The impedance dependence of a tuning-fork-shaped quartz oscillator on gas pressure is theoretically analyzed on the basis of a string-of-beads model of the quartz oscillator. The theoretical results are numerically compared with experimental data. The analysis has been already carried out in molecular flow and viscous flow region. In this paper, the impedance behavior in the intermediate flow region is formulated by making use of the theory of slip effect. Furthermore, by the formal extension of this formula to the molecular flow region, a single formula describing the impedance dependence on gas pressure over the whole pressure region is obtained. This formula is found to be in good agreement with experimental data. However, there is still a slight discrepancy (<20%) between the two in the intermediate flow region. This shows the limit of the slip theory. For this reason, the Millikan’s empirical formula is adopted in the intermediate flow region. The unified formula obtained thusly is in numerical agreement with experimental data for various kinds of gases.
No takes yet. Share an insight, caveat, or question.
KOKUBUN et al. (1987) studied this question.