On the dynamics of non-spherical magnetic microbubbles

Abstract

Magnetic microbubbles are a relatively recent development with the potential to greatly improve the efficacy of the minimally invasive drug-delivery procedure sonoporation. However, very little is known about the dynamics of magnetic microbubbles, in general. In this paper, a novel mathematical model and numerical method are developed to simulate the dynamics of non-spherical magnetic microbubbles in vitro. The ambient fluid is assumed to be inviscid and the flow irrotational, enabling a generalized Bernoulli equation to be derived that includes surface tension effects and the effect of the applied magnetic field. The governing equations are solved using the boundary element method in which both the bubble surface and the velocity potential are represented by cubic splines. Results show that magnetic microbubble dynamics are highly dependent on the magnetic susceptibility difference, Δχ, between the bubble and the ambient fluid, with the sign and magnitude of Δχ dictating the direction and velocity of any formed liquid jets. Importantly, it is shown that the magnetic field can provide an additional means of flow control to the experimental investigator: in the presence of surface tension, weak magnetic fields do not generate jets. However, increasing the magnitude of the magnetic field can instigate jet formation, and increase the maximum and time-averaged jet velocities. Experimentally relevant parameter values are also considered, and results suggest that a combined application of magnetic and ultrasound fields is required to generate the high-speed bubble collapse events most likely to maximise cell poration and drug delivery.