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

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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.