... an ideal TFR doesn't exist and at this point the discussion could be stopped, otherwise it gets philosophic.
But let us exceptionally be philosophic for controlling the consistency of our definitions !
An ideal TFR exhibits the macro-mixing property of 'totally not-back-mixing' (i.e. no axial dispersion). The fluid 'drops out of the reactor outlet in differential discs'. This is the same as the micro-mixing behaviour of segregation. But what, if you collect the fluid, - is it segregated ? No, it is like it was before! Segregation occurs only along the length of an ideal TFR, - but fictitious and not in reality! Suppose that we have a TFR with a slight axial dispersion. In this case we will realize the difference between a segregated and a not segregated fluid in the same way as for the CSTR (REM: we could model this reactor with a series of CSTRs). This reactor cannot produce a segregated fluid from the input of a molecular dispersed fluid.
Of course you could state that the area-method is valid for an ideal TFR, - but this holds only true because the (fictitious) macro-mixing behaviour (contacting pattern) of an ideal TFR exhibits (fictitious) segregation. And indeed you can apply the area-method to the RTD of an ideal TFR without error, - you should try that some time. What are you doing in that case ? (think of the STR as 'brother' of the TFR !!) What are you doing ?
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