Nernst-Plank equations

The interdiffusion coefficient, D , between Cs and Na for example, can be defined by the Nernst-Plank Equation,... 

Predicting Function from Structure using the Poisson-Nernst-Plank Equations Sodium... 

All these methods lead to a set of parameters (membrane thickness, pore volmne, hydraulic radius) which are related to the working (macroscopic) permselective membrane properties. In the case of liquid permeation in a porous membrane, macro- and mesoporous structures are more concerned with viscous flow described by the Hagen-Poiseuille and Carman-Kozeny equations whereas the extended Nernst-Plank equation must be considered for microporous membranes in which diffusion and electrical charge phenomena can occur (Mulder, 1991). For gas and vapor transport, different permeation mechanisms have been described depending on pore sizes ranging from viscous flow for macropores to different diffusion regimes as the pore size is decreased to micro and ultra-micropores (Burggraaf, 1996). 

See Nernst-Plank equation, diffusion, Stokes-Einstein equation. 

In film diffusion controlled situations, a co-ion is present in the external solution. Consequently, the Nernst-Plank equation for co-ions needs to be considered along with the role of co lons in the electroneutrality and no electric current conditions (Helfferich, 1962) in deriving the exact flux... 

No attempt has been made so far to relate the membrane phctse concentration of an ion to its external concentration. A relation of the type (3.3.120e, f) may be derived by using the relation (3.3.118b) for Donnan equilibrium as well as the electroneutrality relations in the membrane and in the external solution. The ionic flux of any ion through an ion exchange membrane may then be obtained from the Nernst-Plank equation (3.1.106). If is to be eliminated from such an equation, then the following procedure may be adopted. Write down the flux for /J and /j. If there is some constraint like Jl 0 (as in (3.4.121)), the problem is easily solved. In some cases, /J = (for example, in battery separators for alkaline Ni/Zn batteries, KOH is the electrolyte and/k+ = /oh-)- This will also allow elimination of V(i. Then one can express / in terms of the concentrations of two solutions on the two sides of the membrane by integrating across the battery separator membrane at steady state. 

This equation is known as Nernst-Plank equation. Under steady state conditions ... 

These equations, for the case of solid diffusion-controlled kinetics, are solved by arithmetic methods resulting in some analytical approximate expressions. One common and useful solution is the so-called Nernst-Plank approximation. This equation holds for the case of complete conversion of the solid phase to A-form. The complete conversion of solid phase to A-form, i.e. the complete saturation of the solid phase with the A ion, requires an excess of liquid volume, and thus w 1. Consequently, in practice, the restriction of complete conversion is equivalent to the infinite solution volume condition. The solution of the diffusion equation is... 

Substituting eq. (4.2) into (4.8) yields what may be called the Nernst-Plank-Faraday (NPF) equation for the current density... 

Use these three equations to eliminate V

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