A Three-Dimensional Digital Twin of Advanced Coupled Resonance Sensors (ACRS)

Advanced coupled resonance sensors (ACRS), built by integrating micropillar arrays onto quartz crystal microbalance (QCM) substrates, have emerged as a powerful platform for high-sensitivity measurement of viscosity, water contamination, temperature, and purification in liquid environments. Despite their demonstrated performance, the systematic role of pillar geometry, material properties, and fabrication tolerances on device behavior has not been investigated. This work presents a three-dimensional finite element digital twin of an ACRS device operating in air and liquid, in which pillar height, cross-sectional shape, elastic modulus, density, and internal loss factor are treated as independent input parameters. The model resolves the full coupled fluid–structure interaction using the linearized Navier–Stokes equations in the liquid domain, viscoelastic damping inside the pillar, and the periodic acoustic loading imposed by the QCM substrate. The framework was validated against pillar-height-dependent response in air and in deionized water for square (critical height 15 µm in air, 13 µm in water) and circular (11 µm in air, 9.5 µm in water) cross-sections, and against bulk-liquid viscosity loading across a sucrose–water series spanning approximately 1–15 cP, in which the model reproduced frequency shifts up to 85 kHz. Sensitivity enhancement exceeded a factor of 22 for both geometries near their critical heights, and the normalized peak shear displacement peaked at the critical height for both cross-sections in air and in water, exceeding the substrate amplitude by more than an order of magnitude. A Monte Carlo uncertainty propagation analysis demonstrated that operation at the critical height amplifies the standard uncertainty in resonance frequency by more than an order of magnitude relative to sub-critical operation, with geometric tolerances dominating over material property variability by a factor of two to four. The analysis recommends sub-critical operation for quantitative measurement, where the fabrication-driven combined coefficient of variation stays below 0.2% under realistic fabrication conditions. The model is validated for Newtonian liquids under fully wetted conditions and against the frequency response only. The viscosity response is validated over approximately 1–15 cP, and use outside this interval is an extrapolation of the calibration. The digital twin provides a metrologically grounded basis for ACRS design and material selection.