1. Introduction
The speed of sound,
c, in a pure gas is dependent on its molecular mass (
M) according to the following equation:
γ is the adiabatic index (which depends on the nature of the gas),
R is the universal gas constant,
T is the absolute temperature. For mixtures of different gases, the speed of sound is determined by the mean molecular mass,
Mmix [
1].
For biatomic gases
γ is nearly constant at a value of 1.40 [
2], but for mixtures involving other types of gases
γ also shows a dependence on the composition [
1].
While not widely used, it is therefore possible to determine the composition of gas mixtures from the measurement of the speed of sound. One possibility is to use the time of flight method, in which the transit time of a pulse is measured (see for example [
3,
4]). An alternative method is the resonance frequency shift method. The principle was exploited as early as 1913 in a device designed by Fritz Haber (who is better known for the development of the artificial nitrogen fixation process) for the detection of methane build-up in underground mining [
5]. This worked without electricity, the miners would simply listen to the sound from the whistle. As the frequency of the sound coming from a whistle is dependent on the composition of the gas a change in pitch would alert them to the danger. More recently electronic devices based on this principle have been reported. Garret [
1] reported an analyzer for hydrogen and methane based on a copper cylinder as the resonator, which was fitted with a loudspeaker and microphone for creating and pick-up of the sound waves. Ruffine and Trusler [
6] described a similar arrangement designed for use in gas pipelines employing two planar piezoelectric transducers at the ends of a cylindrical resonator for sound creation and pick-up. Suchenek and Borowski [
7] employed a slightly different approach for sensing of Ar and CO
2 in nitrogen in that the acoustic wave was produced by the photoacoustic effect with the help of carbon black. However, instead of the intensity measurement, as employed in photoacoustic spectrometry, the change in the resonance frequency was monitored. Cicek et al. [
8] described a system for CO
2 and CH
4 measurements based on a ring resonator fitted with phononic crystals, which employed an ultrasonic transducer for sound generation and a microphone for pick-up. A commercial instrument (BGA244) for determining the ratio of binary gas mixtures based on the change of the resonance frequency in a cylindrical cavity is available from Stanford Research Systems (
www.thinksrs.com, accessed 20 January 2022).
For a gas contained in a tube, the fundamental resonance frequency,
f, along its length,
L, is given by the following equation:
For a tube which is open at both ends, an end correction factor has to be applied [
9,
10]:
where
r is the radius of the tube and the factor 0.6 is an approximation.
To implement the measurement two transducers are normally required. A frequency scan is carried out with some kind of a loudspeaker or ultrasonic transducer to excite the resonance and a microphone to determine the peak in the spectrum. In photoacoustic spectroscopy similar resonance tubes fitted with a microphone are also employed, but the acoustic signal is produced by the absorption of light energy by the gas. The modulation of the light intensity at the resonance frequency of the measuring cell provides an inherent amplification of the signal before pick up by the microphone as transducer. Recently Keeratirawee and Hauser [
11] demonstrated that it is possible to implement gas phase photoacoustics with a resonance tube made from piezoelectric material (lead zirconium titanate, PZT) as the resonance body. The tube was coated with silver electrodes on the in- and outside and could serve directly as transducer from the acoustic to the electric domain, thus eliminating the need for coupling a microphone to the measuring cell.
In this study, the determination of the composition of binary gas mixtures by evaluating their resonance frequency in such a piezoelectric tube is reported. To our knowledge, the use of such a device, to serve at the same time as the resonance body and the transducer of the signal into the electrical domain, has not previously been reported.
2. Materials and Methods
2.1. Materials
The piezoelectric tube (PT-130.10), with 30-mm length and 6.35-mm outer and 5.35-mm inner diameter, was obtained from PI Ceramic (Lederhose, Germany). The signal from the piezoelectric transducer was amplified with an operational amplifier (OPA602AP, Texas Instruments, Dallas, TX, USA) fitted with a feedback resistor of 6.8 kΩ. The small loudspeaker (diameter = 15 mm)(KSSG1508) was purchased from Farnell (Zug, Switzerland). A purposed made audio amplifier circuitry (LM386N, Texas Instruments) was employed as a loudspeaker driver. The sine wave was produced by the function generator built-in into the lock-in amplifier employed for acquiring the frequency spectra (MFLI from Zurich Instruments, Zurich, Switzerland). The diecast aluminum case (92 × 38 × 31 mm) used as measuring cell was a product of Hammond Manufacturing (Eddystone 27969PSLA, Guelph, Canada). Swagelok (Wohlen, Switzerland) fittings and tubes were employed to allow passing of the test gases (N2, O2, CO2, and He, obtained from PanGas, Pratteln, Switzerland) through the cell. Binary gas mixtures were created by setting appropriate flow rates from two tanks with mass flow controllers (models F-201CV-200-AAD-22-V and Fe201CV-1K0-AAD-22-V with maximum flow rates of 200 and 1000 mL/min, purchased from Bronkhorst, Aesch, Switzerland). Silver loaded epoxy was obtained from RS Components (Wädenswil, Switzerland).
2.2. Measurement Set-Up
The set-up is shown schematically in
Figure 1 and a photograph of the cell in
Figure 2. The piezoelectric transducer tube was placed inside a small hermetically sealed case serving as the measuring cell. This also contained the loudspeaker for excitation and in- and outlet for the test gases. The piezoelectric tube was freely suspended by the two wires making the electrical connections. These were attached to the inside and outside electrodes of the tube using a small amount of silver loaded epoxy. The piezoelectric output signal was amplified with an operational amplifier. The transimpedance configuration, which was found to be superior to the voltage amplifier configuration in our previous study [
11], was again employed. A computer based lock-in amplifier and computer controlled mass-flow controllers employed for producing the test gas mixtures complete the system.