Biomedical Engineering Reference
In-Depth Information
Example 5.1
(
Network model for hydrodynamic focusing
). The microchannel network depicted in
Fig. 5.13
is made of silicon and glass by deep reactive ion etching and anodic bonding. The micro-
channel has a width of 100
m. The three inlet channels are 5 mm long, while
the mixing channel is 20 mm long. What is the range of pressure ratio between the sheath flow and the
sample flow? What is the required pressure ratio for a focusing width of 1
m
m and a height of 10
m
m
m?
Solution
. With a low aspect ratio
h
¼
H
/
W
¼
0.1, the relation between the flow rate and the pressure
derived in Example 2.3 can be used:
H
3
W
p
12
mL
ð
D
Q
z
1
0
:
630
h
Þ:
Thus, the fluidic resistance of the microchannel with a length
L
is
H
3
W
:
Because the cross-section of the microchannel network remains constant, the fluidic resistance is
proportional to the channel length. From the geometry of the given channel network, we have
R ¼
D
p
Q
¼
12
mL
1
0
:
63
h
5mm
5mm
¼
a
¼
1
20mm
5mm
¼
b ¼
4
:
The maximum and minimum pressure ratios are
2
b
1
2
b
¼
þ
2
4
þ
1
r
max
¼
4
¼
1
:
125
2
b
4
r
min
¼
a
¼
1
¼
0
:
8
:
b
þ
4
þ
For a focusing width of
W
f
¼
1
m
m, we have
W
f
W
¼
1
þ
2
b
2
br
1
þ
2
ar
1
100
¼
1
þ
2
4
2
4
r
9
8
r
2
r
:
Solving the above linear equation results in the required pressure ratio for a focused width of 1
¼
1
þ
2
1
r
1
þ
m
m:
901
802
:
r
¼
5.5.2
Streams with different viscosities
The following model analyzes the effect of hydrodynamic focusing for reducing the width of the
mixing streams. In the model, the sample stream is sandwiched between two identical sheath streams
(
Fig. 5.14
). The sample stream and the sheath stream are assumed to be immiscible.
Figure 5.14
shows
the geometry of the channel cross-section with the above two phases. The channel has a width 2
W
and
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