A unified model for electrostatic sensors in fluid media

We present a unified model of electrostatic sensors comprising cantilever microbeam resonators in fluid media. The model couples Euler–Bernoulli beam equation to the nonlinear Reynolds equation. Static, damped eigenvalue, and dynamic reduced-order models were developed and validated by comparing a nonlinear frequency response of a gas sensor to its experimentally measured counterpart. Experiments were conducted to verify the capability of the developed model to predict the out-of-plane and in-plane natural frequencies of the sensor. The models were also used to investigate the potential operation of electrostatic chemical sensors based on different sensing mechanisms. While in-plane and out-of-plane vibration modes were found to be viable alternatives for resonant gas sensors, only in-plane modes were suitable to implement resonant chemical sensors due to the added mass and damping of liquid media. Similarly, higher-order modes were found more sensitive than lower order modes. Further, evidence was found for elastic interaction between out-of-plane modes and liquids in the channel underneath them but none for in-plane modes. Finally, the model predicts that in-plane modes provide the multi-valuedness necessary to implement bifurcation chemical sensors in liquid media.