Single-particle approach for analyzing flow systems. Part II: Regional residence times and local flow rates



The analysis of Part I (Rubinovitch and Mann, 1983) is continued here, considering the movements of a single particle in an arbitrary flow system in terms of the total times it resides in various flow regions. Results from the theory of Markov chains are used to derive expressions for the joint distribution of number of visits and total residence time in a flow region and for the total regional residence time distribution. Further, the relationships between the local particle flow rate, number of visits to a flow region, and net flow rate through the system are derived. Specifically, it is shown that

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This relation is valid for any general flow system and any general region in the system. It holds true irrespective of the number of inlets and outlets to the region or of the nature of the internal mixing in the region. It is further shown how this relation leads to an experimental method for measuring local flow rates.