Abstract
A new system of dynamical equations was obtained by using the perturbation and potential flow theory to couple the pulsation and surface deformation of the second-order Legendre polynomials (P(2)) of three bubbles in a line. The feasibility and effectiveness of the model were verified by simulating the radial oscillations, surface deformation with P(2), and shape evolution of three bubbles. The spherical radial pulsation and surface deformation of the three bubbles exhibit periodic behavior. The maximum secondary Bjerknes forces (SBFs) on the three bubbles are found not to depend on the system's resonance frequency. Within a stable region, the SBFs of the three bubbles increase with increasing sound pressure amplitude but decrease with increasing distance between the bubbles. The primary Bjerknes force (PBF) on a bubble is significantly higher than the SBF on it.