Biomedical Engineering Reference
In-Depth Information
When the two spheres contact each other,
r = a
and
�
2
α
2
2
F contact
(
)
= -
6
µ π
a H
(9.47)
1
0
0
3
æ
3
ö
a
r
æ
ö
1
-
α
ç
ç
÷
÷
è
ø
è
ø
Equation (9.47) shows that the binding force between two similar beads is propor-
tional to the square of the bead radius and to the square of the magnetic field. In
the same way that we have shown the existence of magnetic attraction and repul-
sion regions at a wire surface, it can be shown that the same exists at the surface of
a spherical bead [22]. The two regions around the bead aligned with the external
magnetic field are magnetically attractive, and the region around the “magnetic
equator” of the bead is a repulsion zone (Figure 9.30).
Under the action of the Brownian motion, beads randomly contact each other;
contacting beads tend to stick together by their attraction regions and progressively
will form a linear chain of beads aligned in the external field (Figure 9.31). These
binding forces are more efficient for larger beads (1
μ
m) than for smaller beads
(50 nm), and nano-sized beads—those under 50 nm—are often dispersed by the
Brownian motion.
Magnetic chains are new tools in biotechnology (they can even be stabilized by
polymer coating) and they have found an application for DNA separation: these
chains are used to separate DNA segments in the same way as a gel. Let us first re-
call how DNA separation works in a gel. Under an electric field, the DNA segments
migrate under electrophoretic forces (see Chapter 10) at a different speed depending
on their size (Figure 9.32).
The longer the strand of DNA, the more it encounters obstacles and the more it
is delayed in its motion. This technique has been widely used to decrypt the human
genome. The major drawback is that a characteristic time for the separation is of
Figure 9.30
Magnetic attraction and repulsion regions around a spherical bead. The external mag-
netic field is oriented from left to right. Only one-fourth of the space has been represented.
