional systems. 

---