Ramani Duraiswami
DYNAFLOW, Inc., 7210 Pindell School Rd., Fulton, MD 20759
Acoustical techniques have long been used to estimate the bubble density function. The conventional technique assumes isolated (non-interacting) scatterers, and results in a Fredholm integral equation of the first kind relating the bubble density and the measured scattering is obtained. These ill-posed equations are numerically challenging to solve, especially when the data---obtained from experiments---inevitably contain noise/error. Usually these equations are solved by assuming resonant scattering, or by accounting approximately for off-resonance scattering. Additionally the conventional model used for the bubble scattering, does not properly account for thermal losses in the bubble oscillations. In the present work, a multiphase model for sound propagation through bubbly liquids (due to Caflisch et al.) is combined with Prosperetti's model for bubble oscillations, to develop two new equations for determining the bubble population function from measured phase-velocity and attenuation data. The new theory/equations address perceived drawbacks in the conventional technique. The equations are evaluated for their potential for determining the bubble population, by testing them with analytical data with varying artificial noise. Numerical algorithms using new regularization techniques are developed. [Work supported by NSF.]