Biomedical Engineering Reference
In-Depth Information
9.10  Example of MFFF
In this section we illustrate how to calculate particle trajectory and concentration
by taking the example of magnetic field flow fractionation. In biology and bio-
technolgy, there is a constant need to separate particles, depending on their mass,
electric charge, or magnetic properties. For example, this is the case for purification
of proteins or for obtaining monodisperse magnetic beads. A very common method
for separation of particles is called field-flow fractionation (FFF).
In a typical FFF device, the carrier fluid flows horizontally in a channel and the
particles experience a horizontal drag force; depending of the type of separation
that is searched (mass, electric charge, magnetic properties) a relevant force field
(gravity, electric field, magnetic field) is set up to act perpendicularly to the flow.
Trajectories of the different particles differ in the FFF force field. Similar particles
have similar trajectories and gather at the same location on the channel lower wall.
A magnetic FFF is sketched in Figure 9.26.
Much work has been done in the domain of sedimentation field flow fraction-
ation (SdFFF) [18]; however, recently, new applications for biological processes—
such as cell separation—have required the use of submicronic paramagnetic particles
that are not much influenced by gravity but magnetic field-flow fractionation (MFFF
or simply MF) is a well-suited method to separate these particles according to their
size and magnetic permeability [19, 20].
The velocity field is well known in the case of a laminar flow between two hori-
zontal parallel plates (the Reynolds number is much less than 1). From hydrody-
namics considerations, it is well known that the velocity profile across any section
is parabolic and given by
2
æ
ö
3
V
y
0
(9.32)
V
=
1
-
ç
÷
f
2
2
è
d
ø
where d is half the distance between the channel walls and V 0 the average velocity.
Figure 9.26  Schematic view of MFFF. The upper solid wall is called the depletion wall and the lower
wall is the accumulation wall.
 
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