Micromixers based on molecular diffusion - Micromixers Fundamentals Design and Fabrication - page 172

advection. Forced splitting and lamination are achieved at low Reynolds number with a complex
channel design. Chaotic advection occurs at a higher Reynolds number and will be discussed later in
Chapter 6. The implementation of the concept depicted in Fig. 5.8 is referred to as sequential lami-
nation with vertical lamination and horizontal splitting. Similar transformations can be achieved with
horizontal lamination and vertical splitting. This mixing concept requires relatively complicated three-
dimensional fluidic structures. According to (2.201) and (2.202), the sequential concept results in
much faster mixing compared to the parallel concept with the same device area. Due to their complex
geometry, most of the reported sequential lamination mixers were fabricated in silicon, using bulk
micromachining technologies, such as wet etching in KOH [24,25] or deep reactive ion etching
(DRIE) technique [26] . Polymeric micromachining is another alternative for making sequential
lamination micromixers. Lamination of multiple polymer layers also enables making complex three-
dimensional channel structures. Schoenfeld et al. [21] realize this mixing concept on PMMA. He et al.
extended the concept of sequential lamination to electrokinetic flows [27] .

5.3 SEQUENTIAL SEGMENTATION
Sequential segmentation is a process where the solvent and the solute streams are broken up into segments
along the axial direction. Because mixing occurs in the axial direction, the axial dispersion may lead to
faster mixing. According to Section 2.3, the axial dispersion coefficient may be of several orders of
magnitudes higher than pure molecular diffusion. Sequential segmentation is implemented by alternate
switching of the inlet flows ( Fig. 5.9 (a)) [28] . Switching is realized by two inlet valves or by controlling
the pumps of the mixing liquids . The mixing ratio can be adjusted by the switching ratio ( Fig. 5.9 (b)).
With a mean flow velocity u of both fluids in the m ixing channel and a switching period T , the
characteristic mixing length is the segment length L

¼ uT ( Fig. 5.10 ). The transport Eqn (2.22) can be

reduced to the transient one-dimensional form [29] :

vx ¼ D * v 2 c

vc

vt þ u vc

(5.16)

vx 2

where D * is the dispersion coefficient (see Section 2.3). The periodic boundary condition at the inlet
( x ¼ 0) (Fig. 5.9 (b)) is

FIGURE 5.9

Sequential segmentation: (a) alternate switching of the inlet streams and (b) switching ratio a determining the
mixing ratio.