Intensity of Segregation versus Time in a Semi-Continuous Reactor

Consider a semi-continuous reactor fed with and (the inlet flow rates of species and ). Initially, the content of the reactor and the feed are completely segregated; , where is the segregation intensity, which varies from zero (perfect mixing) to unity (no mixing).
If the inlet flows are constant and the reactor is initially empty, the volume of the reactant in the reactor, , varies from zero to (total reactor volume).
We have and , where is the residence time of the reactor and is the total flow to the reactor.
Before the reactor gets full (i.e., for ), the segregation intensity obeys the following ODE:
, where is the mixing time.
When the reactor is full and overflowing (i.e., for or ), the segregation intensity is the solution to the following ODE:
This Demonstration plots versus time for values of the mixing time and residence time to be fixed by the user. The red portion of the curve corresponds to for while the blue section of the curve gives for .


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J. Ingham, I. J. Dunn, E. Heinzle, and J. E. Prenosil, Chemical Engineering Dynamics, 2nd ed., Weinheim, Germany: Wiley-VCH, 2000 pp. 444–449.
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