Micromixers based on chaotic advection - Micromixers Fundamentals Design and Fabrication - page 214

Secondary transverse flow generated by slanted ridges on the channel wall can be used for
designing chaotic advection in microchannels. Stroock et al. [25,26] proposed a mixer design with
a pair of slated ridges called the staggered herringbone mixer (SHM; Figure 6.21 ). These structures
generate a pair of counter-rotating vortices. The flow pattern changes within a mixing unit; thus, both
rotational and extensional secondary flows are available in a mixing unit. Repeating these rotational
and extensional flows leads to chaotic advection. The mixing efficiency is determined by the asym-
metry of the herringbone structure p ¼W 1 / W and the number of ridges for a particular flow pattern. At
the optimal angle of 45 , the number of ridges determines the angular displacement per half cycle
DF half cycle . The flow in the mixing channel is not chaotic if p

0 .For p ¼ 2/3 1/2 and DF half cycle /

/

60 , chaotic advection occurs in the mixing channel. Figure 6.22 shows the typical
concentration distribution inside a staggered herringbone mixer. The counter-rotating vortices stretch
and fold the mixing liquids, reducing the striation thickness significantly.
A number of numerical works have been reported on the optimization of the mixers depicted in
Figs. 6.19 and 6.21 . Sch¨nfeld and Hardt [29] numerically investigated the helical flows of the mixer
shown in Fig. 6.19 . The strength of the vortices or the change of angular displacement is proportional
to the square of the relative height a of the ridge height as predicted with equation (6.9) . Furthermore,
the simulation results confirm that the flow pattern is almost independent of the Reynolds number.
Thus, the mixing concept based on slanted ridges on a channel wall can work with a wide range of
Reynolds number. The change of angular displacement almost doubles with ridges on both top and
bottom walls of the mixing channel. Hassel and Zimmerman [30] investigated the SHM design. Kang
and Kwon [31] used the so-called colored particle tracking method (CPTM) to investigate both the
helical design and the SHM design. The method first runs a flow analysis to obtain the periodic velocity

and DF half cycle >

FIGURE 6.21
Micromixer with staggered herringbone (SHB) structure.