Experimental and theoretical analysis of secondary Bjerknes forces between two bubbles in a standing wave

• Acceleration of two approaching bubbles measured at separations <0.2 mm.
• Accelerations measured over a range of pressures, frequencies and bubble sizes.
• Secondary Bjerknes forces were predicted under the same experimental conditions.
• Differences in size of bubbles caused variations in magnitude of attractive forces.

Bubbles in an acoustic field are affected by forces such as primary and secondary Bjerknes forces, which have been shown to be influenced by acoustic pressure, frequency, bubble size and separation distance between bubbles. However, such studies are predominantly theoretical, and are mostly focused on the sign reversal of the secondary Bjerknes force. This study provides experimental data on the effect of a range of bubble sizes (8–30 μm), distances (⩽0.2 mm), acoustic pressures (20–40 kPa) and frequencies (40–100 kHz) on the relative acceleration of two approaching bubbles. Under these conditions, only variations in the magnitude of the attractive force were observed. Using coupled equations of radial and translational motions, the acceleration and secondary Bjerknes force were calculated and compared to the experimental data. The variations in the magnitude of the secondary Bjerknes forces were explained by simulating bubble radius and coupled volume oscillation as a function of time.