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Motivated by the high energy focusing found in rapidly collapsing bubblesthat is relevant to implosion processes that concentrate energy density, suchas sonoluminescence, we consider a calculation of an empty cavity collapse in acompressible Euler fluid. We review and then use the method based on similaritytheory that was previously used to compute the power law exponent $n$ for thecollapse of an empty cavity in water during the late stage of the collapse. Weextend this calculation by considering different fluids surrounding the cavity,all of which are parametrized by the Tait-Murnaghan equation of state throughparameter $\gamma$. As a result, we obtain the dependence of $n$ on $\gamma$for a wide range of $\gamma$, and indeed see that the collapse is sensitive tothe equation of state of an outside fluid.

Power law singularity for cavity collapse in a compressible Euler fluid with Tait-Murnaghan equation of state