Virtual mass effect in dynamic micromechanical mass sensing in liquids

Abstract

Weighing individual micro- or nanoscale particles in solution using dynamic micromechanical sensors is quite challenging: viscous losses dramatically degrade the sensor's performance by both broadening the resonance peak and increasing the effective total mass of the resonator by the dragged liquid. While the virtual mass of the resonator was discussed frequently, little attention has been paid to the virtual mass of particles attached to the resonator's surface and its impact on the accuracy of mass sensing. By means of the in situ detection of a polystyrene microbead in water using a bridge-based microresonator, we demonstrate that the virtual mass of the bead significantly affects the observed frequency shift. In fact, 55% of the frequency shift was caused by the virtual mass of the adsorbed bead, predicted by Stoke's theory. Based on the observed shift in the resonator's quality factor during particle adsorption, we confirm this significant effect of the virtual mass. Thus, a quantitative analysis of the mass of a single adsorbed particle is strongly diminished if dynamic micromechanical sensors are operated in a liquid environment.