Method of the viscosity measurement by means of the vibrating micro-/nano-mechanical resonators

• We provide a fundamental analysis of the vibrating micro-/nano-cantilever in fluid.
• Recipes for viscosity extraction from frequency response are proposed.
• The sensitivity limit of the viscosity detection is put forward.

Atomic force microscopes, micro-/nano-mechanical resonators and nanowires or carbon nanotube can detect even a small change of properties of fluids and therefore they are often considered to be the prospective ultrasensitive micro/nano viscometers. However, due to the complicated physics behind such devices, the interpretation of experimental data including the viscosity extraction is mostly performed based on some approximations or data fittings. In this paper, the complete analysis of the vibrating cylindrical micro-/nano-cantilever submerged in a viscous fluid is presented. Based on the obtained results a simple way of the viscosity extraction from the maximum vibrational amplitude (MVA), the bandwidth and the resonance frequency shift, is proposed. The simple formulas for the achievable accuracy of the viscosity sensing are given. These results can be used in future development of the ultrasensitive micro/nano viscometers integrated on micro systems or flow meters.