Growth of a Vapor-Filled Cavity near a Heating Surface and Some Related Questions

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Abstract
The growth of a vapor bubble on a heating element immersed in a liquid which is at saturation temperature or subcooled far from the heating surface but which is superheated near the heating surface, is treated as a problem of heat conduction with evaporation on a boundary. The results show, in agreement with experiment, that in a liquid at saturation temperature the radius grows as t½ at first (t is time) and as t¼ for t → ∞; for a subcooled liquid the radius as a function of time is given as an infinite series in terms of a quantity H, later identified with the thickness of the thermal boundary layer. Several relations between boundary layer thickness in a boiling liquid, maximum radius attained by the cavity before collapse and superheat and subcooling are derived and compared with experiment. For large subcooling the boundary layer thickness is shown to be about one-half (or less) the size of the maximum radius. Physical considerations concerning the mechanism of heat transmission to a boiling liquid lead to the definition of a heat diffusivity, the exchange diffusivity a* = M2 a, with M the dimensionless ratio of enthalpies of superheated liquid and of saturated vapor. The dimension of the thermal boundary layer is shown to be the diffusion length for the exchange diffusivity.

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