Numerical simulation of diffusion processes at recessed disk microelectrode arrays using the quasi-conformal mapping approach

In this work, we present a theoretical analysis of diffusion processes at arrays of recessed microelectrodes and evaluate the dependence of these processes on the main geometrical parameters (distance between electrodes in the array and slope of side walls of conical recesses) of this complex system. To allow for faster computation time and excellent accuracy, numerical simulations were performed upon transforming the real space allowed for diffusion using a quasi-conformal mapping introduced for this array geometry in our previous work (Amatore, C., Oleinick, A. I. and Svir, I. J. Electroanal. Chem. 2006, 597, 77−85). The applied quasi-conformal mapping is perfectly suited to the considered microelectrode array geometry and ensures that the abrupt change of boundary conditions reflecting the contorted geometries of the considered microelectrode array are treated efficiently and precisely in the simulations.