Biomedical Engineering Reference
In-Depth Information
Figure 9.35
Left: schematic view of an organic-based ferrofluid. Right: view of ferrofluid drops
attracted by a magnet.
The advantage of magnetic fluids is that they can be actuated externally by
a micromagnet or a microelectromagnet and that they can be inserted as “active
plugs” in microsystems (Figure 9.36) to pump or regulate the flow [26].
9.12.2 Magnetic Force on a Plug of Ferrofluid
Suppose that a ferrofluid plug in a capillary tube is controlled by an external mag-
netic field (Figure 9.37).
The magnetic forces on the plug result in a magnetic pressure difference be-
tween the two edges of the plug according to Rosensweig's formula [27]. If index
a
stands for the advancing front and
r
for the receding front, we have
H
a
µ
0
2
2
ò
D
P
=
µ
MdH
+
(
M
-
M
)
(9.48)
mag
0
n a
,
n r
,
2
H
r
where
H
is the magnetic field along the capillary axis,
M
the magnetic moment, and
M
n
is the magnetic moment normal to the plug interface with water. Now if we note
that a ferrofluid behaves like a paramagnetic media, in the limit of low magnetiza-
tion
M
=
cH
and after substitution in (9.48), one obtains
1
µ
2
2
D
P
=
(
µ µ
-
)(
H H
-
)
(9.49)
magnetic
0
a
r
2
µ
0
Figure 9.36
Ferrofluid plug in a capillary tube (diameter 200
μ
m).
