435 



III what follows hvo special cases will be treated, which it has 

 been possible to realize experimentally, and which can be used for 

 the separation of gas mixtures. In both cases a gas medium flowing 

 with a constant velocity v is used, the direction of which will be 

 chosen as direction of the negative .I'-axis. For this case the differ- 

 ential equation is: 



o ox 



When we assume q=zq^ for .i'=:0, and q =zO for .r=oo, we 

 get as a first example the case of diffusion against the gas current. 

 The solution is easily seen to be: 



vx 



The density of the gas diffusing against the current decreases, 

 therefore, according to an exponential function, the gradient of which 

 depends on the ratio of the current velocity to the diffusion constant. 

 When now a mixture of two gases whose partial pressures for .r=:0 

 are (>„ resp. q\ diffuses against the current, the following equation 

 is found for the ratio of their partial pressures as function of the 

 place : 



^ -^'Kt-T') 



e 

 Q ^0 



This distribution agrees in form with the distribution of the partial 

 pressures in the field of gravitation determined by the barometer 



V 



formula, with the exception only that here the quantity - takes the 



Ö 



place of the specific gravity, and the whole pressure gradient can 

 be brought about at a distance of the order of a millimeter. 



If this phenomenon is to be used for the separation of a mixture, 

 the gas present at a certain place, e.g. at .i: = I, must be pumped 

 off. The limiting conditions then become q =z q^ for .v := and 

 ^ = for iv =z I. The solution then becomes: 



Q 



J' vx vl ^ 



in which 6' is a constant. If, as in practice, e s is small compared 

 with 1, (J is approximatiely equal to o^. We thus find for the 



1) Compare S. Holst Weber, Handelingen van het 17e Nederlandsch Natuur- 

 en Geneeskundig Congres, Leiden 1919. 



