Objective Trace gas detection is related to various fields in today's world, including industrial and agricultural production, environmental monitoring, medical research, and safety protection. With the rapid development of laser technology, laser absorption spectroscopy has been widely employed in trace gas detection. Quartz- enhanced photoacoustic spectroscopy (QEPAS) based on quartz tuning fork (QTF) for detection is known for its simplicity, robust interference resistance, low cost, and quality factor. Meanwhile, resonance tubes are often coupled on both sides of the tuning to form standing sonic waves and improve the sound pressure in the QTF, which can thus enhance the tuning fork resonant for increasing the QEPAS detection performance. Although theoretical models for one-dimensional acoustic resonant tubes in co-axial QEPAS have been proposed, there remains a need for advancements in modeling, simulation techniques, and also comparative experiments to further refine the gain performance of the resonant tube in co-axial QEPAS technology. Methods A commercial QTF operating at 32 kHz (Fig. 1) is utilized, and the theoretical model of QTF cantilever beam vibration is built, with the resonant coupling model between the QTF and resonant tubes proposed. Meanwhile, finite element analysis is employed to conduct a series of simulated studies to assess the gain performance of co-axial and asymmetric resonant tubes. The influence of the resonant tube parameters on gain performance is investigated, including the internal diameter, the length, and the gap between the tube and the tuning fork. To verify the simulations, we establish a QEPAS gas detection system. Initially, five resonant tubes with different parameters along with bare tuning forks are selected for experimental testing. By comparing the experimental results of these five resonant tube systems with the bare tuning fork system, the gain performance of the resonant tubes is confirmed. Subsequently, the optimized resonant tube system undergoes long-term measurement of standard methane gas with a volume fraction of 5x10(-3), which verifies the stability and sensitivity of the system configured with resonant tubes. Results and Discussions The effective vibration mode of the tuning fork in the simulation is identified as its fourth-order modal ( Fig. 3), characterized by two opposing cantilever vibration modes. The corresponding characteristic frequency at this mode is 32772 Hz, which is close to the commonly adopted commercial tuning fork calibration frequency of 32768 Hz, with an error of 0.01%. This confirms the effectiveness of the model and simulation approach. The simulation reveals that the optimal laser incidence position for the commercial quartz tuning fork is 0.7 mm away from the top. The closer distance of the resonant tube to the tuning fork leads to a stronger coupling effect. In co-axial symmetrical resonant tube systems, as the inner diameter of the resonant tube decreases, the corresponding optimal length increases, bringing about a more significant gain effect ( Fig. 6). In the same conditions of the minimum inner diameter of the resonant tube, symmetrical structures exhibit superior gain performance than asymmetrical structures (Fig. 7). The simulation-optimized tube has the inner diameter of 0.3 mm and length of 5.12 mm. The QEPAS system is set up (Fig. 8), and experimental results show that by employing this resonant tube in the detection system, the gain performance increases 15 times compared to the bare tuning fork system (Table 2). This system is further subjected to long- term measurement of standard methane gas with a volume fraction of 5x10(-3). Allan variance analysis reveals that the detection limit of this system reaches a volume fraction 2.07x10(-6) under the integration time of 72 s (Fig. 10). Conclusions Currently, there is a lack of comprehensive and systematic research on the gain performance of resonant tubes widely adopted in QEPAS systems. To this end, we start by building a model for a commercial 32 kHz QTF. Subsequently, we employ finite element analysis to investigate the gain performance of both co-axial symmetrical and asymmetrical resonant tubes and conduct validation experiments. Our research shows that within co- axial symmetrical resonant tube systems, a decrease in the inner diameter of the resonant tube leads to correspondingly rising optimal length, bringing about a more significant gain effect. In the same conditions of the minimum inner diameter of the resonant tube, symmetrical structures exhibit superior gain performance than asymmetrical counterparts. However, excessively small inner diameters of the resonant tubes can introduce assembly complexities and limit the beam size. Finally, the system configured with the optimized resonant tube (inner diameter of 0.5 mm, length of 5.04 mm) exhibits a 15 times improvement in gain performance compared to the bare tuning fork system. The system undergoes long-term measurement of standard methane gas with a volume fraction of 5x10(-3), with the results indicating that the system's detection limit is 2.07x10(-6) under the integration time of 72 s.
