Thermal Effects of Internal Gas on the Oscillations of a Cluster of Bubbles

Abstract

The governing equations of a cluster of bubbles are derived by taking account of the thermal effects of the internal gas and the three-dimensional translational motion and deformation of each bubble. The equations are applied to the nonlinear oscillations of multiple interacting bubbles. The frequency response curves are obtained for two typical arrangements of bubbles with the same radii. The present results are compared with the results of polytropic analysis in which the thermal effects are evaluated using the effective polytropic index and the effective viscosity. It is shown that the heat transfer inside the bubble is important in investigating the nonlinear bubble oscillations. The polytropic relation for the internal gas does not hold when the nonlinearity of the radial oscillation becomes strong. Both radial and surface oscillations are affected by the translational motion of each bubble. It is also shown that the subharmonic oscillation of interacting bubbles occurs more easily than that of an isolated bubble due to the bubble-bubble interaction.