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#### The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

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http://dx.doi.org/10.1007/s002490050223

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##### Citation

Syganov, A., & Von Kitzing, E. (1999). The drift approximation solves the Poisson,
Nernst-Planck, and continuum equations in the limit of large external voltages.* European Biophysics
Journal,* *28*(5), 393-414. doi:10.1007/s002490050223.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-A287-D

##### Abstract

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude