204 



mixing. As long as no perfect equilibrium has set in, two layers 

 will continue to exist and the formation of the equilibrium will 

 take place, the solid substance S difïusing fi-om the more concen- 

 trated layer into the other one. 



In this sense each lixixiation process is a diffusion pi-ocess. 



We assume that the quantity of weight of the substance >S', which 

 in a short time unit dt, diffuses from the volume v into the volume 

 V can be represented in the following manner : 



ds =^ KO (h—a) dt (4) 



wherein K represents the quantity of the substance S which diffuses 

 in the time unit per unit of surface and per unit of (constant) con- 

 centration difference ; represents the surface of the dividing layer 

 between the two volumes of liquid, b — a represents the (during 

 the time dt, constant) difference in concentration M. 



We now distinguish the following three cases : 



I. Discontinuous lixiviation according to the counter-current })rin- 

 ciple with a limited number of volumes which, in regard to the 

 concentra-tion are homogeneous. 



II. Semi-continuous lixiviation according to the counter-current 

 principle with a limited number of volumes which, with regard to the 

 concentration are homogeneous. 



III. Continuous lixiviation according to the counter-current principle 

 with a very large number of layers homogeneous with regard to the 

 concentration. 



1. Discontinuous Uxiviation according to the counter-current principle. 



We have already detailed above this method of woriiing p. 202). 

 Only, this time the filtration is not postponed until the equilibrium 

 has set in. 



Let us consider the changes in concentration in one element during 

 the finite period of lixiviation. 



In. the first element we have before the diffusion the concentrations 

 [\ and a^, afterwards b^ and a^. This again gives rise to the equation: 



0^ + xa^ == h^ -4-- xa^ . (3) 



We can now find another relation between the same quantities 

 if we ascertain how the initial and final condition are converted 

 into each other during the diffusion time A^. 



The amount of the substance >S which in a small unit of time 

 dt passes from the one layer into the other, may be expressed in 

 three ways: 



1) Gf. note 2 p. 201. 



