It has been suggested that bubble-wall velocities cannot exceed the sound speed in the liquid at the bubble wall [K. Yasui, Phys. Rev. E 64, 016310 (2001).10.1103/PhysRevE.64.016310]. Here we show that this upper bound was derived omitting the partial derivatives with respect to time, i.e., assuming that the flow was in the steady state. For collapsing bubbles, however, the steady-flow assumption requires justification, as the partial time derivatives appear to have the same orders of magnitude as the other terms in Euler's and the continuity equations. Furthermore, numerical solutions of the hydrodynamic equations with a hyades hydrocode yielded supersonic velocities in the liquid at and near the collapsing bubble. We also show the spatial distributions of pressure, density, sound speed, and mass flux density around the supersonically collapsing bubble.
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