Chaotic mixing in a planar, curved channel using periodic slip

We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal forces, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. This is used to find the Lagrangian trajectories of fluid particles. Poincare sections taken at periodic locations in the axial direction are used to study the extent of chaos. We study two microchannel designs, called circlet and serpentine, in which the Dean vortices in adjacent half cells are co-rotating and counter-rotating, respectively. The extent of mixing, at low Re and low slip length, is shown to be greater in the serpentine case. Wide channels are observed to have much better mixing than tall channels; an important observation not made for separatrix flows till now. Eulerian indicators are used to gauge the extent of mixing, with varying slip length, and it is shown that an optimum slip length exists which maximizes the mixing in a particular geometry. Once the parameter space of relatively high mixing is identified, detailed variance computations are carried out to identify the detailed features.