The problem of a single acoustically driven bubble translating unsteadily in a fluid is considered. The investigation of the translation equation identifies the inverse Reynolds number as a small perturbation parameter. The objective is to obtain a closed-form, leading order solution for the translation of the bubble, assuming nonlinear radial oscillations and a pressure field as the forcing term. In a second part, the periodic attractor of the Rayleigh-Plesset equation serves as basis for an optimal acoustic forcing designed to achieve maximized bubble translation over one dimensionless period. At near-resonant or super-resonant driving frequencies, it seems one cannot improve much on sinusoidal forcing. However at moderate acoustic intensity and sub-resonant frequencies, acoustic wave forms that enhance bubble collapse lead to displacement many times larger than the case of purely sinusoidal forcing. The survey covers a wide spectrum of driving ratios and bubble diameters including those relevant to biomedical applications. Shape stability issues are considered. Together, these results suggest new ways to predict some of the direct and indirect effects of the acoustic radiation force in applications such as targeted drug delivery, selective bubble driving, and accumulation.
Acoustics Models, Statistical