Radial oscillation of an encapsulated bubble near a planar rigid wall under dual-frequency acoustic excitation in viscoelastic fluids.

Microbubbles play an important role in acoustic cavitation, power ultrasonics, and biomedical diagnosis and therapy. However, the influence of surrounding boundary conditions on the dynamic behaviors of an encapsulated bubble requires more in depth analysis and understanding. This study investigates the dynamic response of a lipid-coated bubble near a planar rigid wall in a viscoelastic fluid, which is transformed into a two-bubble model using the method of images. Assuming the excitation of a dual-frequency wave, the dynamic equation governing the radial oscillation is derived through combining the Rayleigh-Plesset model, the Marmottant model, and the Kelvin-Voigt model. Numerical computations are also performed for the instantaneous bubble radius in the time domain and the spectral amplitude in the frequency domain. Particular attention is paid to the pressure amplitude, the excited frequencies, the bubble-wall distance, the initial bubble radius as well as the elastic modulus and surface dilatational viscosity of the coating layer. The spectral peaks include the fundamental and higher-order resonance frequencies, accompanied by the sum frequency due to interaction between dual frequencies. The planar rigid wall significantly weakens the radial oscillation through suppressing the higher-order peaks in the frequency domain. The beating phenomenon occurs at two close frequencies with the oscillation amplitude changing periodically at the difference frequency. A longer bubble-wall distance corresponds to a weaker suppression effect of the bubble-wall interaction and thus enhances the radial oscillation. The maximum oscillation amplitude is achieved at the resonance radius but not necessarily the resonance elastic modulus of the coating layer. The findings may advantage in the design and optimization of microbubble-based systems across a wide range of applications such as ultrasonic cavitation and biomedical ultrasound.