Definition of Bubbly Liquids Parameters for the Optimization of Their Nonlinear Effects on Ultrasound

Abstract

The aim of this paper is to optimize the generation of frequencies obtained nonlinearly from the propagation of ultrasound in a bubbly liquid. A study is presented for which the number and size of the gas bubbles in the liquid are varied to determine the optimal medium, which is the one that allows the highest amplitude for these frequency components. We use a previously developed numerical software that tracks the nonlinear behavior of both ultrasound and bubble vibrations in time to carry out several simulations. We focus our attention on two one-dimensional configurations, a resonator of length set at a quarter of the wavelength with a free-wall condition and a cavity of length set at sixteen wavelengths with open-field condition. In each case, we analyze the generation of the 2nd, 3rd, and 4th harmonics of the source frequency. Our results show that, in both cases, the use of higher source amplitudes and lower source frequencies is more useful to increase the harmonic amplitudes. Moreover, smaller bubbles are more adequate when the void fraction is kept constant for this purpose in the first configuration, whereas the modification of void fraction has no influence in the second configuration, for which given a void fraction value, bubble sizes whose ratio are 𝑓0/𝑓≈5, 𝑓0/𝑓≈7, and 𝑓0/𝑓≈9 maximize the 2nd, 3rd, and 4th harmonics, respectively. These conclusions could be of interest for some applications.