A straightforward determination of fluid viscosity and density using microcantilevers: From experimental data to analytical expressions

Vibrating microcantilevers are used to measure the density and the viscosity of surrounding fluids. The classical procedure involves experimental acquisition of the deflection spectrum of the beam, but a systematic calibration step is mandatory for obtaining viscosity and density. In the present study, a method is proposed to facilitate these measurements for Newtonian fluids with only one calibration step in air during the cantilever lifetime. Our approach relies on a complete theoretical analysis allowing to approximate semi-analytically the deflection spectrum with a second-order transfer function and to determine an analytical relationship between viscosity, density and the parameters of the transfer function. Fluid parameter determination results are shown for validation and discussed.