Permeation as a function of time

During the continuous operation, the toluene concentration In the heptane Increases and It becomes desirable to predict the concentration of toluene In the tank. A material-balance around the system predicts the toluene concentration In the process tank or the permeate as a function of time, t, membrane rejection, R, toluene concentration In feed, Cf, processing rate, Qp, and tank volume, V. 

Figure 4 compares the toluene concentrations In the feed and permeate as a function of time for the second continuous run. The slower rate of increase in the toluene concentration In the permeate is reflected by the 8% Increase in toluene concentration in the process tank. Again, as was seen In run 1, the data scatter In Figure 4 is more obvious In the feed analysis when compared to the permeate analysis. 

Measurement of the rate of permeation as a function of time as the system approaches equilibrium enables Pick s second law of diffusion to be solved for the boundary conditions of the experiment. Provided that the diffusion coefficient is independent of the concentration of diffusing species in the membrane, and as t oo, the result is ... 

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