Micromixers based on molecular diffusion - Micromixers Fundamentals Design and Fabrication - page 181

FIGURE 5.15

The dimensionless velocity profile ( h ¼ 0.1, k ¼ 1): (a) b ¼ 1/1.8 and (b) b ¼ 1.8.

outlet. Two inlets are used for the sheath flows. The middle two inlets are used for sequential
segmentation. The solvent and the solute are switched alternately so that segments of them are formed
in the focused stream. The final mixing ratio is determined by both, the focusing ratio of the inlet flows
and the switching ratio of the two focused flows.
The analytical model assumes a rectangular microchannel with width W and height H . For
a microchannel with low aspect ratio ( W H ), the flow inside the microchannel is similar to that

between two parallel plates. The model assumes a uniform velocity profile in the transversal direction
( y -axis) and a pressure-driven velocity profile in the channel height ( z -axis):
uðzÞ¼ 6 u 1

[

z
H

z
H

(5.46)

where u is the mean velocity in the flow direction along the x -axis, as shown in Fig. 5.16 (a). The
parabolic velocity profile causes the so-called Taylor-Aris dispersion, which can be described by an
effective diffusion coefficient D *. According to Section 2.3, the effective diffusion coefficient in the
axial direction can be determined as

H 2 U 2
210 D

D *

¼ D þ (5.47)