Effect of contact with an elastic wall on the spectral characteristics of the scattered echo of a contrast microbubble
Résumé
A modified Rayleigh-Plesset equation is proposed to model the oscillation of a contrast microbubble attached to an elastic wall. The equation shows that contact with the wall affects the bubble oscillation as if the bubble oscillated in a liquid with a changed (effective) density. As a result, depending on the wall properties, the natural frequency of the attached bubble can be either lower or higher than the natural frequency of the same bubble in an unbounded liquid. Numerical simulations were made to study the spectral characteristics of the scattered pressure of an attached contrast microbubble. It was assumed that the bubble shell properties are described by the Marmottant model and the properties of the wall correspond to walls of OptiCell chambers commonly used in experiments. It has been found that, depending on the value of the driving frequency, the contact with the wall can noticeably increase or decrease the magnitudes of the fundamental component, the second harmonic, and the subharmonic relatively to their values in an unbounded liquid. These findings can be used to distinguish the scattered echoes produced by contrast agents attached to a wall from echoes produced by agents being at a distance from a wall.
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