Nonlinear analog of the Plesset equation for nonspherical motion of a gas bubble

Abstract

An equation analogous to Plesset's equation that describes the non-spherical motion of a gas bubble in an ideal incompressible fluid is derived. The terms containing the squares of the amplitude of the non-free perturbation were taken into account, whereas in the derivation of the Plesset equation only the linear terms are taken into account. On the basis of the obtained equations numerical calculations of the nonspherical oscillations of the bubble were carried out. A comparison of the obtained results and the Plesset equation showed that with a sufficient increase in the perturbation amplitude, the nonlinear terms begin to affect that is lead to solution limitation.