Unifying boiling and degassing theories: Self-similar and pseudo-steady state analysis

The two phenomena of degassing and boiling, regarding bubble growth in a liquid with a dissolved gas, are studied separately in literature with the corresponding theories to diverge from each other at the boiling temperature. Here a unifying approach is developed in terms of heat and mass transfer conservation laws to describe both phenomena. It is shown that the corresponding system of partial differential equations admits a self-similar solution for constant bubble growth rate conditions. The self-similarity solution is further simplified in order to indicate several asymptotic bubble growth regimes. The case of non-constant bubble growth rate conditions is treated only for the asymptotic regime of quasi-steady growth. Several results for idealized and realistic bubble growth cases are presented. It is shown that the two individual theories of degassing and boiling are unified through the appropriate manipulation of the bubble temperature. Small temperature differences can yield large variation in bubble growth rate in a small range around the boiling temperature. The system water-nitrogen is examined in detail and it is found to be outside of the domain of asymptotic theories (i.e. the complete self-similar solution has to be employed).