A STABILITY-CRITERION FOR ACCURATE SIMULATION OF ELECTROCHEMICAL DIFFUSION-KINETIC PHENOMENA AT THE ROTATING-DISK ELECTRODE AND IMPLICATIONS FOR SIMULATION OF DIFFUSION-MIGRATION AND OTHER PROBLEMS

A stable, accurate, and efficient fully implicit finite difference alg orithm is developed for the simulation of electrochemical behavior at a rotating disk electrode (RDE). Convenient expressions are developed for accurate evaluations of the hydrodynamic velocity profile of the s olution normal to the disk, of the thickness of the diffusion layer, a nd of the minimum thickness of solution which must be considered in a simulation. The simulation algorithm uses an exponentially expanding s pace grid to effect efficient and accurate simulation of systems invol ving homogeneous chemical reactions with reaction layers that may be m uch smaller than the RDE diffusion layer. Stability analysis of the RD E simulation in the absence of homogeneous kinetics produces a simple criterion which precisely delimits the values of the parameters which characterize the exponentially expanding space grid (i.e. the density of the volume elements and the rate of expansion) required for stable and accurate simulations. The RDE simulation algorithm was incorporate d into a generalized cyclic voltammetric simulator which allowed us to simulate RDE responses for complex systems involving various combinat ions of heterogeneous and homogeneous (first- and or second-order) rea ctions: the same stability criterion sufficed. Implications of the ana lysis for finite difference simulations of diffusion-migration problem s are also discussed.