High-resolution bubble sizing through detection of the subharmonic response with a two-frequency excitation technique

Abstract

Sizing bubbles in fluid using a two-frequency excitation technique is not prone to the same drawbacks of some other sizing methods-it has a global maximum at the bubble resonance frequency and allows good spatial resolution. The bubble is insonated with a high fixed imaging signal and a variable pumping signal tuned to the resonant frequency of the bubble, which are coupled at resonance by the high-amplitude oscillation of the bubble wall, with the formation of sum-and-difference terms. This paper examines both the resonance and off-resonance behavior of such combination frequency signals. A coupling of the subharmonic bubble response with the imaging frequency is shown to be a much more accurate and unambiguous detector of the bubble resonance than couplings involving the fundamental resonance. The characteristics of this subharmonic signal are examined using an automated sizing method, and the dependence of the response on the pumping signal amplitude and the frequency step size between two successive pumping frequencies is examined. The location of a definite subharmonic threshold is reported and quantified both for single bubbles held on a wire and for free rising bubbles moving through the focus of the transducers. This amplitude is found to be orders of magnitude lower than that predicted by traditional volumetric pulsation models, but agrees very closely with the theoretical onset of surface waves.

The detection of tethered and rising bubbles using multiple acoustic techniques

“…Initial use of broadband first reduced the test time by a factor of 64. The resolution of i Ϯ p /2 can be dramatically affected by the acoustic pressure at the bubble: While it could be improved to Ϯ12 Hz by insonating at the threshold pressure, 9 there is no guarantee that in the general case this threshold can be accurately delivered. This is particularly true when considering the results from moving bubbles ͑Table III͒, since each bubble is transitory.…”

“…In contrast, other signals may be practicable only at low number densities. 8,9 Several are prone to false triggering, in that some other object ͑e.g., a solid body, or a cluster of small bubbles͒ 10 may give the same signal as that obtained from a given bubble.…”

“…4 Such ''false triggering'' has not to date been found when signals at i Ϯ p /2 are used for bubble sizing. 9 These signals are generated when the amplitude component A of the insonating field PϭA cos p tϩB cos i t exceeds the threshold value required to generate Faraday waves on the bubble surface. Characteristics of the various acoustic sizing techniques are summarized in Table I.…”

“…The ''imaging'' frequency ( i ) scatters geometrically from a target ͑the pulsating bubble͒ whose cross-sectional area varies periodically. 9 The detected signal consists of i , modulated at frequency p , and the resulting detection of i Ϯ p in the received spectrum has been used to size a bubble spectrum by employing the assumption that, bar the presence of resonant bubbles, only i and p are detected. 8,21 The as-sumption fails if the pulsation of nonresonant bubbles, or the presence of a quadratic nonlinearity anywhere in the system ͑for example, through turbulent water motion͒, is sufficient to generate an i Ϯ p signal.…”

On the possible ultrasonic inspection of micro-bubbles generated by the optical fiber tip

“…Bubbles of a given size are generally detected using ultrasound location methods based on recording the amplitude of the subharmonic of the emitted ultrasonic wave. [23][24][25][26][27][28][29][30] Parametric excitation of a bubble at its resonant frequency f 2 ¼ f 1 /2, where f 1 is the frequency of the emitted wave, allows detection of the bubble with a high degree of con¯dence. At the same time, bubbles will be excited on the f 1 frequency as well.…”