The Tanks-in-Series Model and Nonlaminar Flow

This model is based on the view that the liquid flows through a series of ideally stirred tanks of equal size [3.1] or through a network of parallel ideally stirred tanks. The parameters of this model are N, the number of mixing stages (tanks) through which an element of fluid has passed, and T/, the mean residence time of the element of fluid in one mixing stage. For one tank the normalized C curve has the form 

For large N the curve approaches a Gaussian shape (Fig. 3.3), whereas for decreasii N the peak becomes increasingly skewed. The mean residence time T of the element of the trace material in the system is determined from individual residence times Ti by NTt, and coincides with the appearance of the maximum of the (N +, that is, the next) C curve at the exit. Provided that the C curve has a Gaussian shape (i.e., N 10), the variance of the C curve is 

An important feature of this model is that it formally covers the transition from mixed flow to plug flow, and, therefore, the C curves (Fig. 

The important feature of this approach is that it allows estimation of the intensity of radial mixing from the mixing length H, or more suitably, from the radial mass transfer constant a, which is the reciprocal value of the mean residence time of the individual tank, T,. It was Hungerford [3.4] who focused attention on this link between radial mass transfer rate and mixing length and thus reemphasized the importance of this parameter on the design of the FIA reactor. The radial mass transfer rate can be written as 

in formal analogy to chromatographic column, the FIA con ponent (e.g., reactor) with the highest a and N will yield the lowest alT 

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