Phenomenological equations electrokinetic

Example 10.7 Energy conversion in the electrokinetic effect Electrokinetic effects are the consequence of the interaction between the flow of matter and flow of electricity through a porous membrane. The linear phenomenological equations for the simultaneous transport of matter and electricity are (Eqs. (10.89) and (10.90))... 

All the necessary information relating to electrokinetic phenomena is contained in the phenomenological equations (6.8.13) and (6.8.14) or in the equivalent set (6.8.18a) and (6.8.18b). The former set is especially useful if one inquires about state conditions under which either Jv or 1+ is held fixed. The latter set is useful to characterize operating conditions at constant pressure or constant electrostatic potential. The preceding discussion illustrates the... 

In addition to the approach using phenomenological equations for modelling ion transport in soils, the theory of irreversible thermodynamics may be adapted to soils [26], as for the case of ion-exchange membranes. Spiegler [251 and Kedem and Katchalsky [27,28] are the prime examples of this approach to transport models. The detailed review by Verbrugge and Pintauro contains a number of other references to mathematical approaches for modelling the fundamental electrokinetic phenomena. 

Equation 5.378 connects the phenomenological coefficients appearing in electroosmosis (the left-hand side) with those in streaming potential experiments (the right-hand side). We must note that Equation 5.378 is valid even if the surface conductivity is important or when the double layers are not thin with respect to the capillary diameter. Eurthermore, this type of relationship is vahd even for electrokinetic experiments with porous plugs and membranes with pores of nonuniform size and shape. The respective counterparts of the other relations (Equation 5.376) are... 

Cation, anion, and water transport in ion-exchange membranes have been described by several phenomenological solution-diffusion models and electrokinetic pore-flow theories. Phenomenological models based on irreversible thermodynamics have been applied to cation-exchange membranes, including DuPont s Nafion perfluorosulfonic acid membranes [147, 148]. These models view the membrane as a black box and membrane properties such as ionic fluxes, water transport, and electric potential are related to one another without specifying the membrane structure and molecular-level mechanism for ion and solvent permeation. For a four-component system (one mobile cation, one mobile anion, water, and membrane fixed-charge sites), there are three independent flux equations (for cations, anions, and solvent species) of the form... 

---