Solubility of heat and the thermo-mechanics of vapour cavities in liquids

This paper introduces the solubility of heat, a new parameter useful in the modelling of the thermo-mechanical behaviour of two-phase vapour–liquid processes. Unlike other parameters in current use, the solubility of heat is dimensionless and is sensitive to both thermal and mechanical aspects of the process of interest. Large values of the parameter correspond to situations in which the latent heat associated with the generation and condensation of vapour is small so that the system’s behaviour is dominated by mechanical factors. Conversely, smaller values of the parameter indicate a strong effect of the energy cost of phase-change phenomena on the mechanics of the system. These statements are illustrated with a number of examples featuring the thermo-mechanics of vapour cavities in one, two and three spatial dimensions including growth, forced oscillations, condensation and other problems. These examples are based on a generalised formulation of the pertinent equations valid in any number of space dimensions, with the vapour cavity surrounded by a finite or infinite mass of liquid. The general case of a three-dimensional cavity of unspecified shape is also briefly considered.