We would show that a quartz tuning-folk type resonator can measure the viscosity and the molar mass of the gas in which the resonator is vibrating. The vibrating resonator has two kind of outputs which are frequency change (Δf) and impedance change (ΔZ). The Δf and ΔZ are defined as the shift from their origin measured at high vacuum. We reported that the Δf and ΔZ given as a function of pressure are independent, and then the measurement of Δf and ΔZ will give the gaseous viscosity with no need to measure the gaseous pressure [1, 2]. In this report we will show that the molar mass of the measurement gas can be given by measurement of Δf, ΔZ and pressure.

 

In this experiment the temperature controlled measurements were essential because Δf and ΔZ are sensitive to the temperature variation. The measurement apparatus, such as the vibrating sensor, driving circuit for oscillation, mass flow controllers, gas accumulator and the pressure gauges, are in a temperature controlled chamber by 29±0.02ºC. The impedance of the resonator was evaluated by the current passing through the sensor under constant driving AC voltage. The frequency of the resonator was 32kHz. The measured gas was Ne, Ar, N2, O2. The Δf and ΔZ were measured for the pressure between 120 kPa and vacuum. The absolute pressure was measured with a capacitance manometer.

 

The results showed that the ΔZ(P) and Δf(P), give as a function of pressure, are larger for higher pressure. The ΔZ(P) and Δf(P) for Ar, N2, O2 gases do not have the intersection. However Ne gas, having smaller molar mass but larger viscosity, crossed the other curves. So we cannot distinguish the gas species simply by ΔZ(P) or Δf(P) measurements. To discriminate the gas species with their viscosity the ΔZ-Δf plot is useful. We found that the characteristic curves of ΔZ-Δf lied in the descending order of the viscosity, i.e., Ne, Ar, O2, and N2. These curves do not across each above 1 kPa.

 

We found the molar mass can be derived with the vibrating sensor. The product of molar mass and pressure can be evaluated without pressure measurement. The molar mass can be given with additional pressure measurement. The results showed that above 10kPa of the gas pressure the deviation of measured molar mass is less than a few percent.

 

[1] A. Kurokawa, H. Hojo, T. Kobayashi, AVS 57th Int. Sympo. Exhibi. (2010, Albuquerque).

[2] A. Kurokawa, H. Hojo, T. Kobayashi, Appl. Phys. Express 4 (2011) 037201.