THE MULTIDIMENSIONAL UPWINDING METHOD AS A NEW SIMULATION TOOL FOR THE ANALYSIS OF MULTIION ELECTROLYTES CONTROLLED BY DIFFUSION, CONVECTION AND MIGRATION .1. STEADY-STATE ANALYSIS OF A PARALLEL PLANE FLOW CHANNEL

A new numerical method is presented for the calculation of concentrati on, potential and current distributions in two-dimensional electrochem ical cells controlled by diffusion, convection and migration of ions. The numerical model, for reasons of generality developed for an explic it time-dependent solution, has been made implicit such that it can ea sily deal with electrochemical cells at steady-state involving multipl e ions. The electrolyte solutions are considered to be dilute and at a constant temperature. This new method, the multi-dimensional upwindin g method, originates from the field of fluid mechanics. It is an alter native approach to both finite element methods and finite volume metho ds. In order to evaluate the method, steady-state computations have be en performed on two plane, parallel electrodes embedded in the walls o f a flow channel. Tertiary current distributions have been calculated using Butler-Volmer polarisation laws and with the applied cell voltag e as a driving force for concentration and potential gradients. Electr olytes with two and three ions were considered and the results, in cas e of an excessive amount of supporting electrolyte, were compared with the Levecque solution. In all cases, the numerical results are found to be in good agreement with analytical or numerical solutions from li terature.