Physics >4 



at which they move diminishes. Free diffusion might occur between two 

 volumes of gas where free diffusion was allowed to occur. This follows 

 the kinetic equation: N = Do (dP) 



AT (dL) . Thus the number of molecules that 

 will diffuse is related to the area, the time, and the diffusion coeffic- 

 ient which is characteristic somewhat of the system and the gas with re- 

 spect to the differential of pressures per unit length change. 



But in soils, we are not dealing with free diffusion, because diffusion 

 does not occur in soil as rapidly as it would in a f I'ee volume system . 

 This is due to the impedance by the pore system of the soil. So there 

 must be another factor introduced which is the diffusion coefficient of 

 the gas through the pore spaces. 



We say that the ratio of the diffusion coefficient in a porous medium to 

 the diffusion coefficient in a free diffusion system is some ftinction of 

 the porosity of the system expressed as D_ = f (S) . 



Do 



Curiously enough, this sort of derivation was worked out aroiind 190U by 

 Buckingham when he was working for the Bureau of Soils at that time. Not 

 a great deal was done concerning diffusion of gases until some time in 

 the 19U0'3. I am sure that Great Britains are familiar with the work of 

 Penman during the early 'UO's, in which he re-evaluated some of the earli- 

 er work of Buckingham. Since that time, other work has been done in the 

 last ten years or so, more or less confirming some of the same facts that 

 Penman discovered in England. 



This term "porosity" is, I think, the actual volume that is occupied by 

 gas. If one takes volume occupied by gas divided by the volume of the 

 soil that is occupied by the solid material, plus the volvane that is 

 occupied by water, plus the volume that is occupied by gas,-- all of which, 

 of course, is the total soil volume that give the percentage porosity in 



that system (S = Vg ) 



( Vg + Vw + Vs). There is fairly general agreement that 

 this ratio of D_ = .663. D_ 



Do Do again is the rate of diffusion through the 

 porous medium with respect to the rate of diffusion in a free volume and 

 is somewhat in relation to the distance through which the diffusion 

 occurs. For example, gas in a free volume might diffuse twice the dis- 

 tance in the time required for gas to diffuse a certain distance in a 

 porous system. 



There are other factors, of course, than the porosity of the soil that 

 will affect this rate of diffusion. Not only is the size of pores, 

 wliich is really some function of the area through which the gases must 

 diffuse, but also the much lengthened path that the gases must follow 

 because of the irregular shapes of the soil pore system. Also, for very 

 fine pores, there seems to be an interrelation between the impact of the 

 molecule against the wall of that pore and with the other molecules in 

 the gas system. 



