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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