Dropwise condensation as affected by vapor diffusion and molecular sticking

Experimental values of heat flux in dropwise condensation on a gold plated vertical copper surface were determined in presence and absence of (or minute traces of) noncondensable gas. The noncondensable gas concentration varied from 0.0045% to 7.5% over a range of subcooling from 2.155 to 17.13°F and system pressure of 4.124 to 16.67 psia. The calculated heat transfer coefficient ranged from 1,545 to 11,135 Btu/hr-ft²-°F. In the part of the experiment where precautions were taken to avoid the presence of noncondensable gas in the water vapor, much higher values of heat flux were observed. Values of heat transfer coefficient ranging from 8190 to 35,591 Btu/hr-ft²-°F were obtained for a subcooling range of 0.7 to 8.69°F and pressure range of 2.86 to 17.20 psia. By comparing these data with the data of other investigators, presence of minute traces of noncondensable gas of the order of 8 to 13 ppm was suggested. No comparison of results for 1% to 7.5% noncondensable gas concentration could be made because of the lack of available data. A diffusion based theoretical model was established and results of heat flux were obtained for a range of concentrations varying from 3% to 20%. Conventional diffusion approach in a binary gas mixture was considered to find the rate of diffused water vapor molecules. A correlation was established between condensation of the diffused molecules and evaporation of molecules from the liquid surface to determine the net rate of condensation. Diffusion layer thickness, active condensing surface area and the sticking coefficient were found to be the controlling parameters of the net rate of condensation. A diffusion layer very close to the surface of the liquid droplets was considered where all the concentration changes of water vapor and noncondensable gas were assumed to take place. The thickness of this layer was assumed to be some magnitude of the order of the mean free path of the water vapor. An expression for the partially active condensing surface area was formulated in terms of the degree of subcooling, concentration of noncondensable gas, condensing vapor pressure and saturation temperature. Sticking coefficient was assumed to be unity for the active surface area and less than unity for the partially active surface area. Good agreement between the theory and the experiment in general was observed and comparisons between the theory and the experiment were made for 3% and 5% noncondensable gas concentrations. A better agreement can be obtained with the knowledge of the exact behavior of the three controlling parameters discussed above. The proposed theory is applicable only in presence of a significant amount of noncondensable gas and breaks down below the level of 1% concentration. The reduction of heat transfer because of the presence of minute traces of noncondensable gas may not be entirely due to the phenomenon of diffusion --Abstract, pages ii-iv