Harmonic Cascading in Bubble 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. 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 to solve for nonlinear effects in a semi-infinite layer containing bubbles with a distribution size. A phenomena termed harmonic cascading is seen to take place due to presence of distribution of bubble sizes. This phenomena 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 ratio of the amplitude of the second harmonic response to the amplitude of the first harmonic response is observed to increase when the number of small bubbles is increased relative to the number of large bubbles. The response is also seen to be weakened by an increase in the total number of bubbles per unit liquid volume at constant void fraction.