Radiative decay of bubble oscillations

What is it about?

Long-time evolution from nanobubbles to microbubbles is a long-standing challenge in the field of cavitation. It is associated with millions cycles of oscillation and cannot be simulated by any numerical model. In this work, a leading-order analytical solution of the bubble radius history is obtained for bubble oscillation in a compressible liquid with significant acoustic radiation based on the Keller–Miksis equation using a multi-scaled perturbation method. The theory has excellent agreement with experimental results and the numerical solutions over thousand cycles of oscillation. Some important formulae are derived including: the average energy loss rate of the bubble system for each cycle of oscillation, an explicit formula for the dependence of the oscillation frequency on the energy, and an implicit formula for the amplitude envelope of the bubble radius as a function of the energy. Our theory shows that the energy loss rate on the long compressible time scale being proportional to the Mach number.

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Why is it important?

This article is internationally excellent in terms of originality, significance and rigour because these asymptotic predictions have excellent agreement with experimental results.