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A simple add-on algorithm to extend one-dimensional finite difference diffusion calculations to include charge coupling

The importance of interionic charge coupling in chemical and biological diffusion problems is discussed, and the Nernst-Planck (ionic) and Onsager-Fuoss (neutral component) methods are considered. A novel single pass charge-coupling algorithm 'Q-COUPLE' is proposed, which should be usable as a separate add-on subroutine with many one-dimensional finite difference diffusion calculations. Its mode of operation is explained with the help of elementary electrostatics and by reference to listings in BASIC. The algorithm is being applied in a finite difference model of diffusion-with-reaction in dental plaque, with 12 ions or ionizable molecules diffusing and interacting with fixed charges. It is shown to be invariant with respect to the direction of sweep, and in the simple case of coupled diffusion of a single polyvalent electrolyte is found to compare well with the analytical solution. Advantages and limitations of the proposal are discussed.