Comparative Study of Estimation Methods of the Tortuosity in Ion-Exchange Plugs

In this work a comparative study of estimation methods of tortuosity in ionexchange plugs has been carried out. The surface conductivity contribution has been estimated for the plugs of different structural characteristics. The tortuosity of these plugs has been determined by the equation used for inactive porous media. Subsequently, the tortuosity has been also determined by means of the models used for ion-exchange membranes. In order to know which method provides the most reliable value of the tortuosity, the cross-phenomenological coefficient, /21, has been calculated and compared with the experimental value. On the basis of the numerical values of the tortuosity factor an indirect estimation of the selfdiffusion coefficient of water in ionic plugs has been performed. Introduction The Thermodynamics of Irreversible Processes is often used to study transport processes through ion-exchange membranes and ionic plugs. The phenomenological coefficients (Lik), which relate forces and fluxes, can be experimentally obtained [1-3]. These coefficients, however, are not able to provide an internal insight on the structure of membranes. Thus, a full up characterization of the membranes, as porous media through which a great variety of transport processes can take place, requires to know some internal parameters [4, 5] such as the tortuosity and the surface conductivity, for instance. When ionic plugs are used the surface conductivity plays, generally, a decisive role on electrical transport mechanisms. Sometimes in electrified interfaces, this anomalous electrical conduction may account for the discrepancies between theoretical and experimental values of transport parameters. The structural parameter usually employed for characterizing porous media is the formation factor, also called Structural Resistance Coefficient, F [6], since it J. Non-Equilib. Thermodyn. , Vol. 12, 1987, No. 4 Copyright © 1987 Walter de Gruyter Berlin · New York 292 F. J. de las Nieves Lopez et al. is determined by the geometry of the pore space. Furthermore, Fis independent of the nature of liquid permeants, as long as the interaction Between permeant and porous media is not strong enough to alter the equivalent pore radius. Thus, the formation factor is related to tortuosity (f) and porosity (p) of the porous system, and it constitutes a method to calculate t once the porosity is known. Fis constant and greater than unity for high electrolyte concentration. However, with decreasing concentration, several authors [6] have found that it tends to decrease. This decreasing trend of F, has been attributed to the contribution of excess ions of the double layer to conductance, that is said, to the surface conductance effect. An alternative method of calculating t, without the necessity of performing electric conductance measurements, is by means of the MackieMeares equation [7]. Using the classical theory of electrokinetic processes and the values of tortuosity previously found, the theoretical cross-phenomenological coefficient /21 can be obtained. The aim of this work is to discern which method of calculating / gives /21 values that better fit those experimentally obtained [8]. 1. Materials and methods Ion-exchange resins, Amberlite IR112, 120 and 122, H + form, were employed throughout this work. These particles were mixed with particles of teflon, which was utilized as binder. Ionic plugs with different composition (ratio resin to teflon by weight), as well as with different compactness, were made by mechanical compression of a mixture of resin and binder contained in a glass cell similar to that previously described [8]. The geometric characteristics are given in Tab. 1. More details about the preparation method and other characteristics of the ionic plugs can be found in an earlier paper [8].