Physics of microbubble scattering

The earliest reference to bubbles as sound sources was made by Bragg [1] who attributed the murmuring of a brook and the plonk of droplets falling into water to entrained air bubbles Minnaert [2] has since shown that the sound generated by gas bubbles in liquids is associated with simple volume pulsation of the bubble without changing shape. The bubble behaves as a simple damped oscillating system with one degree of freedom. Therefore, the differential equation of motion is of the same form as the classical mass-spring system. He derived for this system the frequency at which resonance occurs, assuming an adiabatic equation of state for the gas in the bubble and neglecting surface tension and damping factors. At that time experiments showed that liquids containing gases possess higher sound damping characteristics than those which are gas free. Sorensen [3] concluded that just a few widely dispersed bubbles, which are so small as to be invisible, can have an appreciable acoustic effect. Fox et al. [4] also carried out attenuation measurements on bubbly liquids and came to a similar conclusion.

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