A gas-filled bubble in a liquid will generally dissolve because of diffusion of gas out of the bubble into the surrounding liquid. However, when set into motion by an acoustic field, a bubble may grow by a process called rectified diffusion. This process can counteract the effect of diffusion for values of the acoustic-pressure amplitude greater than some threshold value. This threshold has been determined by a theory that uses computed radius-time curves for bubbles pulsating nonlinearly rather than assumed infinitestimal, sinusoidal motions. For radius-time curves calculated by a digital computer, this threshold has been computed for a sequence of values of gas concentration, bubble radius, and acoustic frequency.
A vocabulary useful in describing cavitation in an acoustic field will be defined, and concepts will be introduced to facilitate the interpretation of complex, many-bubble phenomena in terms of single-bubble dynamics. A distinction between stable cavities and transient cavities will be made and the roles of these two limiting types of bubbles in “gaseous” and “vaporous” cavitation will be examined. Under the influence of an acoustic field, cavitation bubbles grow either slowly or explosively from small gas nuclei in a liquid. The conditions determining whether a gas nucleus will become an explosively growing, transient cavity or a slowly growing, stable cavity will be summarized, and the dynamics of the two types of cavities will be contrasted. In particular, a conceptual model of a transient cavity will be proposed, and calculations based on this model will be used to characterize the life history of such a cavity from its nucleation to its catastrophic end. The rationalization of specific cavitation phenomena (such as the erosion of solids and the acceleration of chemical reactions) in terms of the pulsations of a stable cavity or the violent collapse of a transient cavity will be considered. Finally, an attempt will be made to indicate where our understanding of the basic physical processes of cavitation needs to be deepened.
Under proper conditions, bubbles driven by a sound field will pulsate periodically with a frequency equal to one-half the frequency of the sound field. This frequency component is the subharmonic of order one-half and is generated when the acoustic-pressure amplitude exceeds a threshold value. The threshold for subharmonic generation is calculated by means of a theory that relates the presence of the subharmonic to properties of Hill's equation. It is found that, for a given bubble, the threshold is a function of the driving frequency and is a minimum when the driving frequency is approximately twice the linear resonance frequency of the bubble. In addition, solutions of a set of nonlinear equations for the motion of the bubble wall, obtained on a computer, illustrate the growth of subharmonics and are used to determine the steady-state amplitude and phase of the subharmonic for a sequence of values of various parameters.
Transient behavior of small gas bubbles in a liquid set into violent motion by ultrasonic pressure waves is of interest because of widespread use of microsecond pulses in diagnostic ultrasound. Such pulses contain only a few pressure cycles and the transient pulsations of bubbles set in motion by such pulses would determine the bubble-ultrasound interaction. A computer study has been made to obtain a global representation of the pulsation amplitudes R (t) of small gas bubbles (nuclei) in water during the first few cycles of a cw ultrasonic pressure. One objective was to obtain a better understanding of cavitation phenomena where many nuclei with initial radii R, from 0.1-20 pm are set in motion at pressures ranging from 0.5-5 bars and at frequencies from 0.1-10 MHz. Results allowed construction of surfaces showing the relative bubble amplitude R/R, as a function of R• and of the time t/TA, where TA is the acoustic period. One finding is that, in the range of peak pressures found in diagnostic pulses, transient cavities would be generated during the first pressure cycle from nuclei with initial radii as small as a few microns (pm). Nuclei that grow into transient cavities in the first pressure cycle are here called "prompt" nuclei. At a specified pressure, the size range of radii R n in which they occur decreases with increasing frequency. At 5 bars, the range of Rn for prompt nuclei is 0.166-11.35 pm at 0.5 MHz and vanishes at 10 MHz.
Under proper conditions, bubbles driven by a sound field will pulsate periodically with a frequency equal to one-half the frequency of the sound field. This frequency component is the subharmonic of order 12 and is generated when the acoustic pressure amplitude exceeds a threshold value. The threshold for subharmonic generation is calculated by means of a theory that relates the presence of the subharmonic to properties of Mathieu's equation. It is found that, for a given bubble, the threshold is a function of the driving frequency and is a minimum when the driving frequency is close to twice the resonance frequency of the bubble. In addition, solutions of a nonlinear equation of motion for the bubble wall, obtained on a computer, illustrate the growth of subharmonics and are used to determine the steady-state amplitude of the subharmonic for a sequence of values of various parameters. [Work supported by Acoustics Programs, Office of Naval Research.]
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