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Dynamical equations for oscillating nonspherical bubbles with nonlinear interactions. (English) Zbl 1355.76070

Summary: In this study, dynamical equations for interacting nonspherical bubbles are derived in the framework of Lagrangian formalism with multipole expansion of bubble surfaces. These boundaries are expanded using spherical harmonics to study the deformation and translation of the bubbles. To compose the Lagrangian of the system, corresponding amplitudes of the spherical harmonics are chosen as generalized coordinates. This study considers orders of the spherical harmonics up to the third (octupole) mode, which is the lowest oscillation mode contributing to the asymmetrical deformation of a bubble. The derived equations represent the motion of interacting nonspherical bubbles and agree qualitatively well with experimental results, including the onset of jetting. The equations reveal the mechanism of initiation of shape oscillations which is accurate to the quadratic order in the mode amplitudes.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
70H03 Lagrange’s equations
65Z05 Applications to the sciences
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