Steady-state currents of planar interdigitated electrode arrays in shallow cells

Analytical equations for the steady-state current at shallow electrochemical cells with embedded interdigitated electrode (IDE) arrays were found by solving the diffusion equation in steady state using conformal transformations. These equations consider the cases where the IDE is used with an external counter electrode (four-electrode configuration) and where one of its arrays is used as internal counter electrode (three-and two-electrode configuration). Since the expressions for the current depend on Jacobian elliptic functions, we found approximations which depend only on trigonometric and hyperbolic functions which can ease the calculations at the expense of an error below 5%. Additionally, we provide expressions for steady-state voltammograms for the case of Nernstian (reversible) electrode reactions. The obtained theoretical results agree with theoretical and simulation results from the literature and with our own experiments. These results can be useful as criteria for designing electrochemical cells based on IDEs, and as benchmarks for assessing their performance, especially for polymer-or paper-based microfluidics.