Based on the theory of shape instability and diffusive instability for single bubbles, we have studied the instability of an individual bubble in a bubble chain and found that its stable area enlarges the narrower the distance between bubbles. The spatial stability of the bubble chain is due to the secondary Bjerknes force between bubbles. Numerical calculations show the tension of the bubble chain varies with bubble distance and maxima appear at certain distances which could correspond to the stable states of the bubble chain.

• Received 13 March 2013

DOI:https://doi.org/10.1103/PhysRevE.87.053023