Assumption of ideal mixing. Residence time

In the theory of continuous stirred-tank reactors, an important basic assumption is that the contents of each tank are well-mixed. This means that the compositions 

In the treatment which follows, it will be assumed that the mass density of the reaction mixture is constant throughout a series of stirred tanks. Thus, if the volumetric feed rate is v, then in the steady state, the rate of outflow from each tank will also be v. Material balances may then be written on a volume basis, and this considerably simplifies the treatment. In practice, the constancy of the density of the mixture is a reasonable assumption for liquids, and any correction which may need to be applied is likely to be small. 

The mean residence time for a continuous stirred-tank reactor of volume Vc may be defined as Vc/v in just the same way as for a tubular reactor. However, in a homogeneous reaction mixture, it is not possible to identify particular elements of fluid as having any particular residence time, because there is complete mixing on a molecular scale. If the feed consists of a suspension of particles, it may be shown that, although there is a distribution of residence times among the individual particles, the mean residence time does correspond to Vc v if the system is ideally mixed. 

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