Microbubble dynamics in a viscous compressible liquid subject to ultrasound

When a microbubble is subject to ultrasound, non-spherical oscillation or surface modes can be generated after many acoustic cycles. This phenomenon has wide applications, including ultrasonic cleaning, sonochemistry, and biomedical ultrasonics. Yet, the nonlinear develop- ment of the bubble shape modes over dozens of cycles is not well understood. Here, we describe a grid-free and robust model to simulate the phenomenon. A viscous pressure correction is introduced to compensate the non-zero tangential stress at the free surface in the potential flow model, based on conservation of energy. Consequently, the phenomenon is modeled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through the boundary conditions. The computations have been carried out for axisymmetric cases; however, the numerical model can be extended for three-dimensional cases in a straightforward manner. The numer- ical results are shown to be in good agreement for many cycles with some independent viscous and compressible theories for axisymmetric bubbles and experiments for microbubbles undergoing shape oscillation subject to ultrasound. The development of the shape oscillation of a bubble after a dozen cycles, the formation of a reentry jet and its penetration through the bubble, and the topological transformation of the bubble are simulated and analyzed in terms of the amplitude and frequency of the ultrasound. The computations and physical analysis are carried out for the development of shape modes due to a resonant volume oscillation, strong pressure wave, or the matching of the acoustic wave frequency with the shape mode frequency.