Modulation of the secondary Bjerknes force in multi-bubble systems

The behaviours of insonated bubble clusters are regulated by the secondary Bjerknes force between bubble pairs. While the force has been investigated extensively for two-bubble systems, the modulation of the force by nearby bubbles remains unclear. This problem is investigated in this paper by theoretical analyses and numerical simulations of a three bubble system. For weak oscillations, the third bubble is found to have strong effects when its radius is close to the resonant radius. The equilibrium distance between the bubble pair is reduced when the radius of the third bubble is smaller than the resonant threshold, and increased when it is larger. For strong oscillations of bubbles with radii of a few microns, the third bubble reduces the magnitude of the force, hence increasing the equilibrium distance. The modulation effects depend strongly on the relative sizes of the bubbles. Stronger effects can be produced when the third bubble is placed closer to the smaller bubble in the bubble pair. The findings highlight the need for a more accurate parametrization of the secondary Bjerknes force in the simulation and manipulation of bubble clusters.