Theoretical Analysis of Growth and Collapse of Spherical Cavities

In the present study, the analytical equations of conical functions are used to describe the growth and collapse of vapor and spherical cavities in liquids (cavitation). The equations describing the expansion of the spherical finite universe from the cosmological models are also applied to the study of growth and collapse of vapor and air cavities within liquids. The relative simple method used here has the advantage of prescinding numerical and/or computational simulations and other methods. Although the differences between the results of the adiabatic collapse and the isothermal collapse are very small, according to the literature. The hypothesis of the isothermal collapse of the bubble is used and justified based on the concept of characteristic time for heat transfers. Consequently, available theoretical and experimental data for isothermal collapse of such cavities are also used and, in the sequence, adjusted to polynomial equations. These were used to describe the radius as a function of time during the collapse and growth of the cavities. An auxiliary function was used here with the time variable, resulting in a linear function of it. The results are presented in graphs showing the bubble radius as a function of time, for collapse or growth of the cavity, or bubble.