Automatic derivation of the governing equations that describe a transient electrochemical experiment, given a reaction mechanism of arbitrary complexity .2. Governing equations in one-dimensional geometry

A systematic procedure for deriving the governing equations that describe a transient electrochemical experiment, given a reaction mechanism of arbitrary complexity under conditions of controlled-potential or controlled-current transients methods, is outlined. The procedure is based on the analysis and transformations of the stoichiometric matrix and other data, and applies to the class of reaction networks involving electrochemical, heterogeneous non-electrochemical and homogeneous reactions between bulk species (subject to semi-infinite diffusion and/or convection in one-dimensional spatial geometry) and interfacial species (located at electrodes). Equilibrium, non-equilibrium reversible and irreversible reactions are allowed, as well as the presence of species with invariant concentrations, The corresponding governing equations are proven to take the form of coupled sets of partial differential equations with initial and boundary conditions (for the concentrations of bulk species), and differential-algebraic equations (for the concentrations of interfacial species). The procedure is a part of the algorithm of an automatic, computer-aided translation of electrochemical reaction mechanisms into corresponding texts of the governing equations.