Abstract
We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu’s equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave.
Highlights
It was shown theoretically that bubble levitation during single-bubble sonoluminescence (SBSL) conditions is accompanied by translational oscillations[19]
There was no translational motion in pure water even when the bubble was driven at the maximum acoustic pressure
In contrast to SBSL experiments, the submillimeter bubbles of our experiments undergo radial oscillations with very small amplitude compared to the amplitude of a sonoluminescence bubble during its periodic collapse
Summary
A custom designed rectangular stainless steel sonochemical reactor affixed with 500 kHz transducer on one of the side walls was used for the experimental work. The size of the sonochemical tank was 23 × 23 × 23 cm with transducer area of 73 cm[2]. The maximum pressure amplitude of the wave was measured to be 2.3 atm using a HCT-0310 hydrophone (Onda Corporation, Sunnyvale, CA, USA) and a USB 5133 oscilloscope (National Instruments Corp., Austin, TX, USA) with acquisition rate set at 6 million samples per second. The set-up was equipped with a one megapixel digital high-speed camera (Phantom v711, Vision Research Inc., Wayne, NJ, USA) for imaging bubble trajectories at 4,000–10,000 frames-per-second (fps) and 1280 × 800 or 400 × 800 display resolution
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