ON THE CONCENTRATION OF A SOLUTE. DAVIS. 



293 



Where T = time. 



c = concentration of solute, 



x = distance from any fixed plane perpendicular 

 to the direction of flow. 



D = a constant for that particular solvent and solute. 



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

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



To get this problem 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 to end so that the end of greatest 

 concentration in one meets the end of greatest concentration 

 in the other (Fig. 2). 



tr, 



Diffusion begins and the solute in the tube M N flows in the 

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

 concentration at the plane M P therefore decreases and that at 

 n Q increases. But since there is no gradient at the plane 

 P M or at the plane n Q, so solute can pass through them, 

 which is the condition required in our problem. 



Now, since the concentration in M n obeys Fourier's linear 

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

 P M, and of the time T , and may be expanded in a Fourier's 

 series, but since 3> (x) = & ( #) only cosine terms enter. 



