An improved tangency condition for fog formation in cooler-condensers

In 1950 Johnstone et al. (Ind. Engnq Chem. 42, 2298-2302 (1950)) introduced the tangency condition to determine fog (or mist) formation in binary mixtures in cooled channels. In the present analysis it is demonstrated that their condition is erroneous and an improved equation is derived. The condition is based on the heat and diffusional mass transfer rates to a condenser wall, and the slope of the saturation line of the vapour component at the wall temperature. The transfer rates follow from a thorough analysis of the energy and diffusion equation in a stagnant film next to the wall (the classical ‘film model’ or ‘film theory’). The validity of the improved tangency condition is assessed against wall condensation experiments by Johnstone et ai., concerning mixtures of nitrogen with vapours of water and n-butyl alcohol, yielding satisfactory agreement.