Nernst-Planck equations, problems with

Another problem with the Nernst-Planck equations for studying ion... 

The main difficulty when working with thin conducting polymer membranes is the lack of quantitative theory of ion diffusion within the membrane. Various theoretical schemes and approximations have been suggested, but the most difficult problem seems to be in the analytical solution or even approximation for the boundary problem of the combined Nernst-Planck and Poisson equations. The latter equation comes from the fact that electroneutrality cannot be assumed to prevail inside the thin membrane. Doblhofer et al." have made an attempt to solve the problem numerically, but even then certain initial approximations were made. Also the brute force method of finite differences does not allow to see clearly the influence of different parameters. 

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