Assessing the accuracy of the coupled-spherical-bubble approach for bubble pairs in an acoustic field

This study evaluates the accuracy of coupled-spherical-bubble models in acoustic fields by comparing them to direct numerical simulations (DNS). The coupled-spherical-bubble approach refers to the method of modeling multi-bubble systems, where the spherical bubble dynamics are governed by a simplified equation and these equations are coupled through the pressure emissions of the bubbles. Tested spherical models are the Keller-Miksis and Gilmore equation, and pressure emission models include the incompressible, quasi-acoustic and Kirkwood-Bethe hypothesis. Emphasis is placed on peak bubble pressure during collapse and the accuracy of pressure emission models. First, a single bubble in a spherical standing wave is analyzed. Among the simplified approaches, the Gilmore model provides closer agreement with DNS at Mach numbers approaching unity in water. In high-viscosity glycerol spherical models break down independently of the Mach number. Pressure wave emissions are accurately tracked by all tested models that assume a finite propagation velocity; however, shock wave emissions at high compression ratios can only be tracked by the Kirkwood-Bethe model. In the second part, a bubble pair is subjected to an ultrasonic pulse, and spherical volume oscillations and pressure emissions of bubbles are compared using various coupled-spherical-bubble approaches. DNS results show that jetting during collapse reduces gas compression, leading spherical models to overpredict internal pressure. While spherical models are effective for isolated bubbles in ideal conditions, DNS is essential for accurately capturing inter-bubble interactions. Nevertheless, spherical models provide good accuracy in the case of a bubble collapse without jetting, even when perfect sphericity is not preserved.