Micromixers based on chaotic advection - Micromixers Fundamentals Design and Fabrication - page 200

mixing channel. The design reported by Wong et al. [5] has a cross-section of 30 m m 30 m m. The

obstacles are square protrusions of 10 m on the channel walls. At a Reynolds number on the order of

200, improved mixing can be achieved right after the obstacles. Results from numerical simulations
show that increasing the number of obstacles and placing them at the entrance further improve the
mixing performance. Such a mixer would require a pressure of about 2 bars to reach Reynolds numbers
of 200 or higher.
Wang et al. numerically investigated the role of cylindrical pillars in a mixing channel, as depicted
in Fig. 6.6 (b), at high Reynolds numbers [7] . The results showed that these obstacles can improve
mixing at high Reynolds numbers. The obstacles and inertial forces alter the flow directions and create
transversal mass transport. In general, the more obstacles in the channel, the better is the mixing effect.
However, placing the obstacle groups asymmetrically along the mixing channel results in better
mixing than having a large number of obstacles.
Lin et al. [8] used cylinders placed in a narrow channel to enhance mixing ( Fig. 6.6 (b)). The
micromixer was fabricated in silicon. Seven cylinders of 10

m

m m diameter were arranged in

a50 100 100 m mixing chamber. The micromixer was fabricated using standard photolitho-

graphic techniques. The cylinders are etched in the same process with the mixing channel. The device
was subsequently bonded to a glass wafer for sealing and enabling optical access. The two liquids flow
through the 50

m

m

m-wide microchannel before entering the mixing chamber. The micromixers work
with a Reynolds number ranging from 200 to 2000. At a flow velocity on the order of 20 m/s, vortices
caused by the obstacles ensure efficient mixing at these high Reynolds numbers.

6.1.3 Dean flow with repeated turns in mixing channel
As mentioned in Section 5.1.1.1, Dean vortices at the 90 turn on a T-mixer are responsible for chaotic
advection at a high Reynolds number. Thus, repeating the turns would allow the effect of Dean flow to
intensify. Figure 6.7 shows the basic concept of Dean vortex in a circular channel with a rectangular
cross-section. At Dean numbers above the critical number of 150 [9] , two vortex pairs appear. We can
use this critical Dean number to estimate the required Reynolds number for a micromixer based on
Dean flow. The definition equation of the Dean number (2.110) leads to
Re cr ¼ De cr

p

R=D h (6.1)

where R is the radius of curvature and D h is the hydraulic diameter. Thus, for the best case scenario of
R ¼D h the critical Reynolds number is Re cr ¼ De cr ¼ 150. For most cases, the working range of planar
micromixers based on Dean flow is Re 150.

Although the closed circular channel as depicted in Fig. 6.7 can be realized with pumping concept
based on magnetohydrodynamics, as discussed later in Section 6.6, it is not realistic for pressure-
driven flow. However, Dean vortices can be achieved in a planar microchannel by repeating the curved
sections as depicted in Fig. 6.8 [9] . The alternate signs of radius of curvature make the two vortices at
low Dean numbers ( Fig. 6.7 (a)). This effect causes folding of fluid interfaces, but not enough for
efficient mixing. At a high Dean number above the critical value of 150, a second vortex pair appears.
These smaller vortices sweep from one side to another, making the secondary flow asymmetric. This
flow pattern at high Dean numbers makes chaotic advection in the micromixer possible. The mixer
reported by Jiang et al. [9] was machined in a PMMA substrate. The mixing channel was sealed by
solvent bonding to a PMMA layer. Because large Reynolds number and Dean number are required for

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