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Journal of Membrane Science, Vol.150, No.2, 211-225, 1998
Electrochemistry of capillary systems with narrow pores. VI. Convection conductivity (theoretical considerations)
Generally, the electrical convection current and the electrical convection conductivity (Smoluchowski's surface conductivity) have to be taken into account to describe transport phenomena across membranes with narrow pores although the electrical charge distribution within the pores cannot be described as a Helmholtz electrical double layer. In collodion membranes, which have a comparatively low fixed ion concentration, the contribution of the convection conductivity to the electrical conductivity of the pore fluid may be neglected. This assumption was made tacitly in the analysis of our data obtained with this type of membrane. In this communication equations are derived which take the convection conductivity into account. They are in agreement with the phenomenological transport equations developed by Staverman on the basis of the thermodynamics of irreversible processes. The electrical convection conductivity can be considered to be the contribution of the fixed ion concentration to the electrical conductivity. It is argued that this contribution cannot be neglected in ion exchange membranes with a high fixed ion concentration and a high mechanical permeability. Neglecting the electrical convection conductivity in such systems could lead to considerable differences between experimental conductivity data and the theoretical predictions. An electrical conductivity term for the fixed ions is proposed which can be used as a correction factor in the equations in which the contribution of the electrical convection conductivity has been neglected. Suggestions are made for the measurement of the electrical convection conductivity in systems with narrow pores and high electrical conductivity (e.g. ion exchange resins). The consequences of the electrical convection conductivity in practical applications of ion-exchange resins are discussed (acceleration of the rates of ion exchange; improvement of the separation properties by the application of a direct electrical current flow).