Micromixers based on chaotic advection - Micromixers Fundamentals Design and Fabrication - page 201

(a)

(c)

(b)

FIGURE 6.7

Dean vortices at different Dean numbers: (a) the basic channel configuration; (b) secondary flow pattern at a low
Dean number (De < 150); and (c) secondary flow pattern at a high Dean number (De > 150).

the mixing concept, a relatively large channel with 1 mm 2 cross-section was used. The large channel
allows the realization of Dean numbers ranging from 35 to 351 or Reynolds numbers ranging from 78
to 785 at a reasonable driving pressure provided by a syringe pump. Experimental results show that
mixing time is inversely proportional to the Dean number. The slope clearly changes at the critical
Dean number of around 140, indicating the change in secondary flow pattern ( Fig. 6.7 ).
Sharp turns or meandering mixing channels can also induce spatially periodic flows at high
Reynolds numbers ( Fig. 6.8 (b)). Mengeaud et al. [10] used the ratio between the spatial period s and
the channel width w as the optimization parameter. The periodic turns cause chaotic advection. A two-
dimensional model predicts chaotic advection at Reynolds number above 80. For a given Reynolds
number, an optimal ratio exists between the spatial period and the channel width. Both small and large
ratios make the mixing channel approach the asymptotic case of a straight channel. For instance,
numerical results show an optimum value of 4 at Re ¼ 267. However, the results of Mengeaud et al.
[10] only consider a two-dimensional model and cannot capture the effect of Dean vortices. The
micromixers were made of polyethylene terephthalate (PET). Microchannels with a width of 100 m m,