Nonlinear bubble oscillations

Abstract

Numerical solutions have been obtained for the motion of a gas bubble in an incompressible liquid when harmonic pressure oscillations are imposed. The mean pressure in the liquid was taken to be 1 atm and the ratio of oscillating pressure amplitude, A, to the mean pressure was given the values 0.2, 0.5, 1.0 and 2.0. The equilibrium bubble radius was chosen to be $\mathrm{R}{}_{\text{o}}={10}^{-2}$ , ${10}^{-3}$ and, ${10}^{-4}\text{cm}$ , and the angular frequency of the pressure variations was $\mathit{\omega }=0.2\times {10}^5$ , $0.7\times {10}^3$ , and $1.2\times {10}^5$ per sec. The phenomena of bubble ‘explosion’ or ‘collapse’ were found for large A, i.e., 1.0 and 2.0. For the smaller values of A, the bubble radius varied with time within well-defined limits, but nonlinear effects were evident.