A theoretical-experimental framework for the analysis of the dynamic response of a QEPAS tuning fork device immersed in a fluid medium

Quartz-enhanced photoacoustic spectroscopy (QEPAS) is a trace gas sensing technique that employs a designed high-quality factor quartz tuning fork (QTF) as acousto-electric transducer. The first in-plane skew-symmetric flexural mode of the QTF is excited when weak resonant sound waves are generated between the QTF prongs. Thus, the performance of a QEPAS sensor strongly depends on the resonance properties of the QTF, namely the determination of flexural eigenfrequencies and air damping loss. In this work, we present a mixed theoretical-experimental framework to study the dynamic response of a QTF while vibrating in a fluid environment. Due to the system linearity, the dynamic response of the resonator immersed in a fluid medium is obtained by employing a Boundary Element formulation based on an ad hoc calculated Green's function. In particular, the QTF is modelled as constituted by a pair of two Euler-Bernoulli cantilevers partially coupled by a distributed linear spring. As for the forces exerted by the fluid on QTF structure, the fluid inertia and viscosity as well as an additional diffusivity term, whose influence is crucial for the correct evaluation of the system response, have been taken into account. By corroborating the theoretical analysis with the experimental outcomes obtained by means of a vibro-acoustic setup, the fluid response coefficients and the dynamics of the QTF immersed in a fluid environment are fully determined.