Chaotic oscillation of a bubble in a weakly viscous dielectric fluid under electric fields

The dynamics of a bubble in a weakly viscous dielectric fluid under electric fields is studied. The dynamical equations for the volume and shape mode oscillations are derived using the domain perturbation method with first-order accuracy in deformation. For the volume mode oscillation, we obtain the modified Rayleigh–Plesset equation which includes a forcing term due to the effect of electric field. For the shape mode oscillations, the Prosperetti–Seminara equation [Phys. Fluids 21, 1465 (1978)] is also extended. The dynamical equations are analyzed with two types of electric fields: the uniform field and the axisymmetric straining field. Equilibrium analysis is performed to find the equilibrium points in the phase planes and their stabilities in static electric fields. Then, the effects of time-periodic electric fields on the bubble dynamics are considered at two levels of viscosity effect [the inviscid limit and the case of Re=O(10)]. The nonlinear dynamics theory is used for analysis of the complicated volume and shape mode oscillations.