Resonant Modes of Hollow Micro-cantilevers for Characterization of Liquids in Picolitre Volumes

Abstract

Micro and Nano-mechanical resonators are becoming increasingly ubiquitous in the areas of particle characterization and biological sensing. For biological sensing, however, the presence of a liquid environment is a pre-requisite. Hollow cantilevers, which allow fluids to be transported inside the resonator, often have high quality factors even when the channels are filled with fluids. This makes them attractive for both sensing mass and determining fluid properties in small volumes. This work aims at determining the density of fluids in picoliter volumes with high resolution using hollow cantilevers. In order to achieve this, we obtain the resonance frequencies of the vibrating microstructure linked to three different modes: the first two flexural modes and the first torsional mode. The first torsional mode is unique to our device and is enabled by the specific geometry of the hollow cantilever. Our approach involves filling the resonator channels with three different fluids in vacuum and monitoring the resonance frequencies and quality factors of the three modes. As the mode number increases, we observe that the shifts in resonance frequency and quality factor for each liquid also increase. This implies that as we approach higher mode numbers there is an improvement in the sensitivity and resolution of the density measurement technique. The quality factors for the three fluids for a specific mode are not significantly different. It is found that in order to achieve higher sensitivities and improved resolution in determining fluid properties, studying higher modes of hollow cantilevers in improved vacuum could indeed be an effective solution.