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A model for acoustic transmission through a 2D square crystal of R-radius bubbles with a lattice constant L was previously proposed. Assuming a purely monopole response of the bubbles, this model offers a simple analytical expression of the transmission. However, it is not applicable when the bubbles are too close to each other (    L / R&lt; 5). This article proposes an extension of the model by including the dipole response of the bubbles. Comparisons with numerical and experimental results show that the new expression gives a good estimate of the concentration at which the monopole model is no longer valid, but fails at properly predicting the transmission.

Acoustics of Bubble Arrays: Role Played by the Dipole Response of Bubbles