Abstract
Hamilton's principle is used to derive two models for a bubbly liquid containing bubbles of different sizes. In the first model, the bubbly liquid is treated as a mixture of a liquid and several bubble “continua”, each consisting of bubbles of a different size. In the second model, the bubbly liquid is treated as a mixture of a liquid and a bubble continuum with a prescribed continuous distribution of bubble sizes. The theories are linearized and used to calculate the phase velocity and attenuation of acoustic waves.
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