Mathematical modelling and optimisation of a coulometric sensor-actuator system based on three-dimensional diffusion

A mathematical model describing the processes taking place in a measuring cell with a coulometric sensor-actuator system was developed both for the cases of titration of strong and weak protolytes. It takes into consideration the three dimensional diffusion which occurs in the volume of the measuring cell. The boundary conditions express the fact that the walls of the measuring cell are impermeable to the chemical species participating in the protolytic interactions and that a constant current is applied at the actuator electrode. The model was numerically solved by the implicit alternating-direction finite-difference method. Experimental titration of diluted solution of nitric, acetic and butyric acid and potassium hydroxide with various concentrations were performed. The good agreement between the experimental results and the predictions of the model confirmed its validity and showed that the model can be used successfully for the quantitative description of real sensor-actuator systems. On the basis of model simulations, some important guidelines for manufacturing sensor-actuator systems with optimal design with respect to their performance (e.g., high sampling rates) were formulated. The conditions under which the general three-dimensional model can be reduced to a two dimensional one for speeding up the computations were determined. They cover most of the sensor-actuator systems currently used in practice. It was shown that the one-dimensional model, used until now, failed to describe quantitatively real sensor-actuator systems and can be applied only for deriving qualitative trends.