Approximate mapping method for prediction of chaotic mixing in spatial-periodic microchannel

The use of approximate Poincaré maps for prediction of chaotic mixing in spatial-periodic channel is investigated in this article. The maps are constructed based on the corresponding distribution of discrete tracers on two successive Poincaré sections. Three methods are analysed including the triangular weighted interpolation, Shepard's method and weighted-least-square polynomial fitting (WLS-PF). Their application to a three-dimensional (3D) chaotic micromixer is demonstrated. Relevant results show that all the schemes can provide reliable predictions of the mixing quality within a limited number of mixer units. Among the three, the WLS-PF is less influenced by the grid-sizes. The mapping approach provides an alternative way to examine the performance of the spatial-periodic chaotic micromixer. It will greatly reduce the enormous efforts involved in 3D computational fluid dynamics (CFD) analysis.