On the gas pressure inside cavitation bubbles

The validity of the reduced order [Delale and Pasinlioglu, "Acoustic cavitation model based on a novel reduced order gas pressure law,"AIP Adv. 11, 115309 (2021)] and of classical polytropic gas pressure laws during the response of a bubble to variations in the pressure of the surrounding liquid is investigated. In particular, from the exact expression of the gas pressure coupled to the thermal behavior of gas bubbles, we identify the conditions where the reduced order gas pressure law and the classical polytropic law hold. We then distinguish three regimes for the change of state of the bubble during its nonlinear oscillations as the nearly isothermal, transition, and nearly adiabatic regimes, depending on the value of the polytropic index, and we determine the mean value of the polytropic index in each regime by averaging over a parameter, which is a function of the Peclet number based on the characteristic thermal diffusion time. The results of the temporal evolution of the bubble radius, the bubble wall temperature, and the partial gas pressure inside the bubble are presented using an acoustic cavitation model based on the reduced order gas pressure law for both constant and variable interface properties.