Biomedical Engineering Reference
In-Depth Information
allow the evaluation of mixing in the microchannel. The extent of mixing is measured numerically by
the folding quality:
L
L
0
f
¼
1
(7.20)
where
L
is the length of material lines in a segment with a dimension of d
x
d
y
. The reference length
4d
y
p
.
Figure 7.4
shows the contour plot of folding quality
f
, which is
calculated numerically. Generally, stretching and folding and subsequently good mixing are achieved
with
d
x
2
is determined as
L
0
¼
þ
a
. That means, low-frequency with a large velocity magnitude will allow good mixing in this
type of micromixer. However, there are areas of poor mixing called “spatiotemporal resonance” as
depicted in
Fig. 7.4 [6]
. The solid lines in
Fig. 7.4
are the resonance lines described by the following
relation between
a
and
U >
U
:
s
15
16
1
C
2
U
C
2
a
¼
U
;
(7.21)
2
p
ð
n
þ
1
=
2
Þ
where
n
are positive integer and
C
1.239.
z
FIGURE 7.4
Contour plot of mixing extend expressed as folding quality
f.
The solid curves are the resonance lines according to
(7.21).
(Reprinted with permission
[5]
.)
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