Viscosity measurements based on experimental investigations of composite cantilever beam eigenfrequencies in viscous media

Abstract

Experimental investigations have been conducted to study the multimode dynamic response of composite cantilever beams in various viscous media and to determine their viscosity. Theoretical eigenfrequencies are computed using the analytical model proposed by Sader [J. Appl. Phys. 84, 64 (1998)] based on the analysis of the hydrodynamic function of cantilever beams. A good agreement is found between theory and experiment for the first two resonant frequencies of composite beams operated in air and in water. The same experimental approach is used to determine the viscosity of ultrapure ethanol. Thus, it is established that Sader’s model represents an accurate alternative for the determination of liquid viscosity in small volumes (about 50 μl) which might be of great importance for microfluidics applications. Finally, the limits of the method are underlined by monitoring the dynamic response of cantilever beams in silicon oil.