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With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid-gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid-gas solution. The effect of surface tension on the diffusion process is also considered.

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Vapour bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)½ where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For \[ \Delta p/\rho = 10^6 {\rm cm}^2/\sec^2 \approx 1\, \hbox{atm/density of water} \] the jet had a speed of about 130m/sec in the first case and 170m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapour are not important.

The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius-time behavior is made with experimental observations in superheated water, and very good agreement is found.

The conditions for the stability or instability of the interface between two immiscible incompressible fluids in radial motion are deduced. The stability conditions derived by Taylor for the interface of two fluids in plane motion do not apply to spherical flows without significant modifications.

Three regimes of liquid flow over a body are defined, namely: (a) noncavitating flow; (b) cavitating flow with a relatively small number of cavitation bubbles in the field of flow; and (c) cavitating flow with a single large cavity about the body. The assumption is made that, for the second regime of flow, the pressure coefficient in the flow field is no different from that in the noncavitating flow. On this basis, the equation of motion for the growth and collapse of a cavitation bubble containing vapor is derived and applied to experimental observations on such bubbles. The limitations of this equation of motion are pointed out, and include the effect of the finite rate of evaporation and condensation, and compressibility of vapor and liquid. A brief discussion of the role of “nuclei” in the liquid in the rate of formation of cavitation bubbles is also given.

Some 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. The liquid flow during the rebound, which occurs after the minimum radius has been attained, is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is valid even for fairly high pressures, and this fact is used to determine the peak intensity of the pressure wave as it moves outwards at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage.