Modeling the time response of current using interdigitated arrays in a shallow electrochemical cell

The interdigitated array of electrodes (IDAE) is a common choice for integration in small electrochemical sensors due to the amplified currents and fast response times. The design and assessment of IDAE performance in microfluidic cells require the use of mathematical models, in which the diffusion equation is widely applied. Analytical solutions for this equation are available for IDAEs in tall cells; however, they are not currently available for shallow cells, as is the case with microfluidic devices. The issue of whether it is possible to model the time response of IDAEs in shallow cells using simple exponential functions is addressed in this work. This is achieved by numerically solving the diffusion equation to obtain the time response of the current and later by applying non-linear regression to obtain exponential models. The current response is generally complex due to the many Fourier harmonics involved. However, the findings reveal that when the elapsed time is greater than some characteristic time, the current response can be approximated by an exponential curve. Furthermore, higher currents can be obtained at the expense of longer response times when the cell is tall, while shorter response times can be obtained at the expense of lower currents when the cell is shallow.