Understanding the periodic driving pressure in the Rayleigh–Plesset equation

The Rayleigh–Plesset equation is the basis of most theoretical analyses of bubble dynamics. Surprisingly, experiment and theory do not agree on the spatial location and the value of the periodic driving pressure. In the experiment the driving pressure is located near the bubble, whereas, the theory assumes that the driving pressure is far from the bubble. The paradox is resolved by deriving a modified equation that is valid for compressible flows in a finite spherical geometry. The modified equation is identical to the incompressible Rayleigh–Plesset equation with the driving pressure at infinity replaced by the actual driving pressure, which is located within 25 bubble radii of the bubble. We show that a hydrophone at the center of the flask measures this driving pressure, which is why the theory and experiment agree when an incompressible Rayleigh–Plesset equation is used to describe compressible flows.