The effect of viscosity on the spherical stability of oscillating gas bubbles

Gas bubbles driven in radial oscillations are subject to an instability of the spherical shape that is opposed by surface tension and viscosity. An ex act linear formulation for the study of the phenomenon has been available f or many years, but its complexity has discouraged a detailed investigation. With the recent theory of sonoluminescence of Lohse and co-workers [Hilgen feldt ct nl., Phys. Fluids, 8, 2808 (1996)], there has been a renewed inter est in the problem and new data have become available. This paper presents a numerical method for the solution of the pertinent equations and compares the theory with these new data. The coupling of the strong nonlinearity of the bubble radial oscillations with the parametric mechanism of the surfac e instability results in a very complex structure for the stability boundar y. Nevertheless, a good agreement between theory and data is found. A compa rison with earlier approximate models is also made. (C) 1999 American Insti tute of Physics. [S1070-6631(99)04106-9].