where C is the maximum local concentration and Cm is the mean concentration of tracer at complete mixing.

A more comprehensive way of analyzing mixing, applicable to continuous systems, is a study of the residence time distribution (RTD). Although ALRs are usually operated in a batch-wise manner, at least in the laboratory, advantage is taken of the fact that the liquid circulates on a definite path to characterize the mixing in the reactor. Hence, a single-pass RTD through the whole reactor or through a specific section is usually measured. Based on the observed RTD, several models have been proposed. These models have the advantage of reducing the information of the RTD to a small number of parameters, which can later be used in design and scale-up.

The axial dispersion model, which has the advantage of having a single parameter, is widely accepted for the representation of tower reactors. This model is based on visualization of the mixing process in the tower reactor as a random, diffusion-like eddy movement superimposed on a plug flow. The axial dispersion coefficient Dz is the only parameter in the formulation:

where C is the concentration of a tracer. The boundary conditions depend on the specific type of tower reactor. This model is attractive, since it has a single parameter, the Bodenstein number (Bo), which is used to describe the mixing in the reactor:

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