Validity of describing resonant viscosity and mass density sensors by linear 2nd order resonators

Resonant viscosity and mass density sensors are based on the determination of a mechanical oscillator’s frequency response at a characteristic resonant mode upon immersion in a liquid. In many cases the sensors’ characteristics and sensitivities are demonstrated by showing the dependence of their quality factor Q and resonance frequency fr to viscosity η and mass density ρ. Commonly, the transfer function of a linear second order resonator is fit into the recorded frequency response to extract fr and Q, which are then related to the liquid’s η and ρ. This approach is widespread in the field of resonant (viscosity and mass density) sensors and thus became a common procedure. However, as from a theoretic point of view, resonators which are interacting with a liquid do not yield linear second order functions, the applicability of this standard approach and its limits are investigated in this work.