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A one-way coupled model for the vibration of tuning fork-based trace gas sensors driven by a thermoacoustic wave

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Abstract

We present a single computational model for both quartz-enhanced photoacoustic spectroscopy and resonant optothermoacoustic detection trace gas sensors. These sensors employ a quartz tuning fork to detect the acoustic pressure and thermal waves generated when a laser excites a trace gas. The model is based on a coupled system of equations developed by Morse and Ingard for pressure and temperature in a fluid. The pressure and temperature solutions drive the resonant vibration of the tuning fork, which is modeled using the equations of linear elasticity. At high ambient pressure, excellent agreement is obtained with laboratory experiments. This result provides the first quantitative match between a fully computational simulation and experiments for a QEPAS sensor. Such a model could ultimately facilitate sensor design optimization. At low ambient pressure (less than 60 Torr), quantitative agreement is obtained after reweighting the contributions from the pressure and thermal components of the signal. While this result is a substantial improvement over previous results in which a scaling factor was required to obtain agreement at any ambient pressure, at low pressures, it appears that a more accurate physical model may be required to match experimental data.

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Acknowledgements

We thank Anatoliy Kosterev for sharing his expertise and for providing the experimental data sets. We also thank Noemi Petra for helpful discussions.

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  1. Artur Safin

    Present address: Eawag: Swiss Federal Institute for Aquatic Science and Technology, Überlandstrasse 133, 8600, Dübendorf, Switzerland

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Texas at Dallas, 800 W. Campbell Rd, Richardson, TX, 75080, USA

    Artur Safin, John Zweck & Susan E. Minkoff

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  1. Artur Safin
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Correspondence to Artur Safin.

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This work was supported by the National Science Foundation under Grant No. DMS-1620293. The numerical simulations were performed on the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562.

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Safin, A., Zweck, J. & Minkoff, S.E. A one-way coupled model for the vibration of tuning fork-based trace gas sensors driven by a thermoacoustic wave. Appl. Phys. B 126, 29 (2020). https://doi.org/10.1007/s00340-020-7376-8

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