Nonlinear Spherical Standing Waves in an Acoustically Excited Liquid Drop

Abstract

Nonlinear evolution of a standing acoustic wave in a spherical resonator with a perfectly soft surface is analyzed. Quadratic approximation of nonlinear acoustics is used to analyze oscillations in the resonator by the slowly varying amplitude method for the standing wave harmonics and slowly varying profile method for the standing wave profile. It is demonstrated that nonlinear effects may lead to considerable increase in peak pressure at the center of the resonator. The proposed theoretical model is used to analyze the acoustic field in liquid drops of an acoustic fountain. It is shown that, as a result of nonlinear evolution, the peak negative pressure may exceed the mechanical strength of the liquid, which may account for the explosive instability of drops observed in experiments.