Bubble size distribution measurement using an inverse acoustic scattering technique: Theory and experiments

Determination of the bubble population in liquids is an important problem in many fields. Acoustic methods have advantages over other methods of measurement in that bubbles are very responsive to sound, that reasonably large volumes may be sampled, and that the method can be relatively inexpensive. However, previous attempts at using acoustical means of measurement have not led to well‐established measurement techniques due to the ill‐posed nature of the problem. In the present work, a multiphase model for sound propagation through bubbly liquids is used to obtain two integral equations of the first kind for determining the bubble distribution from measured phase‐velocity and attenuation data. New algorithms for regularization of the ill‐posed problem by imposing a number of physical constraints in a direct minimization setting are developed. These algorithms have been tested on analytical data with varying artificial noise added, and found to be successful. Based on this technique a new bubble measuremen...