Extraction of bubble size and number data from an acoustically-excited bubble chain

The passive-acoustic measurement of bubbly flows could potentially deliver data useful to many industrial and environmental applications. However, acoustic interactions between bubbles complicate interpretations of measured frequencies in terms of the bubble sizes that are of practical interest. Experiments were undertaken on the emissions of a bubble chain when a just-formed bubble at one end of the chain created a sound pulse. This is an idealised paradigm for many applications. The chain was a one-dimensional line of bubbles fixed with known bubble sizes and inter-bubble spacings. Frequencies naturally emitted by the chain were measured for various bubble sizes and spacings, including cases such that the bubbles were close to touching. Semi-empirical fits were found relating the bubble size and number to the lowest and highest-measurable peak frequencies. It was found that all data collapsed onto two curves, one for the lowest-peak and one for the highest-peak frequency. This was confirmed by running numerical simulations for wider ranges of parameters than available experimentally. The results suggest that for a bubble chain, measurements of two peak frequencies could be used to determine the bubble size and also the number of interacting bubbles.