Analytical Modeling of a Novel Microdisk Resonator for Liquid-Phase Sensing: An All-Shear Interaction Device (ASID)

Extensive research on micro/nanomechanical resonators has been performed recently due to their potential to serve as ultra-sensitive devices in chemical/biosensing. These applications often necessitate liquid-phase sensing, introducing significant fluid-induced inertia and energy dissipation that reduces the resonator’s performance. To minimize the detrimental fluid effects on such devices, a novel microdisk resonator supported by two tangentially-oriented, axially-driven “legs” is investigated analytically and effects of the system parameters on the resonator/sensor performance are explored. Since the device surface vibrates primarily parallel to the fluid-structure interface, it is referred to here as an “all-shear interaction device,” or ASID. Analytical modeling of the ASID includes a single-degree-of-freedom model, in which the leg mass and associated fluid resistance are neglected relative to their disk counterparts, and a generalized continuous-system, multi-modal model, in which inertial and fluid effects are included for the entire structure. The resulting analytical formulae along with the parametric studies predict that ASID designs with slender legs yield a global maximum in the quality factor (Qmax) at a “critical” disk radius approximately twice the device thickness, whereas stiffer legs correspond to Qmax occurring for the axial-mode microcantilever (the no-disk limit of the ASID). Additionally, the highest mass and chemical sensitivities (Sm, Sc) and lowest mass limit of detection (LODm) of an ASID-based sensor correspond to the axial-mode microcantilever limit, whereas the chemical LOD (LODc) has a relative minimum at the critical disk size; thus, the “optimal-Q” disk size may be different than the “optimal-sensing” counterpart. The results also show that utilizing stiffer legs will improve Q, Sm, Sc, LODm, and LODc. The theoretical results show both qualitative and quantitative agreement with existing experimental data on liquid-phase quality factor in heptane and in water, while the corresponding theoretical predictions for the fluid-induced resonant frequency shift (typically \u3c 1%) indicate the effectiveness of this novel design. Moreover, the results suggest that appropriately designed ASIDs are capable of achieving unprecedented levels of liquid-phase quality factor in the 300-500 range or even higher. The new theoretical formulae also enable one to easily map experimental data on ASID performance in one liquid to behaviors in other media without performing additional experiments