For an electrode-bounded cell membrane, the full electrochemistry reduces to a Laplace bulk plus thin screening layers, giving closed-form voltage formulas and a cable-theory circuit at long times.
Hille, Ionic Channels of Excitable Membranes (Oxford University Press, Oxford, 1992)
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Electrochemical response of biological membranes to localized currents and external electric fields
For an electrode-bounded cell membrane, the full electrochemistry reduces to a Laplace bulk plus thin screening layers, giving closed-form voltage formulas and a cable-theory circuit at long times.