Efficient spatial-temporal chaotic mixing in microchannels

A chaotic micro mixer with multiple side channels is designed and investigated, in which fluid can be stirred by pumps through the side channels. By stretching and folding fluid in the main and side channels, chaotic mixing can be achieved. A simple mathematic model is derived to understand the movement of particles in the microchannel. Spatial trajectories of fluid particles are projected to Poincare sections by mapping. The route from the quasi-period to chaos is revealed to be destruction of KAM curves and shrinkage of the quasi-periodic areas. Lyapunov exponents (LE) are used as the mixing index and the criteria to evaluate the chaotic behavior of the system. We found that LE is closely related to the amplitude and frequency of stirring and can be used to optimize our design and operation. From the relationship of LE and striation thickness, the minimal mixing length required can be estimated, which is much shorter than that needed in passive mixer design.