Buckling activated translation of encapsulated microbubbles

The influence of initial shape imperfections on the post-buckling and translational behavior of encapsulated microbubbles is investigated subject to acoustic excitation in an unbounded flow. Bifurcation analysis reveals that imperfections lower the critical overpressure for buckling, guiding the bubble along stable branches with transitions influenced by the nature of the imperfections. The resulting branches emerge as unfoldings of bifurcation diagrams and closely resemble solution families emanating from the standard bifurcation diagram of a perfect sphere. Dynamic simulations for fixed forcing frequency demonstrate that the microbubble buckles at the defective pole and at maximum compression adopts the shape corresponding to the buckled shape that emerges in the static bifurcation diagram for the same pressure disturbance. Simulations further reveal that the deformed microbubble exhibits translational motion in the direction of concavity, driven by the balance between pressure and viscous drag, both aligned with this motion as a result of the deformed shape acquired by the microbubble. The translational speed is highly dependent on the shell stretching and bending elasticities and forcing frequency, with an optimal speed achieved when the forcing frequency equals the difference between the resonance frequencies of the initial shape and the compressed static shape corresponding to the imposed sound amplitude. Higher sound amplitude or lower bending resistance lead to more pronounced deformations that enhance translational motion. The impact of this dynamic response pattern on the recently reported translational motion of properly engineered coated microbubbles to act as microswimmers in modern drug delivery modalities under ultrasound excitation, is highlighted.