Motionless mixers are modeled as open, circular tubes with parabolic velocity distributions except at a few isolated planes where radial mixing occurs via an instantaneous coordinate transformation. Possible transformations are constrained by continuity of volumetric flow. Complete flow inversion appears the theoretically optimal transformation, being superior to complete mixing. A model consisting of intermediate planes of complete mixing approximates existing experimental data on the Kenics Static Mixer when four Kenics elements are made equivalent to a single plane of complete mixing. This model preserves the essential nature of a laminar flow residence time distribution while providing a relatively simple means of estimating mixer performance.
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E. Bruce Nauman (1982) studied this question.