Enchancing radial mixing in microchannel processing of two phase flows for is important so that this feature can be exploited to simplify the design of heterogeneous reaction schemes in microchannel processing. The asymptotic analysis here extends the concept of the Thiele modulus to be the controlling variable in non-uniform systems. We argue that a generalization of a Thiele modulus is the ratio of the time scale for the limiting transport step to the time scale for surface reaction. If the intrinsic kinetics are fast and the reaction nearly irreversible, the latter is actually controlled by mass transfer to the reacting phase. Our analysis methodology naturally identifies the Thiele moduli and reduces the order of the system so that analytic, closed form estimates of the reaction dynamics are found. For parametric optimization, such a form is a good guide. The applicability of this general methodology is argued for microchannel processing and supported by several published studies and experiments.

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