Stability of evaporating water when heated through the vapor and the liquid phases.
The stability of a water layer of uniform thickness held in a two-dimensional container of finite or semi-infinite extent is examined using linear stability theory. The liquid-vapor interface can be heated both through the liquid and through the vapor, as previously experimentally reported. The need to introduce a heat transfer coefficient is eliminated by introducing statistical rate theory (SRT) to predict the evaporation flux. There are no fitting or undefined parameters in the expression for the evaporation flux. The energy transport is parametrized in terms of the evaporation number, Eev, that for a given experimental circumstance can be predicted. The critical Marangoni number for the finite, Macf, and for the semi-infinite system, Mac(infinity), can be quantitatively predicted. Experiments in which water evaporated from a stainless-steel funnel and from a polymethyl methacrylate (PMMA) funnel into its vapor have been previously reported. Marangoni convection was observed in the experiments that used the stainless-steel funnel but not with the PMMA funnel even though the Marangoni number for the PMMA funnel was more than 27,000. The SRT-based stability theory indicates that the critical value of the Marangoni number for the experiments with the PMMA funnel was greater than the experimental value of the Marangoni number in each case; thus, no Marangoni convection was predicted to result from an instability. The observed convection with the stainless-steel funnel resulted from a temperature gradient imposed along the interface.
Das
Kausik S
KS
Thermodynamics and Kinetics Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada M5S 3G8.
MacDonald
Brendan D
BD
Ward
C A
CA