Effect of Load on Quartz Crystal Microbalance Sensor Response Addressed Using Fractional Order Calculus

To accurately model the effect of the load caused by a liquid medium as a function of its viscosity, the fractional order Butterworth–Van Dyke (BVD) model of the QCM sensor is proposed in this study. A comprehensive understanding of the fractional order BVD model followed by a simulation of situations commonly encountered in experimental investigations underpins the new QCM sensor approach. The Levenberg–Marquardt (LM) algorithm is used in two fitting steps to extract all parameters of the fractional order BVD model. The integer-order electrical parameters were determined in the first step and the fractional order parameters were extracted in the second step. A parametric investigation was performed in air, water, and glycerol–water solutions in ten-percent steps for the fractional order BVD model. This indicated a change in the behavior of the QCM sensor when it swapped from air to water, modeled by the fractional order BVD model, followed by a specific dependence with increasing viscosity of the glycerol–water solution. The effect of the liquid medium on the reactive motional circuit elements of the BVD model in terms of fractional order calculus (FOC) was experimentally demonstrated. The experimental results demonstrated the value of the fractional order BVD model for a better understanding of the interactions occurring at the QCM sensor surface.