Numerical study of the interaction between a pulsating coated microbubble and a rigid wall. II. Trapped pulsation

Abstract

The dynamic response of an encapsulated bubble subject to an acoustic disturbance in a wall restricted flow is investigated, when the viscous forces of the surrounding liquid are accounted for. The Galerkin finite element methodology is employed and the elliptic mesh generation technique is used for updating the mesh. As the bubble accelerates towards the wall, the dominant force balance is between Bjerknes forces and the viscous drag that develops. In this process a prolate shape is acquired by the bubble, due to excessive compression at the equator region. When the bubble reaches the wall lubrication pressure develops in the near wall region that resists further approach. As long as the sound amplitude remains below a threshold value determined by the onset of parametric shape mode excitation saturated, or "trapped,"pulsations are performed around a certain small distance from the wall. The balance between Bjerknes attraction and the lubrication pressure that arises due to shell bending along the flattened shell portion that faces the wall generates an oblate shape. Elongation is now observed along the equatorial plane where a local liquid overpressure is established generating large tensile strain. The time-averaged deflection of the microbubble at the pole that lies close to the wall is determined by the bending and stretching resistances of the shell in the manner described by Reissner's linear law for a static compressive load on an elastic shell, corrected for the effect of surface tension. The oscillatory part of the bubble motion in that same region, the contact region, follows the forcing frequency and consists of a pressure driven and a shear flow in the form of a Stokes layer where a significant amount of instantaneous wall shear is generated. The thickness of the film that occupies the Stokes layer is on the order of a few tenths of nm and is determined by the balance between liquid and shell tangential viscous stresses. The steady streaming effect on the wall shear is absent owing to the negligible phase difference between the volume and center of mass pulsations. © 2021 American Physical Society.