The nonlinear characteristics of the pulsations, translations and the secondary Bjerknes force

Abstract

The nonlinear characteristics of the pulsations and translations have been studied for movable cavitation bubbles. The translations of the centers of bubbles also possess nonlinearity as their radial pulsations, and can cause the chaos of the pulsations sometimes. Furthermore, the nonlinear characteristics of the secondary Bjerknes force for a movable pulsating bubble are also calculated by the time evolution and the bifurcation diagram in strong ultrasonic field. A series of snapshots of the density diagrams in parametric space indicate that the secondary Bjerknes force not only is sensitive to the parameters, but also develops nonlinearly. The bifurcation diagrams show that the translations of bubbles can increase the chaos degree of the secondary Bjerknes force. In addition, the bifurcation diagrams are also plotted with respect to variables such as liquid viscosity, driving frequency and ambient radius. The results illustrate that the translations of bubbles make a great contribution to the nonlinear characteristics of the secondary Bjerknes force.