Cavitation in stretched liquids

We consider the thermodynamics of cavity formation in metastable liquids within the framework of classical nucleation theory. We derive analytic expressions for the vapour pressure inside the cavity, the equilibrium liquid/vapour and spinodal volumes and pressures for the van der Waals (vdW) equation of state (EoS). We also, inter alia, derive the analytic formula for the liquid–vapour coexistence (‘binodal’) line of the vdW fluid. We provide analytic formulae within this approximation for the dependence of the vapour pressure inside the cavity on, among other quantities, the temperature and pressure inside the surrounding liquid. We compare these formulae with those derived, making further simplifications of the EoS. We conclude, that, for all practical applications away from the critical point, the ideal gas representation of the vapour in the cavity is sufficiently accurate because the vapour pressure in the cavity is so low. This leads to a relatively simple expression for the cavity vapour pressure which is very similar to, and numerically hardly distinguishable from, the classical Kelvin equation applied to cavities. We propose several dimensionless quantities characterizing the degree of stretching of the liquid, in terms of the vapour pressure inside the cavity, and the pressure in the surrounding metastable bulk liquid. The dependence of the vapour pressure and barrier height on the scaling parameters are quite insensitive to the level of approximation of the EoS (e.g. simplifications inherent in the vdW EoS), when cast in terms of these dimensionless parameters. The maximum tensile strength, coinciding with the spinodal pressure, for liquid water under ambient conditions using the vdW EoS is ca.1 kbar. We also consider the Lennard–Jones fluid, as a representative ‘realistic’ fluid, using a parametrized EoS. This gives a value of ca.2 kbar for the maximum tensile strength near the triple point.