Measuring hydrocarbon viscosity with oscillating microcantilevers

This experimental–theoretical paper presents a reconstruction algorithm that enables the measurement of viscosity from the experimental resonance spectrum of a microcantilever immersed in the fluid under study. An analytical, closed-form solution of the equation of motion, including damping and internal friction, for the microcantilever frequency response is used which allows direct measurement of the fluid damping coefficient. This damping coefficient has a simpler relationship to viscosity than the commonly used quality factor, thus simplifying the process of calibrating and obtaining viscosity from experimental data. We validate the method by experimentally confirming that the relationship between viscosity and damping constant is quadratic. This is done with hydrocarbon liquids spanning a wide range of viscosities. Finally, we apply the method developed here to measure the viscosities of Hexadecane and Dodecane, obtaining very good agreement with accepted values.