Application of a Capacitive Sensor with a ZrO2 Thin Coating and Artificial Intelligence to Determine the Amount of Diesel in Water

Reliable determination of diesel contamination in water remains challenging due to the heterogeneous nature of diesel–water dispersions and the frequency-dependent dielectric response of multiphase systems. This study investigates the performance of capacitive sensors with ZrO2 coatings of 2, 4, and 6 μm thickness and proposes a physics-informed computational framework for predicting sensor response and estimating diesel content in water. Experimental capacitance measurements were performed at 13 frequencies ranging from 10 Hz to 300 kHz using diesel–water mixtures with different fuel contents. The results revealed a general decrease in capacitance with increasing diesel content and measurement frequency, with the most pronounced concentration-dependent differences observed in the 102–104 Hz range. The 2 μm coating exhibited the highest sensitivity to diesel content, whereas the 6 μm coating provided improved measurement stability and the highest calibration linearity (R2 = 0.733) at an operating frequency of 10 kHz. To support sensor interpretation, a six-dimensional process–structure–property (PSP) model was developed to simulate the relationships between ZrO2 deposition conditions, coating microstructure, and functional properties. In parallel, a physics-informed neural network (PINN) incorporating monotonicity and high-frequency stabilization constraints was implemented for forward capacitance prediction and inverse diesel content estimation. The PINN achieved a mean absolute error of 0.29 mL in the reported inverse estimation evaluation, demonstrating the potential of physics-informed learning for interpreting nonlinear sensor responses. The complementary PSP and PINN modules establish a preliminary framework for future digital twin development, although direct numerical coupling between them remains to be implemented. The results demonstrate the feasibility of combining ZrO2-coated capacitive sensing with physics-informed artificial intelligence and provide a foundation for further development of virtual sensors for diesel–water monitoring applications.