Biomedical Engineering Reference
In-Depth Information
Fig. 2.1
The principle of the inertial migration of particles: (
a
) mechanism of the migration of
particles toward their equilibrium positions and (
b
) the equilibrium positions in different channel
geometries
the walls of the longer sides [
1
], because a greater shear rate acts on the particles
along the narrower dimension. In terms of particle separation, a rectangular channel
is preferable because the number of equilibrium positions is reduced and it is easier
to guide particles toward a collecting outlet in a microfluidics device.
The migration length (
L
m
), i.e., the channel length required for the migration of
rigid spheres, is obtained by considering the balance of forces between the shear-
induced migration force and the viscous drag force. Bhagat et al. [
1
] derived
L
m
as
3
;
3
pm
2
rU
W
a
L
m
ΒΌ
(2.1)
where
U
is the average velocity in the channel,
W
the half-width of the channel, and
a
the radius of a rigid sphere. When the channel length is much larger than
L
m
, most
of the particles migrate to equilibrium positions. Consequently,
L
m
is one of the
most important parameters in the design of a microchannel for particle separation.
In Sect. 2.5, we show that (
2.1
) is a good approximation for describing the
migration of rigid spheres. In Sect. 2.6, we show that (
2.1
) does not precisely
predict the migration of cancer cells, as the
L
m
for cancer cells is longer than the
value for rigid spheres.
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