Biomedical Engineering Reference
In-Depth Information
through the gap between two pillars; it is forced into the next channel (e.g., channel
2). This motion is repeated at each row of pillars. Globally the particle follows a
diagonal trajectory with an angle
e
.
The critical particle diameter is then
D
(6.112)
Let us now calculate the value of
b
. Using the notations of Figure 6.62, we
have
= 2
β
g
u x dx u x dx
(6.113)
Assuming a parabolic velocity profile between two pillars, the velocity
u
(
x
) can
be expressed as
β
ò
ò
( )
=
ε
( )
0
0
2
é
ù
2
g
æ
g
ö
u x
( )
=
u
-
x
-
ê
ú
ç
÷
max
è
ø
4
2
ê
ú
ë
û
(6.114)
Upon substitution of (6.114) in (6.113) and integration, the width
b
is the solu-
tion of the cubic equation
3
2
æ
ö
æ
ö
β
3
β ε
-
+
=
0
ç
÷
ç
÷
è
ø
2
è
ø
2
g
g
(6.115)
and, using (6.112), the critical diameter is solution of
3
2
æ
ö
æ
ö
D
D
c
c
-
3
+
4
ε
=
0
ç
÷
ç
÷
è
g
ø
è
g
ø
(6.116)
A plot of
D
c
/
g
versus
e
is shown in Figure 6.67.
A very interesting application of DLD is given in [30] (Figure 6.68), where a cell
is progressively deviated into a lysis solution and is eventually lysed with chromo-
some and cell contents being separated.
6.5.4 Lift Forces on Particles
In this section we assume medium to large velocities of the carrier flow (i.e., a flow
Reynolds number approximately larger than 10).
6.5.4.1 Lift Force on a Particle or Cell
A relatively large rigid particle in a moderate or large Reynolds number flow is
submitted to a drag force expressed by (6.87) and also to a lift force. There are two
types of lift forces on the particle depending on its distance to the solid wall (Figure
6.69).
The first lift force is called the shear-gradient induced lift and is linked to the
flow velocity profile at the location of the particle. Due to its weight and size, the
