Improrement of the efficiency of the mixing of fluids in three-dimensional flows by the use of chaos

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As an example of the static mixers that are typical mixing devices, a model of partitioned-pipe mixer (PPM) was considered which is composed of axially periodic pairs of plane plates of a definite angle within an infinitely long rotating cylinder. The following results were obtained by the examination of the chaotic motion of fluid elements and the efficiency of the mixing due to an approximate velocity field that is composed of the velocity field for an infinitely long plane plate and a transient velocity field: (1) The efficiency of the mixing can be improved by the generalization of the PPM model in which the ratio a of the lengths of a pair of plane plates can be changed from one, and the angle between these plates can be changed from 90 degree. (2) Poincare sections are not sufficient as the index of the efficiency of the mixing in a few. axial periods. Lines of separation U(n), the set of cross-sectional initial locations of fluid particles that move to one of the leading edges o … More f the plates within n periods, can be used as the index of the mixing in n periods. That is, if the region where U(n) is distributed densely is large, the efficient mixing is expected.Next, from the numerical computation of the exact velocity field in PPM, it was found that this velocity field has the reverse-flow region for a small axial pressure gradient and is considerably different from the approximate velocity field. From the Poincare sections based on the exact velocity field, the following results were obtained: (1) The regular region can be reduced by changing a to appropriate values, similarly to the result for the approximate velocity field. (2) U(n) can be introduced even for the exact velocity field. Efficient mixing is expected if the region where U(n) is distributed densely is large.From the computation of the largest stretching rate of fluid line elements in the cross-sectional direction in their axial motion by a definite period, it was found that the line elements starting near the lines of separation are strongly stretched and that this strong stretching mainly contributes to the efficient mixing in PPM. Less