Influence of the accommodation coefficient on nonlinear bubble oscillations

Abstract

This paper numerically investigates the effect of mass transfer processes on spherical single bubble dynamics using the Hertz–Langmuir–Knudsen approximation for the mass flux across the interface. Bubble behavior, with and without mass transfer, is studied for different values of pressure wave amplitude and frequency, as well as initial bubble radius. Whereas mass transfer processes do not seem to play a significant role on the bubble response for pressure amplitudes smaller than 0.9 atm, they appear to have an important effect when the amplitude is greater than or equal to 1 atm. For the later case, where the minimum liquid pressure reaches values around its vapor pressure, the importance of mass transfer depends on frequency. For frequencies in the 10^3–10^5 Hz range and initial bubble radii of the order of tens of microns, bubble implosions with and with no mass transfer are significantly different; smaller radii display a lower sensitivity. In this regime, accurate model predictions must, therefore, carefully select the correct value of the accommodation coefficient. For frequencies greater than 10^5 Hz, as a first approximation mass transfer can be ignored.