Biomedical Engineering Reference
In-Depth Information
magnetophoresis methods. Recently, Kang
et al.
demonstrated a discrimination
between the polymer particles of polystyrene ( PS ), poly(methyl methacrylate)
(PMMA), and borosilicate (BS), by using IMP in the microfl uidic channel [42]. As
the following experimental results and numerical estimation indicate, whilst the
polymer particles of PS and PMMA cannot be discerned with conventional mag-
netophoresis, IMP is indeed able to discriminate the subtle differences in the
magnetic susceptibilities of these materials. Although these present demonstra-
tions of IMP have not included any separations using nanomagnetic materials,
the method is described here because it will surely encourage great advances on
conventional magnetophoretic analysis, and may even be extended to magnetic
nanomaterials in further studies.
In order to verify the theoretical hypothesis, an analytical model has been estab-
lished by composing several functions of magnetic drag velocity,
V
x
(
t,x
), the
magnetic susceptibility gradient,
K
(
t,x
), magnetic fl ux density gradient
B
(
x
), and
particle velocity driven by the parabolic fl ow profi le,
V
y
(
x
) (Equation 3.10 ).
K
(
t,x
)
is obtained from the concentration gradient,
C
(
t,x
) (Equation 3.9), generated across
the microfl uidic channel in accordance with Wiedemann's additivity law (Equation
3.11 ) [115] :
(
)
()
2
R
2
χ
−
K t x
(
,
)
B x
p
(
) =−
Vtx
,
(3.7)
x
9
μη
0
Bx
()=−
2 466 100
.
(
−
x
) +
378 68
.
(3.8)
{
}
1
2
∞
∑
erf
h wx
Dt
+−
+
2
2
h wx
Dt
−+
2
2
Ctx
(
,
)
=
C
erf
(3.9)
0
n
=−∞
2
3
2
450
(
−
x
)
⎛
⎜
⎞
⎟
Vx
()=
v
1
−
(3.10)
y
0
w
2
N
N
∑∑
1
(
)
=
χ
mixture
V
χ
V
(3.11)
ii
i
i
=
i
=
1
(
)
=
(
)
(
(
)
)
Ktx C
,
tx
,
χ
+−
1
C
tx
,
χ
(3.12)
Gd DTPA
−
Gd DTPA
−
Gd DTPA
−
D glu
−
cos
e
where
V
x
(
t
,
x
) is the magnetophoretic velocity at time,
t
(
s
) at position of
x, R
is
the radius of a particle (ca. 7.5
p
and
K
(
t,x
) are the volumetric magnetic
susceptibility of a particle and fl uid, respectively,
B
(
x
) is the magnetic fl ux density
gradient (T
2
m
− 1
),
μ
m),
χ
dynamic viscosity of fl uid (Pa s),
C
0
the initial concentration,
h
is the width of the initial distribution (50
μ
0
is vacuum permeability,
η
μ
m),
w
is
the width of the channel (100
μ
m),
D
is the diffusion coeffi cient of Gd-DTPA
(2.3
1 0
− 6
c m
2
s
− 1
) [116] , and
v
0
is the average fl uid velocity in the channel (mm s
− 1
).
The magnetic susceptibility of Gd - DTPA and D - glucose was obtained from pub-
lished reports [117, 118]. The fi nite element method magnetic (FEMM) program
can be used to estimate the magnetic fl ux density gradient across the microchan-
nel,
B
(
x
), and the magnetic permeability of nickel can be obtained from published
×
