Frequency response of microcantilevers immersed in gaseous, liquid, and supercritical carbon dioxide

The frequency response of ferromagnetic nickel microcantilevers with lengths ranging between 200 μm and 400 μm immersed in gaseous, liquid and supercritical carbon dioxide (CO2) was investigated. The resonant frequency and the quality factor of the cantilever oscillations in CO2 were measured for each cantilever length in the temperature range between 298 K and 323 K and the pressure range between 0.1 MPa and 20.7 MPa. At a constant temperature, both the resonant frequency and the quality factor were found to decrease with increasing pressure as a result of the increasing CO2 density and viscosity. Very good agreement was found between the measured cantilever resonant frequencies and predictions of a model based on simplified hydrodynamic function of a cantilever oscillating harmonically in a viscous fluid valid for Reynolds numbers in the range of [1;1000] (average deviation of 2.40%). At high pressures of CO2, the experimental Q-factors agreed well with the predicted ones. At low CO2 pressures, additional internal mechanisms of the cantilever oscillation damping caused lowering of the measured Q-factor with respect to the hydrodynamic model predictions.