Biomedical Engineering Reference
In-Depth Information
For time-dependent concentration fields of active micromixers, a single image has little infor-
mation about the mixing performance. The extent of the disturbance can be evaluated by averaging
a large number
N
of image frames
[3]
:
N
P
þ
1
I
i
ð
x
;
y
Þ
i ¼
1
I
ð
x
;
y
Þ¼
(8.41)
N
where
I
i
(
x
,
y
) is the intensity matrix of each image, which is equivalent to the concentration field. The
extent of disturbed concentration is indicated by the dispersion of the averaged field. To evaluate the
energy content of the disturbance, the mean square perturbation field can be used
[3]
:
P
Nþ
1
2
1
½
Þ
I
i
ð
x
;
y
Þ
I
ð
x
;
y
2
i
¼
I
0
ð
x
;
y
Þ
¼
:
(8.42)
N
Figure 8.13
shows a typical time-dependent concentration field. The images were recorded from the
micromixer based on viscoelastic instability depicted in Fig. 5.7(b) (Section 5.1.2). The white lines
indicate the channel wall. The time-averaged concentration field depicted in
Fig. 8.14
(a) is evaluated
from 20 images. The result shows the extent of instability by the gray area around the middle stream.
Imaging the concentration field with a long exposure time results in the same image shown in
Fig. 8.14
(a). The mean square perturbation field depicted in
Fig. 8.14
(b) represents the perturbation energy of
the instability. The results show that a large area between the side streams and the middle stream is
highly perturbed. The maximum perturbation can be seen just before the constriction.
8.3.2
Indirect methods
Indirect methods measure the extent of mixing based on the products of chemical reactions or the
change of fluorescent intensity due to the change of pH level in the mixed fluids.
Parallel competing reactions can be used for evaluating mixing efficiency. For instance, when
a mixture of iodate, iodine, sodium hydroxide, and boric acid is mixed with sulfuric acid, the so-called
Dushman reaction occurs
[4]
:
H
2
BO
3
þ
H
þ
#
H
3
BO
3
5I
þ
IO
3
6H
þ
#
(8.43)
3I
2
þ
3H
2
O
I
þ
I
3
:
I
2
#
The first reaction, also called a neutralization reaction, is faster than the second reaction. If the mixing
is good, there is no acid left for the second reaction to form iodine. In other words, the amount of iodine
produced depends on the efficiency of the mixing process. The concentration of I
3
in the mixing
product indicates the degree of mixing. The concentration of I
3
can be measured based on absorbance
at 353 nm. Using this method, the mixing efficiency can be determined as
ABS
ABS
h
mixing
¼
(8.44)
N
where ABS is the reading results of absorbance measurement and ABS
is the absorbance of the fully
mixed solution. The disadvantage of this technique is that the absorbance measurement would need to
N
Search WWH ::
Custom Search