Chaotic mixing due to a spatially periodic three-dimensional flow

Abstract

The chaotic mixing of a fluid due to a slow flow in a spatially periodic system called the partitioned-pipe mixer is studied. This system, originally composed of alternate horizontal and vertical plates of the same length in a duct, is generalized so that both the ratio a of the lengths of these plates and the angle ϕ between neighboring plates can be changed. Using the Poincaré plots of the locations of fluid particles after every period, we find that the mixing performance in many periods can be improved to a considerable extent by choosing appropriate values of a and ϕ. Furthermore, it is shown that the mixing performance in a few periods can be estimated from the distribution of the lines of separation, defined as the set of cross-sectional initial locations of fluid particles which move to one of the leading edges of the plates within a specified period. Using this distribution, we find that this mixing performance also can be improved by the above generalization.