Biomedical Engineering Reference
In-Depth Information
Figure  6.69  The two lift forces on a rigid particle: (a) shear-gradient lift and (b) wall-effect
induced lift.
u y U d where U is the average velocity and d
is the channel depth. The lift force is then proportional to the square of the particle
Reynolds number defined as Re p = U R H / v f . For the lift force to have an effect, the
particle Reynolds must be sufficiently large.
The second lift force is linked to the vicinity of the solid surface [32-34]. It is
sometimes called a wake or wall effect induced lift force. The relative velocity near
the wall side of the particle is reduced by the presence of the wall and the pressure
on the wall side is larger than that on the centerline side. A lift force is exerted on
the particle towards the channel center. This force can be expressed by
field, the vorticity is equal to ω = ¶
¶ »
2
4
F
=
9.22
γ ρ
R
(6.118)
lift
f H
which, in a Poiseuille-Hagen flow is equal to
æ
2
ö
U
4
F
=
9.22 36
ρ
R
(6.119)
ç
÷
lift
f H
2
d
è
ø
where γ is the shear rate at the location of the particle. The lift force may be ex-
pressed as a function of the particle Reynolds number as
2
R
H
2
F
=
9.22 (36 Re
)
µ ν
(6.120)
lift
p
f
f
2
d
showing that the boundary layer lift force is proportional to the square of the par-
ticle Reynolds number. Hence, for this lift force to be noticeable, the particle must
have a relatively large radius and a relatively high velocity.
6.5.4.2 Focusing of Particles in a Straight Channel
Combining the effect of the two lift forces, a rigid particle of a given size tends to be
focused at a constant distance from the wall as shown in Figure 6.70.
 
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