MATHEMATICAL-MODELING AND OPTIMIZATION OF A COULOMETRIC SENSOR-ACTUATOR SYSTEM BASED ON 3-DIMENSIONAL DIFFUSION

A mathematical model describing the processes taking place in a measur ing cell with a coulometric sensor-actuator system was developed both for the cases of titration of strong and weak protolytes. It takes int o consideration the three dimensional diffusion which ocurrs in the vo lume of the measuring cell. The boundary conditions express the fact t hat the walls of the measuring cell are impermeable to the chemical sp ecies participating in the protolytic interactions and that a constant current is applied at the actuator electrode. The model was numerical ly solved by the implicit alternating-direction finite-difference meth od. Experimental titrations of diluted solutions of nitric, acetic and butyric acid and potassium hydroxide with various concentrations were performed. The good agreement between the experimental results and th e predictions of the model confirmed its validity and showed that the model can be used successfully for the quantitative description of rea l sensor-actuator systems. On the basis of model simulations, some imp ortant guidelines for manufacturing sensor-actuator systems with optim al design with respect to their performance (e.g., high sampling rates ) were formulated. The conditions under which the general three-dimens ional model can be reduced to a two dimensional one for speeding up th e computations were determined. They cover most of the sensor-actuator systems currently used in practice. It was shown that the one-dimensi onal model, used until now, failed to describe quantitatively real sen sor-actuator systems and can be applied only for deriving qualitative trends.