Effects Of Vapour Pressure On The Acoustic Cavitation Effect

The ultrasonic cavitation technology has long been extensively utilised in industrial production field, thus came out a new frontier interdiscipline named sonochemistry. In study of ultrasonic cavitation bubble in liquid, two approaches are typically adopted to dispose the vapour: ignoring vapour pressure inside the bubble or considering vapour pressure as constant. But some researches indicate that the vapour inside bubble has certain influence on cavitation effect. Accordingly, it is necessary to explore the influence of vapour on bubble dynamic behavior and cavitation effect in theory.Based on Rayleigh’s cavitation theory, this paper took the phase transition of water vapour at the bubble wall into consideration and a kinetic model with phase boundary layer was established. Meanwhile, the dynamic timescale and phase change timescale were introduced to acquire the constant vapour pressure model and the constant vapour content model by comparing the relative magnitude of those two timescales.According to the assumptions in the model, the mass flux of water vapour at bubble wall was simplified by differential approximation method considering phase change of vapour, and the dynamic equations of the two models were deduced from the equation corrected by Sochard. The forth-order Runge-Kutta algorithm was applied in MATLAB to calculate and analyse the dynamical behaviour of cavitation bubbles in different vibration modes. The results reveal that the kinetic characteristics of bubbles under the constant vapour content model are consistent with those of the model without vapour. The bubbles under the constant vapour pressure model exhibit larger amplitudes and collapse delays, move more violently to generate acoustic cavitation effect than the constant vapour content model. Moreover, vapour content exerts certain influence on the maximum radius, minimum radius and collapse intensity of bubbles. With the accumulation of water vapour, the maximum radius, minimum radius and collapse intensity change nonlinearly and the variations of these parameters caused by changes in water vapour content are relatively obvious when the molar fraction of vapour is low.The heat transfer model with thermal boundary layer were developed for further exploration of the influence that vapour pressure exerts on the thermodynamic effect of cavitation bubble. Using the Fourier law, the radial temperature distribution, central temperature and pressure of bubble were derived. Analysis suggests that instantaneous high temperature and pressure are generated in partial space during bubble collapse. The peak pressure is significantly increased and the peak temperature is reduced by nearly an order of magnitude for the inclusion of vapour. The enormous temperature difference between inside and outside of the bubble facilitates the formation of thermal boundary layer. The heat inside the bubble transfers outwards with great gradient and diffuses to the ambient water through the thermal boundary layer. With the accumulation of water vapour, the peak pressure and temperature are significantly reduced. Furthermore, the actual molar fraction of water vapour should be between ten percent and fifteen percent according to analysis and calculation.