Diffusion in ion exchange

Lapidus, L. and Amundson, N. R. J. Phys. Chem. 56 (1952) 373. Mathematics of adsorption in fixed beds — The rate determining steps in radial adsorption analysis ibid 56 (1952) 984. The effect of longitudinal diffusion in ion exchange and chromatographic columns. 

Cooper, R.S. (1965) Slow particle diffusion in ion exchange columns. Chem. Eng. Fund., 4, 308. 

Glueckauf, E. Derived first comprehensive equation for relationship between HETP and particle size, particle diffusion, and film diffusion in ion exchange. 

The effective diffusion coefficients were calculated from the experimentally observed data (time, amount of cation exchanged, temperature), using Paterson s solution of Fick s second law, or published approximate solutions (8, 16). Taking into consideration particle shape and particle size distribution, the differential coefficients of internal diffusion in ion exchange can be ascertained by a method previously described (9). 

Graham, E.E., and JK.S. Dranoff. 1982. Application fo the Stefan-Maxwell equation to diffusion in ion exchangers. Ind. Eng. Chem. Fundam. 21 360-369. 

Nikolaev, N.I., Diffusion in ion exchange membrane, Khimiya, Moscow, 1980. 

Lapidus L, Amundson NR (1952) Mathematics of adsorption in beds VI. The effect of longitudal diffusion in ion exchange and chromatographic columns. J Phys Chem 56 984-988 Leigh DC (1968) Nonlinear continuum mechanics. McGraw-HiU, New York Lewis RW, Schrefler BA (2000) The finite element method in the static and dynamic deformation and consolidation of porous media Wiley, Chichester... 

Graham-Uranoff They studied multicomponent diffusion of electrolytes in ion exchangers. They found that the Stefan-Maxwell interaction coefficients reduce to limiting ion tracer diffusivities of each ion. 

In ion-exchange resins, diffusion is further complicated by electrical coupling effec ts. In a system with M counterions, diffusion rates are described by the Nernst-Planck equations (Helfferich, gen. refs.). Assuming complete Donnan exclusion, these equations canbe written... 

Diffusion through liquid films is usually better understood than that through porous bodies. In ion exchange, however, there is an additional flux through the him of mobile co-ions which are not present in the resin. The co-ions will be affected by the relative mobilities of the counter-ions. 

Ion exchange is similar to adsorption, since mass transfer from a fluid to a solid phase is common in both processes, i.e. they are basically diffusion processes. Ion exchange is also a sorption process, but ions are the sorbed species in contrast to adsorption, where electrically neutral species are sorbed (Noble and Terry, 2004 Perry and Green, 1999). It is generally accepted that adsorption and ion exchange can be grouped together as sorption for a unified treatment in practical applications. 

The use of simplified diffusion models in ion-exchange systems It is well-known that in practice, several simplified models for the representation and design of ion-exchange systems are used. In the following sections, such models are analyzed. 

The use of isotopic models in the literature—practical limits of usage As mentioned above, simplified solutions are employed in ion exchange for the estimation of diffusion coefficients. For example, the equations of Vermeulen and Patterson, derived from isotopic exchange systems, have been successfully used, even in processes that are not isotopic. Inglezakis and Grigoropoulou (2001) conducted an extended review of the literature on the use of isotopic models for ion-exchange systems. 

In ion exchange equipment, cations or anions from the fluid deposit in the solid and displace equivalent amounts of other ions from the solid. Suitable solids are not necessarily porous the ions are able to diffuse through the solid material. A typical exchange is that of H + or OH ions from the solid for some undesirable ions in the solution, such as Ca++or SOa. Eventually all of the ions in the solid are replaced, but the activity is restored by contacting the exhausted solid with a high concentration of the desired ion. for example, a strong acid to replace lost hydrogen ions. 

More details on diffusion of sugars in ion-exchangers can be found elswhere (ref.10). 

Also, in the late 1950s and 1960s some particularly seminal papers on ion exchange kinetics appeared by Helfferich (1962b, 1963, 1965) that are classics in the field. In this research it was definitively shown that the rate-limiting steps in ion exchange phenomena were film diffusion (FD) and/ or particle diffusion (PD). Additionally, the Nernst-Planck theories were explored and applied to an array of adsorbents (Chapter 5). 

Concurrent Processes Involved in Ion Exchange 103 Rate Laws for Film and Particle Diffusion Phenomena 105 Differentiating between Film- and Particle-Diffusion-Controlled... 

Schlogl, R., and Helfferich, F. (1957). Comment on the significance of diffusion potentials in ion exchange kinetics. J. Chem. Phys. 26, 5-7. 

FIGURE 38 Selective diffusion across ion-exchange membranes. (a) Anion exchange, and (b) cation exchange. Metal cations are designated by M+, anion A-, proton H+, and the fixed charges in the membrane by + and -. 

The author of this book has been permanently active during his career in the held of materials science, studying diffusion, adsorption, ion exchange, cationic conduction, catalysis and permeation in metals, zeolites, silica, and perovskites. From his experience, the author considers that during the last years, a new held in materials science, that he calls the physical chemistry of materials, which emphasizes the study of materials for chemical, sustainable energy, and pollution abatement applications, has been developed. With regard to this development, the aim of this book is to teach the methods of syntheses and characterization of adsorbents, ion exchangers, cationic conductors, catalysts, and permeable porous and dense materials and their properties and applications. 

While alginate salts with alkali metals such as sodium or potassium are soluble in water salts with divalent cations such as calcium, copper and zinc (Ca2+, Cu2+, and Zn2+, respectively) are insoluble in water. In this experiment, you will observe what happens when a drop of a sodium alginate solution is added to an aqueous solution of a divalent cation. The transformation from polymer solution to gel involves the concepts of polymer solubility, diffusion, and ion exchange. 

The variation of diffusivity with ion exchange in the Na-CaA zeolites has been shown to be consistent with a simple model based on a random distribution of open (5A type) and partially closed (4A type) windows(36). The model predicts a sharp change in both diffusivity and activation energy at 33% Ca H" exchange and this is confirmed by the experimental data. 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

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