ON THE CONCENTRATION' OF A SOLUTE. DAVIS. 



298 



Where T =^ time. 



c =: concent i-ation of solute, 



.T = distance from any fixed ])lane perpendicular 

 to the direction of flow. 



D ^ a constant for that ])artieular solvent and solute. 



Assuming this, the other condition Ave have is that no solute 

 passes through the limiting layers A X or B M (Fig. 1). 



To get this ]iroblem into a form suitable for mathematical 

 analysis let us" imagine that we have an infinite number of 

 tubes of solution such as in (Fig, 1) of length I, and with a 

 concentration gradient as in final equilibrium. Suppose now 

 we place these together end ti) end so that the end of greatest 

 concentration in one nieet^, the end of greatest concentration 

 in the other (Fig. 2). 



h7 Ai 



Diffusion begins and the solute in tlic \\\W M X flows iu tin- 

 direction of the gradient and similarly in the nther tubes. The 

 concentration at the plane M P therefore decreases and that at 

 n Q increases. But since there ?.s no (jradieiif at the plane 

 F M or at the plane n Q, so sohile can ))((ss l/iroiir/h tJiein. 

 which is the condition required in our j)roblt'm. 



jSTow, since the concentration in M n obey.s Fourier's linear 

 diffusion law. it is a function of the distance x from the plane 

 P ]\r, and of the tinu* T , and may be expanded in a Fourier's 

 series, but since 4> (x) = 4> ( — x) only cosine terms enter. 



