Bubble Sizing with High Spatial Resolution

Abstract

A new method, based on the double frequency technique, in which the imaging signal fi is pulsed at a repetition frequency fr is proposed. The received signal from a range cell at a given depth is processed in the same way as in a conventional pulsed Doppler velocimeter (demodulation at fi, sample and hold at fr.). In most cases the pump frequency fp is greater than fr, and the demodulated signal is undersampled. If fp is different from nfr (where n is an integer), we demonstrate that the frequency of the demodulated signal is given by I fP ± nfr I min and that its amplitude is maximum when the bubble resonates. An explanation is given for why the maximum amplitude cannot be detected when the repetition frequency is a multiple of the pump frequency using a conventional Doppler flowmeter. The modifications of the signal processing needed to overcome this drawback are discussed and implemented in the conventional Doppler flowmeter. Using this modified set-up, the lateral and the longitudinal range resolution are the same as in conventional Doppler flowmeters (less than 1 mm). The resonance frequency obtained in this manner is also compared to the resonance frequency measured by the double Doppler frequency method described earlier. Some practical improvements are proposed to make the system very easy to use. Using this latest version, the resonant frequencies for ten different sizes of bubbles are measured and compared. The case where the nonlinearity effect (due to bubble on resonance) generates upper sidebands and lower sidebands not in phase is discussed, and we demonstrate that this effect is so feeble that it is not necessary to take it in account. © 1990, IEEE