Microbubbles have the potential to be used for diagnostic imaging and therapeutic delivery. However, the transition from microbubbles currently being used as ultrasound contrast agents to achieve its’ potentials in the biomedical field requires more in depth understanding. Of particular importance is the influence of microbubble encapsulation of a microbubble near a vessel wall on the dynamical behaviour as it stabilizes the bubble. However, many bubble studies do not consider shell encapsulation in their studies. In this work, the dynamics of an encapsulated microbubble near a boundary was studied by numerically solving the governing equations for microbubble oscillation. In order to elucidate the effects of a boundary to the non-linear microbubble oscillation the separation distances between microbubble will be varied along with the acoustic driving. The complex nonlinear vibration response was studied in terms of bifurcation diagrams and the maximum radial expansion. It was found that the increase in distance between the boundary and the encapsulated bubble will increase the oscillation amplitude. When the value of pressure amplitude increased the single bubble is more likely to exhibit the chaotic behaviour and maximum radius also increase as the inter wall-bubble distance is gradually increased. While, with higher driving frequency the maximum radial expansion decreases and suppress the chaotic behaviour.
Unified discrete‐map modelling and dynamical behaviour analysis of current mode controlled tri‐state dc–dc converters
