Green’s function approach to modeling spherical bubble pulsation between viscoelastic layers.

Abstract

Experiments have shown that bubbles oscillating near surfaces of elastic media experience a translational force whose direction, toward or away from the surface, depends on elastic moduli and standoff distance. [Brujan et al., J. Fluid. Mech. 433, 251–314 (2001).] Bubble translation has also been observed in ex vivo blood vessels following acoustic excitation. [Chen et al., J. Acoust. Soc. Am. 127, 1977–(2010).] A model is developed for a stationary spherical bubble pulsating between two parallel viscoelastic layers. A Green’s function for particle displacement is derived via angular spectrum decomposition and is used to calculate the translational force on a bubble due to pressure reflections from the layers. The predicted dependence of the direction of the translational force on elastic properties and standoff distance is in qualitative agreement with the reported measurements. The reflected pressure is also incorporated in a Rayleigh–Plesset equation for the nonlinear pulsation of the bubble. Evaluation of the Green’s function on the surfaces of the elastic layers yields their displacements due to the bubble pulsations. Predicted surface displacements exhibit characteristics in agreement with wall displacements observed in blood vessels by Chen et al. [J. Acoust. Soc. Am. 125, 2680–(2009).] [Work supported by NIH DK070618.]