Acoustic measurement of bubble size distributions: Theory and experiments

Abstract

Among methods of measurement of bubble size distributions, a successful acoustic method has advantages in that bubbles are very responsive to sound, large volumes may be sampled, and the method can be inexpensive. However, inversion of the data to recover the bubble density is difficult. In the present work a model for sound propagation in bubbly liquids is used to develop two Fredholm integral equations of the first kind relating the attenuation and phase velocity to the bubble density. These equations are ill-posed, and require special solution. New solution algorithms based on a constrained minimization method were developed. These were first tested on analytical data with added noise, and were successful in recovering the bubble density. Bubble populations were then generated using electrolysis and air injection. Short bursts of sound at different frequencies were generated at a source, and received at a hydrophone after passage through the medium. The attenuation and phase velocity were obtained, along with other information, that are used to develop constraints on the solution. Results obtained for the bubble population are compared with microphotography and show that the method is accurate. In ongoing work an integrated PC-based instrument is being developed. [Work supported by NSF.]