Bubble expansion rates in viscous compressible liquid

A new equation has been derived for radial expansion of a bubble in viscous liquid, taking into account the compressibility of liquid. This model is important in understanding the time-evolution of the bubble growth in a cavitating flow. We solved the equation of motion of viscous liquid and obtained the velocity field and the pressure distribution in liquid. It is found that the expansion rate of a bubble in viscous compressible liquid is governed by the friction force due to viscosity as well as the surface tension, the inertial force, and the gas pressure. Further, the bubble expansion rate is brought by the same expression to that in an incompressible liquid only in the case that the liquid is in a hydrostatic state before the bubble grows.