Biomedical Engineering Reference
In-Depth Information
where
i
is the imaginary unit and
R
indicates the real component of a complex number. Nguyen and
Huang used piezoelectric disks as active valves
[30]
. The mixer was fabricated by CO
2
laser and hot
lamination of the multiple polymer sheets. Hydrodynamic focusing was used to eliminate the side
effect of Taylor-Aris dispersion in a rectangular microchannel.
5.4
SEGMENTATION BASED ON INJECTION
Segmentation based on injection introduces the solvent into the solute flow through a nozzle array.
This concept also decreases the mixing path and increases the interfacial area between the solvent and
the solute.
Figure 5.11
shows a simple two-dimensional model of the concentration distribution around
a single circular nozzle. The nozzle has a radius of
R
. The mass flow rate of the solute is
m
1
(kilograms
_
per second), while the mass flo
w
rate of the solvent is
m
2
and an inlet concentration of
c
0
. The solvent
flow has a uniform velocity of
u
and a concentration of
c
_
0.
Considering a steady-state, two-dimensional problem and neglecting the source term, the transport
equation reduces to the form
¼
v
2
c
vx
2
þ
v
2
c
vy
2
:
u
D
vc
vx
¼
(5.21)
The general solution of
(5.21)
is the product of a velocity-dependent term and a symmetric term
G
:
exp
ux
2
D
c
¼
Gð
x
;
y
Þ:
(5.22)
Substituting
(5.22)
into
(5.21)
results in
u
2
D
v
2
v
2
G
vx
2
þ
G
vy
2
:
G ¼
(5.23)
FIGURE 5.11
Two-dimensional model of the concentration distribution around a circular nozzle.
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