Dynamic growth of a spherical bubble in a time-periodic electric field

Abstract

The dynamics of a spherical bubble in a time-dependent electric field is investigated via the modified Rayleigh-Plesset equation where the effect of an electric field is added. The effect of an imposed electric field is found to be equivalent to the increase of the ambient pressure by the amount of 3/8e0e1E02(2S-1), where e0e1 is the electric permittivity of the gas inside the bubble, E0 the strength of the imposed electric field, S the permittivity ratio of the outside fluid to the inside gas. The effects of a time-periodic electric field have been studied by using two methods of analysis; the two-timing perturbation analysis for the regular dynamics near the stable steady solution and the Poincare map analysis for the global dynamics. It is revealed that an O(e1/3) response in the oscillation of bubble radius can be obtained from an O(e) resonant time-periodic forcing in the neighborhood of a stable steady solution. By the Poincare map analysis, it is also shown that the bubble can either undergo bounded oscillation, or else respond chaotically and grow very rapidly. The probability of escape to rapid growth is found to be a strong function of the forcing frequency, of which the optimal value is slightly lower than the intrinsic resonant frequency of oscillation under the steady electric field.