Kinetic modeling, liquid membranes

The foregoing interpretation of the mechanism, although necessarily somewhat speculative, provides a useful kinetic model [10]. Let X, Y, and Z be the concentrations of the key chemicals Xj, the concentration of surfactant at and/or near the interface Yi the concentration of alcohol near the interface Zj the concentration of the aggregate or complex of surfactant and alcohol at and/or near the interface. Scheme 1 can be considered as a possible explanation for the mechanism of oscillation in a liquid membrane. Xb and Yb are the concentration of the surfactant and alcohol, respectively, in the bulk aqueous phase. 

Theoretical models (analytical and numerical), developed for simulation of the BOHLM and BAHLM transport kinetics, are based on independent experimental measurements of (a) individual mass-transfer coefficients of the solutes in boundary layers and (b) facilitating parameters of the liquid membrane (LMF potential) and lEM potential in the case of ion-exchange membrane (lEM) application. Satisfactory correlation between experimental and simulated data is achieved. 

Kislik, V., Eyal, A. (2000). Aqueous hybrid liquid membrane process for metal separation. Part I. A model for transport kinetics and its experimental verification. J. Membr. Sci., 169, 119-32. 

Rhodes and coworkers"1527have studied the extraction of various organic acids by liquid membranes (type 1 facilitated transport). They developed a two-phese kinetic model for the transport of a substance from tbe aqueous donor phese (continuous phase) across the liquid membrane into the internal phase. This mode is described by Eqs. (19,3-3) and (19.3-4), ... 

The design and scale-up of liquid-membrane separation processes need separation and concentration mathematical models as reported in Section 29.2.1. When complex solutions such as wastewaters are treated, several simplifications according to the specific characteristics of the system are usually assumed in order to reduce the number of parameters and mathematical complexity of the EPT model. From a kinetic point of view, the transport through the membrane... 

Cross-linked PVA membranes were also used for the PV separation of the liquid mixtures of water-acetic acid and water-acetic acid-n-butanol-BuAc (Liu et al. 2001). The permeation fluxes of water and acetic acid as a function of the composition were studied. The esterification of acetic acid with -butanol catalyzed by Zr(S04) 4H2O was carried out at a temperature range of 60°C-90°C. It was noticed that mostly water, less acetic acid, much less -butanol, and actually no BuAc permeated through the membrane during PV separation of the quaternary mixture of water-acetic acid-n-butanol-BuAc. From the results obtained from this study, Liu et al. (2001) developed a kinetic model equation for the esterification then, it was taken as a model reaction to study the coupling of PV with esterification. 

Biswas, S., Pathak, P.N. Roy, S.B. (2013) Kinetic modeling of uranium permeation across a supported liquid membrane employing dinonyl phenyl phosphoric acid (DNPPA) as the carrier. Journal ofindustrial... 

Several models have been developed for the transport of different types of species through supported liquid membranes. The transport is described by subsequent partitioning, complexation and diffusion. Mechanistic studies are mainly focussed on diffusion limited transport of cations in which diffusion of the complex through the membrane phase is the rate-limiting step of the transport. Recently, kinetic aspects in membrane transport have been elucidated for new carriers with which the rate of decomplexation determines the rate of transport. 

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. 

Various mathematical models have been developed to describe facilitated transport in liquid membranes (32-39). Under certain conditions (rapid complexation kinetics, large facilitation factors) the models allow calculation of the separation factor... 

Acyclic oligoamides, 167-168,170/ Advancing front model, description, 116 Alkali metal cation facilitated transport through supported liquid membranes with fatty acids electrogenic processes, 79-81 electroneutral transport, 76-80 experimental description, 77 kinetics, 81-85... 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

New glycolipids have to be synthesized to get further insights into liquid crystal properties (mainly lyotropic liquid crystals), surfactant properties (useful in the extraction of membrane proteins), and factors that govern vesicle formation, stability and tightness. New techniques have to be perfected in order to allow to make precise measurements of thermodynamic and kinetic parameters of binding in 3D-systems and to refine those already avalaible with 2D-arrays. Furthermore, molecular mechanics calculations should also be improved to afford a better modeling of the conformations of carbohydrates at interfaces, in relation with physical measurements such as NMR. 

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