Rayleigh–Taylor instability for thin viscous gas films: Application to critical heat flux and minimum film boiling

Abstract A number of hydrodynamic models for critical heat flux and minimum film boiling rely on interfacial instability theories. Rayleigh–Taylor instability is one of the important theories, and has been usually analyzed for inviscid flows. An inviscid flow analysis is acceptable for general circumstances. However, when the gas film becomes thin to the extent of creeping flow, the viscous force is dominant over the inertia force, and thus the gas viscosity cannot be neglected. In this study, four approaches are considered for Rayleigh–Taylor instability: (1) classical inviscid flow analysis, (2) viscous potential flow analysis, (3) fully viscous flow analysis, and (4) lubrication theory. In particular, the dispersion relation including phase change is derived based on the lubrication approximation. It is shown that the most dangerous wavelength should be λ d = 2 π [ 2 σ / ( Δ ρ g ) ] 1 / 2 instead of λ d = 2 π [ 3 σ / ( Δ ρ g ) ] 1 / 2 for thin viscous gas film. This result is applied to the existing critical heat flux models for saturated pool boiling on horizontal surfaces. As a result, the prediction accuracy is improved at elevated pressures. In addition, the most dangerous wavelength and the most rapid growth rate for viscous thin films are shown to be applicable to the minimum heat flux condition.