Acoustic microbubble dynamics with viscous effects.

Microbubble dynamics subject to ultrasound are associated with important applications in biomedical ultrasonics, sonochemistry and cavitation cleaning. The viscous effects in this phenomenon is essential since the Reynolds number Re associated is about O(10). The flow field is characterized as being an irrotational flow in the bulk volume but with a thin vorticity layer at the bubble surface. This paper investigates the phenomenon using the boundary integral method based on the viscous potential flow theory. The viscous effects are incorporated into the model through including the normal viscous stress of the irrotational flow in the dynamic boundary condition at the bubble surface. The viscous correction pressure of Joseph & Wang (2004) is implemented to resolve the discrepancy between the non-zero shear stress of the irrotational flow at a free surface and the physical boundary condition of zero shear stress. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble oscillating in a viscous liquid for several cycles of oscillation for Re=10. It correlates pretty closely with both the experimental data and the axisymmetric simulation based on the Navier-Stokes equations for transient bubble dynamics near a rigid boundary. We further analyze microbubble dynamics near a rigid boundary subject to ultrasound travelling perpendicular and parallel to the boundary, respectively, in parameter regions of clinical relevance. The viscous effects to acoustic microbubble dynamics are analyzed in terms of the jet velocity, bubble volume, centroid movement, Kelvin impulse and bubble energy.