Nonlinear oscillations of air bubbles near and on a rigid boundary with time delay effects

A fundamental understanding of the effect of a surface on the resonance frequency of bubbles will be useful in the future development of diagnostic medical ultrasound equipment. In this paper we look at wall effects on the nonlinear resonance frequency response of air bubbles in water, continuing from an earlier paper which dealt with the linear response (E. M. B. Payne, S. Illesinghe, A. Ooi, and R. Manasseh, J. Acoust. Soc. Am. 118, 2841-2849 (2005)). Numerical results for micron-sized bubbles near a rigid boundary are presented, showing a shift in frequency due to the boundary, and nearby bubbles, and a significant reduction in the amplitude of oscillations at resonance. Time delay effects are also included, which show a damping of the frequency response. Simulations are limited to the case where all bubbles oscillate in phase. An experimental method for measuring the resonance response of an air bubble attached to a surface is also outlined.