Transport and Transference Numbers

The transport number Ti and the transference number t of an ion i are given by:

Here Ti indicates the fraction of the total current carried by the ion i, and ti determines the number of moles of the ion i transported per mole of electrons, i.e. per Faraday.

The transference number is directly related to the ion concentration and their mobility and its sum is 1. Thus:

For the definition of symbols in this and all other equations, see Table 1. Ji is the flux in the direction perpendicular to the membrane surface and z refers to the number of charges carried by an ion and indicates whether these charges are positive or negative.

A boundary condition for describing the mass transport in electrolyte solutions is the electroneutral-ity requirement which postulates that on a macroscopic scale there is no excess in positive or negative charges. Thus:

The transference numbers of different salt ions in solution are not very different. In an ion exchange membrane, however, there are the fixed ions of the membrane in addition to the mobile ions of the electrolyte. The fixed ions do not contribute to the transport of electrical charges. Their transference number is therefore 0. Furthermore, the concentration of the counterions is much lower than that of the co-ions. Their concentration in the membrane determines the permselectivity of a membrane.

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Solar Panel Basics

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