The thermal regime of vapour bubble collapse at different Jacob numbers

Abstract

For the case when heat transfer is the main process responsible for the collapse of bubbles, the numerical solution is obtained for a non-linear non-steady problem of heat and mass transfer between a spherical vapour bubble and liquid with external pressure increasing step-wise. The Jacob number is the only similarity criterion of this problem. A set of functions R( t) ( R is the bubble radius and t the time) is tabulated over a wide range of Jacob numbers (0.01 < 1000). It is shown that the variation of Ja entails a qualitative change in the form of the function R( t). When Ja = 0, the function R( t) is convex. When 0 < Ja < 2, the curves R( t) are S-shaped, and when Ja > 2 they are concave. Tabulated numerical results taken together with analytical formulae for the limiting cases Ja ← 0 and Ja ← ∞ constitute a simple method of calculating R( t) for specific bubbles. An interpolation formula is obtained for determining the time of complete collapse of a bubble. The results of predictions are compared with experimental data.