There is a substantial body of literature dealing with description of the mass transfer in FIA systems. Since the first attempt to lay ground to theory of FIA (Ruzicka and Hansen 1978 and 1988) to most recent reviews (Kolev 2008 and Inon and Tudino 2008) 30 years have passed, but not much progress has been made in this field, partially because of the complexity of the issue, and due to discrepancy between the focus  of theoretical considerations. and the ways in which real life FI and SI system operate. The examples this dichotomy is the lack of theory treatment on the process  dispersion at confluence point, description of dispersion at accelerated or reversed flow, and failure of theoretical guidance to identify the tools for breaking laminar flow at low Reynolds number values, typical for FI and SI systems.

Yet despite a slow progress, there are elements of theory of flow that are valuable for understanding why and how FI and SI systems work. Due to the limited framework of this Tutorial we shall consider only few relevant aspects of the deterministic models, such as dispersion model and tank-in-series model, and for optimization purposes we will briefly review the principles of impulse-response (“black box”) model.

Also in order to simplify discussion we will only consider physical mass transfer phenomena in circular pipes and compare them with experiments using tracer dye technique.