Numerical Study on the Effects of a Boundary on the Chaotic Behavior of a Small Cluster of Microbubbles in an Ultrasonic Field - Fatimah, Dzaharudin; Ummu Kulthum, Jamaludin; Mohd Nazri, Kasuan (2016)
The potential of microbubbles in biomedical applications such as drug and gene delivery may redraw the boundaries of the biomedical field thus inspiring numerous studies on the dynamics of microbubbles. This study will investigate the dynamical behaviour of a small cluster of microbubbles subjected to ultrasound near a solid boundary in order to elucidate the effects of microbubble oscillation near endothelial cells in real clinical scenarios. A mathematical model that governs the radial oscillation for bubbles near a plane rigid wall is derived using method of images and solved numerically for a given set of ultrasound parameters. In this paper, it is assumed that all bubbles in the system have the same equilibrium radius and are equidistant from one another and from the solid boundary. With the current mathematical model, it is demonstrated that the presence of a solid wall has a significant effect on the bifurcation structure and the route to chaos of the bubble system. As separation distance between microbubbles and solid boundary is decreased, the chaotic regions shift to occur at different ultrasound frequencies. Furthermore, the chaotic behaviour of the microbubbles influences the amplitude oscillation associated with the bubble response.