Nemst-Planck diffusion equations, applied membranes

The Nemst-Planck flux equation has been widely applied to explain transport phenomena in ion exchange membranes and solution systems. When ion i diffuses... 

The Nemst-Planck equation is conventionally applied to measure iontophoretic flux and arises from the theoretical development of Eq. 1 to define the flux of an ionic solute /, across a membrane (a) by simple diffusion due to the solute concentration gradient and (b) as a result of the electric potential difference across the membrane (electrochemical transport) [68-70]. 

UF and RO models may all apply to some extent to NF. Charge, however, appears to play a more important role than for other pressure driven membrane processes. The Extended-Nemst Planck Equation (equation (3.28)) is a means of describing NF behaviour. The extended Nernst Planck equation, proposed by Deen et al. (1980), includes the Donnan expression, which describes the partitioning of solutes between solution and membrane. The model can be used to calculate an effective pore size (which does not necessarily mean that pores exist), and to determine thickness and effective charge of the membrane. This information can then be used to predict the separation of mixtures (Bowen and Mukhtar (1996)). No assumptions regarding membrane morphology ate required (Peeters (1997)). The terms represent transport due to diffusion, electric field gradient and convection respectively. Jsi is the flux of an ion i, Di,i> is the ion diffusivity in the membane, R the gas constant, F the Faraday constant, y the electrical potential and Ki,c the convective hindrance factor in the membrane. 

At the same time Na will diffuse in the other direction since there is a driving force fa concentration difference) but also because electroneutrality must be remained. Since the mobility of the H ions is larger an electrical potential will be generated which accelerates the Na flux. These processes can certainly not described anymore by the simple equation VI - 106 and here the Nemst-Planck equation should be employed. Figure VI -45b right shows the same principle, only anion-exchange membranes have been applied and the anions are the diffusing components. 

The Nemst-Planck equation describes MT due to diffusion, migration, and convection. Convection in nanopores arises from electroosmotic flow (EOF) or due to a mechanical pressure applied across the membrane containing the nanopore. 

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