436 



current density of the cliffiisiFig gaf», i.e. the quantity which diffuses 

 per unit of time through the unit of crosssection against the current: 



If a mixture of two gases which at ^v = have the densities q„ 

 and q\ diffuses, the ratio of the quantities of the two gases which 

 diffuse per unit of time against the current is equal to: 



This quantity represents, therefore, the degree of unmixing reached 

 in such a diffusion process; inversely the product vl is determ- 

 ined by the diffusion constants of the gases that are to be 

 separated, and by the degree of unmixing required. In order to 

 make the efficiency also as large as possible, v should be chosen 

 as large as possible and in accordance with this / small, as follows 

 from the equation of the current density. 



The second case, which in practice has been realized, is the 

 following one: let again v be the constant velocity of the flowing 

 gas, and let the direction of the current be that of the negative 

 a;-axi8. At a certain point in this current we now admit the other 

 gas. This gas will then be carried along with the current, and 

 at the same time be scattered to all sides by diffusion. In this 

 case the distribution of the diffusing gas is found by integration of 

 the differential equation : 



A^ = — — — 

 o Ox 



with the limiting condition that at infinity the density of the diffusing 

 gas must be zero. When the point where the gas enters the current, 

 is chosen as origin of the system of coordinates, and the radius 

 vector is called r, we find the solution: 



r 



(J 

 in which (7 is a constant. The factor — represents diffusion in the 



medium at rest, the exponential function which is due to the 



current, is of the same nature as in the first case; only instead of 



r -\- X 

 r. we have here — - — . If, therefore, a gas mixture is introduced 



into the current, unmixing- takes place in this case as well. Further 



