Viscosity of liquids from the transfer function of microcantilevers

A method is presented to obtain the viscosity and density of a fluid from the mechanical frequency response of a microcantilever beam immersed in fluids. The technique is a practical solution to perform the measurement when only very small quantities of the fluid are available. A novel algorithm is described to measure the viscosity and density of an ambient fluid by comparing experimental results with the theory. The theoretical results are analytical with a closed form solution. The algorithm presented is easier to implement than the standard method currently used by most atomic force microscope practitioners. In addition, unlike the standard method, the new algorithm is applicable to high viscosity fluids that do not produce resonant peaks in the microcantilever power spectra. Experiments were carried out using standard cantilevers in a fluid cell filled with air, water, methanol and commercial oils. The result of comparing theory with experiment validates the algorithm and thus we propose the algorithm as a way to measure density and viscosity of uncharacterized fluids.