Cavitation Bubble Collapse in Water with Finite Density behind the Interface

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Abstract
The collapse of an empty cavity in water has been treated by Hunter, using a similarity solution. Conditions for similarity require that the value of the density of water at the cavity boundary is zero, although the value corresponding to zero pressure given by the Tait equation of state is nonzero. To satisfy the correct boundary conditions on the cavity surface, Hunter's similarity solution is perturbed to take account of first‐order changes in the wall density. The perturbation equations have critical points coinciding with or close to the corresponding singularities of the similarity equations. Regular integral curves passing through all these points can be determined uniquely. Near the cavity wall these can be represented by expansions in powers of the similarity variable. Near the singular characteristic, however, the corresponding expansions must be found in terms of a modified variable, determined by Lighthill's technique. The corrected velocity of the cavity wall can be determined solely in terms of series expansions there.

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