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
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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