Teterev A., Doinikov A., Misychenko N., Rudak L.

A numerical model has been developed for simulating the spatio-temporal dynamics of gas bubbles in a strong acoustic field. Radial oscillations of a bubble are calculated by a Rayleigh-Plesset-like equation. The pressure within the bubble is found as a result of combining the equation governing the radial motion of the bubble wall with a one-dimensional gas-dynamic problem that describes gas flow inside the bubble. Simultaneously solving the above problem with the equation of the radial bubble oscillation is provided by appropriate boundary conditions at the bubble surface. The resulting evolution of the bubble surface makes it possible to trace even insignificant deviations of the scattered field of the bubble as against that calculated on the basis of the conventional approach in which the gas pressure within the bubble is assumed to be spatially homogeneous. The developed model allows one to study the coupling between bubble oscillations induced by an external acoustic forcing and gas flow inside the bubble. Furthermore, it makes possible the determination of the applicability range of Rayleigh-Plesset-like equations depending on the ratio between the incident sound wavelength and the bubble radius. Although both of the approaches have similar limitations, the proposed model can provide a more exact solution near their limits of validity. A modified version of the current model is intended to be applied in future to investigating the dynamics of coated bubbles, such as ultrasound contrast agents which are widely used now in biomedical applications.