Abstract
The potential developed on a membrane with fixed charge plays crucial
roles in many biological and engineering systems. The classic
Teorell-Meyer-Siever (TMS) theory gives an analytical expression of the
membrane potential only for limited cases of simple solutions. A
numerical method that can be applied to the general cases was developed
in this study. With a boundary updating scheme, a numerical solution to
the Nernst-Planck-Poisson equations was obtained rigorously without the
commonly used simplifications and assumptions in previous studies. The
features of the membrane potentials with different fixed charges were
investigated with this numerical method under various conditions. The
validity of this numerical method was verified by identical values of
Donnan potential obtained with well-established analytical methods. The
suitability and applicability of analytical TMS model were assessed by
comparison to the numerical method.