Effect of magnetic field on expansion of ferrofluid-encapsulated microbubble

Magnetic microbubbles (MMBs) have great potential applications in drug delivery and target therapy because they can be controlled by magnetic fields. In this paper, dynamic equations are derived by Lagrangian formalism and the behavior of MMBs subject to a combination field of magnetic and ultrasound field in an incompressible infinite fluid is analyzed numerically. The results show that the magnetic field can promote bubble expansion and hinder its translational motion, and both the enhancement and obstruction effects will weaken with the decrease of bubble size. The initial translational velocity has almost no effect on bubbles motion. Besides, the maximum expansion radius of MMBs increases with the ferrofluid shell thickness, while that of the common MBs is just the opposite. In addition, the periodic change of Levich viscous drag caused by the rebound leads to the step-like translational motion. Finally, the ferrofluid-shell model can be replaced by the model of non-magnetic microbubbles in magnetic liquid at high driving frequency.