13 



the chamber, a cap of violently agitated foam is formed and supported by the spray. The inti- 

 mate mixture and vigorous agitation maintained in this film of emulsified air and water appear 

 to provide an extremely effective process of exposure. This conjecture is supported by the 

 experimental results in conjunction with estimates of the extent of the exposure effected out- 

 side of the emulsified area. 



The extent of the exposure of the sample water which occurs as a result of diffusion of 

 the dissolved gas out of or into the vertical film formed as the water runs down the inside 

 walls of the chamber can be estimated. The thickness 8 of the film and the flow velocity u 

 are given by the well-known Nusselt relations obtained by equating viscous and gravitational 

 forces on each lamina: 



6 = 

 ■ 2C5 



ZQv 



Cg 



1/3 



[4] 





[5] 



in which v is the kinematic viscosity of the liquid, y is distance from the wall, and C is the 

 width of the film. (For the experiments being considered, C, the inside circumference of the 

 glass dome, is 15 cm.) 



Let the coordinate x represent distance measured in the flow direction, i.e., downward, 

 from the top of the film. Then if p{x, y) represents the excess concentration of dissolved gas 

 in the film, the equation describing the steady-state distribution resulting from convection in 

 the a!-direction and diffusion in the y-direction is^'' 



,fP_Z^^=0 [6] 



Here D is the diffusivity of the dissolved gas. 



The mixing efficiency r/' which would result if the exposure of the sample were restric- 

 ted to that which results from diffusion out of such a laminar* film of vertical height x is the 

 fraction of excess (or deficit) of dissolved gas which is removed as the film falls a distance 

 X. If the dissolved gas is assumed to be uniformly distributed at the top of the film, e.g., 

 p(0, y) - P(j, the fraction which has been removed in vertical distance x is then given by 



C ^ 

 ■q =1- — -fup(.x,y)dy [7] 



since the total rate at which the dissolved gas enters the top of the film is PqQ, and the rate 



.11 



•Experience has shown that laminar flow obtains if a Reynolds number 4Q/Cv is smaller than 1000. This 

 condition is well satisfied even for the highest flow rates employed in the present experiments. 



