Some Nonlinear Interactive Effects in Bubbly Clouds

Abstract

Nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. Averaged equations of motion are used and the Rayleigh-Plesset equation is used to include the bubble dynamics. Energy dissipation due to viscous and thermal effects are included while relative motion between the two phases, liquid compressibility and viscous dissipation in the liquid have been ignored. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used in an approximate calculation of the nonlinear frequency response of a bubble layer. Finite thickness of the bubble layer results in characteristic natural frequencies of the layer all of which are less than the natural frequency of a single bubble. The presence of bubbles of different sizes in the layer causes a phenomenon called harmonic cascading. This phenomenon consists of a large response at twice the excitation frequency when the mixture contains bubbles with a natural frequency equal to twice the excitation frequency. The details of these results along with the most important limitations of theory are presented.