Theoretical investigation of the nonlinear dynamics for cavitation bubbles inside liquid drops

The cavitation bubble dynamics inside liquid drops governed by a Rayleigh–Plesset-like equation is investigated theoretically. A strict qualitative analysis is made to determine the bubble dynamic behaviors. Analytical expressions of the collapse times and analytical solutions of the governing equation are derived for different initial conditions. The validity of these analytical solutions is studied by testing numerical algorithms and/or experimental data. As applications of the analytical solutions, analytical expressions in parametric forms for the evolutions of bubble oscillation velocity, oscillation acceleration, kinetic energy, and potential energy are also obtained. Furthermore, the relevant nonlinear bubble dynamic characteristics and motion laws are also revealed based on the obtained results.