Sensitivity of compositional measurement of high-pressure fluid mixtures using microcantilever frequency response

Frequency response of an oscillating microcantilever immersed in a fluid mixture can be used to determine the composition of the mixture over a wide range of temperatures and pressures. The Limit of Detection (LOD) in such measurements carried out at high pressures is of great interest for monitoring technologically important processes such as supercritical drying of aerogels. We studied compositional measurement sensitivity of cantilevers defined as the derivative of the cantilever resonant frequency or quality factor with respect to the fluid mixture composition. On the basis of Sader's model of hydrodynamic interaction of an oscillating immersed cantilever with the surrounding fluid, we derived analytical expressions for the sensitivity that were found to be complex functions of the density and viscosity of the mixture as well as the length, width, thickness, and density of the cantilever. We measured the frequency response of cantilevers immersed in ethanol−CO2 mixtures containing 0 - 0.04 wt fraction of ethanol at 318 K and within the pressure range 10-21 MPa. Using the measured resonant frequency and quality factor together with previously published density and viscosity data for ethanol−CO2 mixtures of various compositions, we calculated the sensitivity at each pressure and temperature and determined the LOD of the measurement. In particular, with our current setup, the LOD ranged from 0.0009 to 0.0071 wt fraction of ethanol in the mixture in the pressure range 10-21 MPa for a 150 μm long cantilever. Our results convincingly illustrate the potential of miniature cantilever-based probes for fast and sensitive in-situ detection of the composition of fluid mixtures in practical technological processes carried out at high pressures.