Biomedical Engineering Reference
In-Depth Information
(b)
(a)
0
<Top view>
z
x
solution
A
2
y
particle
inlet
magnetized
nickel microstructure
PS
PMMA
4
solution
B
z
x
6
y
8
0 0 0 0 0 0
Lateral position across
microfluidic channel /
m
m
Lateral position across microfluidic channel /
m
m
Figure 3.23
(a) Theoretical estimation of the
microparticle displacement in the microfl uidic
channels under conventional
magnetophoresis; (b) Particle traces of the PS
and PMMA particles, supporting the
experimental results as described in Figure
3.22. The plot presents the theoretical particle
traces without particle size deviation.
Considering the practical particle size
deviation, the lateral positions of PS and
PMMA particles in the outlet port become
indiscernible. Reproduced with permission
from Ref. [42]; © 2008, American
Chemical Society.
Cartesian coordinate system, assuming that all parts of a microsphere (polymer
particle) are exerted by the uniform magnetic force. Then, the composite function
(
V
x
and
V
y
) is iterated by increasing the time (from
t
= 0) until the
y
reaches 11 mm
(distance along the microfl uidic channel) (Figure 3.23 ).
The ideal condition for IMP requires the static gradient of
fl uid
over the microfl u-
idic channels, but the present device scheme does not generate the stationary
χ
fl uid
profi les across the microfl uidic channel because of diffusion. Therefore, for a theo-
retical consideration of the present quasi-isomagnetophoretic displacement (due to
transition of the
χ
fl uid
gradient in accordance with time and particle position in
y
-
axis),
V
x
(
t,x
) and
V
y
(
x
) are employed to estimate the particle displacement at time,
t
.
By using this model and the experimental data above,
χ
χ
PS
,
χ
PMMA
and
χ
BS
are dis-
criminated to be
1 0
− 6
, respectively, which are
comparable with published values [120]. Figure 3.24a presents a theoretical predic-
tion of PS and PMMA particles, which shows a clear correlation with the experi-
mental data, comparing the magnetophoretic prediction (Figure 3.24b). For the
apparent verifi cation of IMP compared to magnetophoresis, the (iso)magnetopho-
retic distinction coeffi cient in the microfl uidic devices,
D
=
−
8.75
×
1 0
− 6
,
−
5.40
×
1 0
− 6
, and
−
2.10
×
Δ
x
/
Δ
χ
particle
, has been
newly defi ned, where
particle
are the difference in the lateral posi-
tions of certain types of two particles at the outlet (
P
and
Q,
Δ
x
(10
− 6
m) and
Δ
χ
Δ
x = x
P
−
x
Q
) and in
magnetic susceptibility (
Q
), respectively. We can estimate
D
mag
and
D
iso
, by considering if the particle,
P
, is polystyrene and
Δ
χ
particle
=
χ
P
−
χ
χ
Q
varies from
−
0.75
×
1 0
− 6
to
1 0
− 6
. As reported in Figure 3.24b,c, IMP provides a larger
D
iso
(3.89)
compared to
D
mag
(1.41) and, in addition, it reduces the errors caused by size devia-
tion of the particles, thus supporting the results of Figure 3.22. The dotted-lines
(upper and lower) in Figure 3.24b and c are the plotted results when the particle size
of
P
is 15.0
−
15.75
×
μ
m, and the particle sizes of
Q
are 16.0
μ
m and 14.0
μ
m, respectively.
