Process of Mass Transfer through a Membrane

According to the principle of the transfer of matter through a membrane, the substance diffuses through the thickness of the sheet from one side to the other, while a concentration of matter is maintained on both sides. 

The one-dimensional diffusion of the diffusing substance is expressed by Equation (6.5)  

With the initial conditions expressing that the membrane is initially free from substance  

Equation (6.21) shows that the concentration of the diffusing substance in the membrane increases with time, and the profiles of this substance tend to be linear when the series vanishes, theoretically after infinite time. 

In the same way, from Equation (6.20), the amount of substance emerging from the side of the membrane kept at the lower concentration increases with time as the series in Equation (6.20) vanishes. Thus after a given period of time (infinite time, mathematically speaking) the kinetics of substance leaving the membrane tends to become linear, and the expression of the asymptote is given by  

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