Physics. ''On the Separation of Gas Mixtures by Dijfusion in a 

 Floiuinij Gas'. By Dr. G. Hkrtz. (Communicated by Prof. 

 P. Ehrenfest.) 



(Communicated at the meeting of November 25, 1922). 



As is well known, the differential equation: Ap = 0, in wliicli q 

 represents the density of the diffusing gas, is valid for stationary 

 phenomena of diffusion in media at rest. This equation does not 

 contain the constant of diffusion of the diffusing gas at all. If, 

 therefore, the diffusion of a gas mixture is considered, the ratio of 

 the partial pressures of the components of the mixture is constant 

 throughout the space, i.e. unmixing does not occur with such a 

 stationary diffusion phenomenon. This however, is different, as will 

 be shown in what follows, with stationary phenomena of diffusion 

 in a moving medium. As such a moving medium we take a flowing- 

 gas. Let the velocity of this gas medium be \\ and let it satisfy the 

 condition cliv'o^^O. The constant of diffusion of the diffusing gas 

 under definite circumstances be (i, its density q, which for the cal- 

 culation we shall assume to be small compared with the density of 

 the gas mediuni. The quantity of the diffusing gas passing through 

 the unit surface in the unit of time hence its current density, is equal 

 to the sum of the diffusion and the convection current; it is: 



i = — Ö grad q -\- q v> 



For stationary phenomena div i = 0, so that taking into account 

 that div v> = 0, we get the following differential equation for such 

 phenomena : 



L q z=z ^ {Xi , grad q) 

 o 



In contrast with the equation L q =:0 holding for a medium at 

 rest, this equation contains the constant of diffusion ö. Accordingly 

 the distribution of the density in space is here dependent upon the 

 constant of diffusion. If, therefore, a gas mixture is made to diffuse 

 in a stationary medium the ratio of the partial pressures is constant. 

 On the other hand this ratio is variable in a moving medium; and 

 this brings about the possibility to use this phenomenon for the 

 separation of gas mixtures. 



