Shock waves at final stages of cavity collapse in non-homogeneous liquid with divergenceless flow

We show the emergence of shock waves at the final stages of the complete collapse of a spherical cavity in a liquid with a smoothly decreasing density. The well-known Rayleigh assumption of fluid homogeneity is altered, while maintaining that of divergenceless flow. The fundamental difference between both infinite liquids is that his has an infinite mass, while ours, a finite one. Given the ease of deformation of non-homogeneous media in relation to homogeneous ones, as observed in several materials, all Rayleigh results are modified, including the cavity wall speed and acceleration, total time of complete collapse, and distribution of pressure in the infinite liquid. Rather than the homogeneous Rayleigh fluid, our non-homogeneous liquid can support a finite local sound speed. As a result, we succeed to show the emergence of shock patterns at the final stages of the cavity collapse. The analytical formulation is compared with underwater implosion and explosion experiments and simulations. Possible applications as a benchmark test for hydrocodes are briefly discussed.