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

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 < 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results show that the new expression gives a good estimate of the concentration at which the monopole model is no longer valid, but fails at properly predicting the transmission.