Shape Oscillation of an Encapsulated Bubble in Electric Fields

We investigate the dynamics of an encapsulated bubble in electric fields theoretically, based on the leaky dielectric model. On the bubble surface, the applied electric field generates a Maxwell stress, in addition to hydrodynamic traction and membrane mechanical stress. Our model also includes the effect of interfacial charge due to the jump of the current and the stretching of the interface. We focus on the axisymmetric deformation of the encapsulated bubble induced by the electric field and carry out our analysis using the Legendre polynomials. In our first example, the encapsulating membrane is modelled as an incompressible interface with bending rigidity. Under the steady uniform electric field, the encapsulated bubble resumes an elongated equilibrium shape, dominated by the second and fourth order shape modes. The deformed shape agrees well with experimental observations reported in the literature. For our second example, we considered a bubble encapsulated with a hyperelastic membrane with bending rigidity, subject to an oscillatory electric field. We show that the bubble can modulate its oscillating frequency and reach a stable shape oscillation at an appreciable amplitude.