Oliynyk O. The mathematical modelling of diffusion processes in electrochemical systems with microelectrodes of different shapes

The thesis is focused on the mathematical modelling and development of efficient approaches to the numerical simulation of diffusion processes in electrochemical cells with microelectrodes. The presented techniques are based on the application of conformal and quasi-conformal mappings. The mathematical models of diffusion processes originated by an electron transfer reaction and ECL are considered. A method for deriving coordinate transformation for the modelling of mass transfer processes was proposed for the case when the analytical solution for steady-state is known. New conformal mappings for the simulation of mass transfer in electrochemical systems with disk, ring and two hemi-cylindrical microelectrodes were proposed. The limiting diffusion regimes in electrochemical cells with rings of various thicknesses were investigated. Analytical solutions for the system of two hemi-cylindrical microelectrodes for the generator-collector and ECL regimes were obtained at steady-state.