Time-dependent cavitation in a viscous fluid

Kinetics of nucleation and growth of empty bubbles in a nonvolatile incompressible fluid under negative pressure is considered within the generalized Zeldovich framework. The transient matched asymptotic solution obtained earlier for predominantly viscous nucleation is used to evaluate the distribution of growing cavities over sizes. Inertial effects described by the Rayleigh-Plesset equation are further included. The distributions are used to estimate the volume occupied by cavities, which leads to increase of pressure and eventual self-quenching of nucleation. Numerical solutions are obtained and compared with analytics. Due to rapid expansion of cavities the conventional separation of the nucleation and the growth time scales can be less distinct, which increases the role of transient effects. In particular, in the case of dominant viscosity a typical power-law tail of the quasistationary distribution is replaced by a time-dependent exponential tail. For fluids of the glycerin type such distributions can extend into the micrometer region, while in low-viscosity liquids (water, mercury) exponential distributions are short lived and are restricted to nanometer scales due to inertial effects.