Exchange isotherm, application

ION-EXCHANGE ISOTHERMAL SUPERSATURATION CONCEPT, PROBLEMS, AND APPLICATIONS Dmitri N. Muraviev and Ruslan Khamizov... 

The application of the composite isotherms enables us to model the ion exchange on heterogeneous surfaces, such as rocks and soils. When the structure and composition of the sorbent is well known, we can choose the most probable site affinity distribution function. If not, it is desirable to fit the composite isotherm by different models. The just-described four isotherms provide an opportunity for this. In addition, when adsorption and ion exchange can take place simultaneously, adsorption and ion-exchange isotherms and site distribution functions can be combined (Cernik et al. 1996). 

To enable one to use the results of computer simulation for quantitative evaluation of the interdififiision rate of ions in real systems, it is essential to determine as effectively as possible the accuracy with which one has to specify the magnitude of dissociation constants K,, Kk and diffusion coefficients Dq, D, Dy. To accomplish this, computer simulations were performed to compare results when and Kkq differed by 10-fold and when and were taken to be equal [48,68]. The calculated kinetic curves coincide if the relations K Cq < 10 and Kgg/Cg < are applicable. In this case the concentration of the free ions Q is so low that its variation probably does not affect the electric field in the ion exchanger so that the distribution of the ions in the resin depends only on the ratios Kk /Kkb iind D /Db- this basis, an approximate estimate of the order of exchange isotherm. Also it is evident from Fig. 3 that in the case where the ratio D /Db taken for calculation purposes does not correspond to the real system, an error in determining the process rate will be larger for the unfavorable (relation Kp /KpB < 1) than it is for the favorable (relation > 1) isotherms. 

The application of the Gouy-Chapman theory for describing ion exchange can be illustrated by deriving an exchange isotherm. Consider that the surface excess (in moles per square meter) of an electrostatically sorbed ion i is given... 

The work describes applications of functional polymers for separations of bio-cultivated substances combining primary data with review of previously pubhshed works. An attention is paid to relationships between properties of the selected polymer, target product(s), and contaminants. Exploitation of these relationships for benefits of the separation efficiency is described. Specific phenomena and interactions taking place in phase of the polymer are discussed as well as effect of these phenomena on the separation processes. This includes specific interactions with functional groups and three-dimensional polymeric networks, transformations of substances in the polymer phase, dimerization, ion exchange isothermal supersaturation, etc. 

In general, large industrial fixed beds operate under near-adiabatic conditions, whereas small laboratory-scale fixed beds may approach isothermal operation (Ruthven, 1984). Especially, for most environmental applications, for catalytic, adsorption, and ion-exchange operations, the species to be removed are in such low concentrations that the operarion is nearly isothermal. Thus, the heat transfer to the external fixed-bed wall is often of minimal importance. 

In this section, the basic theory required for the analysis and interpretation of adsorption and ion-exchange kinetics in batch systems is presented. For this analysis, we consider the transient adsorption of a single solute from a dilute solution in a constant volume, well-mixed batch system, or equivalently, adsorption of a pure gas. Moreover, uniform spherical particles and isothermal conditions are assumed. Finally, diffusion coefficients are considered to be constant. Heat transfer has not been taken into account in the following analysis, since adsorption and ion exchange are not chemical reactions and occur principally with little evolution or uptake of heat. Furthermore, in environmental applications,... 

Thermodynamic systems are parts of the real world isolated for thermodynamic study. The parts of the real world which are to be isolated here are either natural water systems or certain regions within these systems, depending upon the physical and chemical complexity of the actual situation. The primary objects of classical thermodynamics are two particular kinds of isolated systems adiabatic systems, which cannot exchange either matter or thermal energy with their environment, and closed systems, which cannot exchange matter with their environment. (The closed system may, of course, consist of internal phases which are each open with respect to the transport of matter inside the closed system.) Of these, the closed system, under isothermal and iso-baric conditions, is the one particularly applicable for constructing equilibrium models of actual natural water systems. 

Another interesting application of micro reactors is to use them as calorimeters. They may show excellent performance in terms of sensitivity [9-12]. Moreover, their performance in terms of heat exchange allows study of the kinetics of fast exothermal reactions under isothermal conditions. Such a development was realized by Schneider [13, 14], who studied such a reaction with a power of up to 160 kW kg-1. This type of calorimeter is simple to use and determines the reaction kinetics in a short time, with very small amounts of reaction mass, and without any hazard for the operator. 

In the more realistic calculations of radiative exchange in furnaces and combustion chambers, a non-isothermal gas space has to be considered. H.C. Hottel and A.F. Sarohm [5.48] developed the so-called zone method for this case, cf. also [5.37], p. 647-652. Other procedures for the consideration of the temperature fields in the gas space have been extensively dealt with by R. Siegel and J.R. Howell [5.37], Chapter 15. The application of the Monte-Carlo method is suggested in particular, cf. [5.37] and [5.66], which despite being mathematically complex, produces results without making highly simplified assumptions. 

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