374 Table 106 



EQUILIBRIUM SUPERSATURATION OVER SOLUTION DROPLETS 1 



Effect of curvature. — Kelvin ' has shown that the curvature of water droplets tends 

 to increase the equilibrium vapor pressure over the droplet in accordance with the 

 equation 



l g.^=-J2- (1) 



e* pRvTr 

 where 



e v = equilibrium vapor pressure over a flat water surface, 

 e'n = equilibrium vapor pressure over a curved water surface, 



7 = surface tension of water, 

 R v = gas constant for water vapor, 



p = density of water, 

 T = temperature, C K., 



r = radius of curvature of the water surface. 



Effect of dissolved substances. — According to Raoult's Law, which is valid for solutions 

 dilute enough to be almost wholly dissociated, the vapor pressure over a solution is 

 given by 



«'-—-= ML_ (2) 



e v M + M' k£} 



where 



e" v = equilibrium vapor pressure over a flat surface of solution, 

 M = number of mols of the solvent, 

 M' = number of mols of the solute. 



Howell shows that the order of magnitude of the molecular concentration present in 

 atmospheric droplets at high relative humidities is such that the validity of Raoult's Law 

 can be presumed for any nucleus likely to be activated during atmospheric processes. 



Combined effect of curvature and dissolved substance. — Howell has computed the 

 equilibrium vapor pressure over solution droplets by combining equations (1) and (2). 

 The percent supersaturation relative to a plane surface of pure water is given for 

 T = 273, 263, 253, 243, and 233 C K. as a function of log™ r and n, where r is the radius 

 of the droplet in centimeters and n the mass of the condensation nucleus, in gram mole- 

 cular weights (mols). Since the molecular weights of the commonest hygroscopic sub- 

 stances in the atmosphere occupy a much narrower range than do the masses of the 

 nuclei, it may be said in general that the activity of soluble nucleus at condensation 

 depends primarily on its mass and only to a minor degree on its chemical composition. 



In the range of relative humidities occurring during its natural formation and dissolu- 

 tion of fog and cloud, the variations of relative humidity from equilibrium are of the 

 same order of magnitude as the degrees of supersaturation indicated in the table. There- 

 fore the vapor pressure in the cloudy air is equal to the equilibrium vapor pressure 

 derivable from the tables only when the droplets are of uniform size and are not under- 

 going growth or evaporation. 



1 Howell, W. E., The growth of cloud droplets in uniformly cooled air, Sc.D. dissertation, Mass. 

 Inst. Techn., 1948. Also Journ. Meteorol., vol. 6, p. 134, 1949. 



2 Kelvin, Lord, Proc. Roy. Soc. Edinburgh, vol. 7, p. 63, 1870. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



