Micromixers based on chaotic advection - Micromixers Fundamentals Design and Fabrication - page 195

categorized by their operation range of Reynolds numbers. A range of Re > 100 is considered in this

section as high. The range of 10 10 is regarded as low.

In the following, only micromixers based on passive chaotic advection are discussed.

< Re < 100 is intermediate. The range of Re <

6.1 CHAOTIC ADVECTION AT HIGH REYNOLDS NUMBERS
6.1.1 T-mixer at high Reynolds numbers
As described in Section 2.8, the Peclet number is about three orders higher than the Reynolds number.
Thus, at Reynolds number higher than unity, convection in the flow direction is more dominant than
transversal diffusion. A simple T-mixer cannot be used for mixing at high Reynolds number.
Duetothesharp90 turn at the entrance, the inertial force is large enough to cause vortices,
which in turn lead to chaotic advection. In general, the laminar regime in a T-mixer consists of three
subregimes: stratified, vortex, and engulfment [2,3] . In the stratified subregime (Re 50), the two

inlet streams flow side by side. Transversal transport only occurs through molecular diffusion. Mass
transport in this subregime has been analyzed in details in Chapter 5. In the vortex regime
(50

<

150), Dean vortices appear, but they are symmetrical across the interface between the
two streams. In the engulfment regime Re

< Re <

150, the vortices become asymmetric and real chaotic
advection occurs. This regime is useful for mixing application. At a Reynolds number of over 400,
the flow becomes unsteady and the flow moves from the transition regime to turbulence. Experi-
mental results based on hot-film measurement indicated turbulent flow at Reynolds numbers beyond
1000 [4] .
Figures 6.1 and 6.2 show the numerically simulated trajectory of liquid flow at the entrance of
T-mixer [2] . At Reynolds numbers on the order of unity, the flow is stable but fast enough to
dominate over molecular diffusion ( Fig. 6.1 (a)). At high Reynolds number (50

>

150), the
trajectories clearly show the existence of vortices due to secondary flow caused by centrifugal force
at the 90 turn of the entrance. The two inlets correspond to two Dean flows (see Section 2.4.2.2).
Each Dean flow has a pair of counter-rotating vortices (Fig. 2.18). However, as shown in
Fig. 6.1 (b), the vortices are symmetric; thus, the solute and the solvent still remain in their
particular half. No mixing occurs at Re ¼ 119 ( Fig. 6.1 (b)). Increasing the Reynolds number further
destroys the symmetry of the vortices ( Fig. 6.1 (c)). The inertial force is strong enough to make fluid
streams to cross the two halves of the mixing channel. Figure 6.3 shows the three-dimensional
concentration distribution measured with confocal microlaser-induced fluorescence (

< Re <

-LIF). The
fact that the confocal measurement is slow proves that the flow and the concentration distribution
are time independent. Thus, the transport process at a high Reynolds number (Re

m

100) is chaotic
advection but not turbulence. Stretching and folding are clearly visible at high Reynolds numbers
( Fig. 6.2 ). The increased interfacial area and the smaller striation thickness lead to improved
mixing. Figure 6.4 shows the mixing regions and boundary layers of the engulfment subregime.
These regions are clearly observed with numerical simulation and measurement [2,3] . The 90
turns cause the two streams to separate and follow a curved path. The separation of boundary layers
leads to the formation of vortices at the top of the junction where the two streams collide. The
vortices cause mixing of the two fluids. Dean vortices occur at the curved paths of the 90 turns.
The secondary flows in the curved path sweep the fluids in the partially mixed region at the top of

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