Hickling, Robert and Plesset, Milton S. (1964) Collapse and
rebound of a spherical bubble in water. Physics of Fluids, 7
(1). pp. 7-14. ISSN 0031-9171
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numerical solutions are presented which describe the flow in the
vicinity of a collapsing spherical bubble in water. The bubble
is assumed to contain a small amount of gas and the solutions
are taken beyond the point where the bubble reaches its minimum
radius up to the stage where a pressure wave forms which
propagates outwards into the liquid. The motion during collapse,
up to the point where the minimum radius is attained, is
determined by solving the equations of motion both in the
Lagrangian and in the characteristic form. These are found to be
in good agreement with each other and also with the approximate
theory of Gilmore which is shown to be accurate over a wide
range of Mach number