Biomedical Engineering Reference
In-Depth Information
Figure 2.42
Sketchoftheseparationdevice.Notethatthemainchannelhydraulicresistancesare
allequalto
R
.
and
é
ù
R
1
R
=
1
+
(2.90)
ê
ú
B n
-
1
α
1 2
+
α
ë
û
Finally
é
ù
R
1
1
ê
ú
R
=
1
+
+
....
+
(2.91)
B
1
α
-
n
1
α
1 2
+
α
(
)
ê
ú
1 2
+
ë
û
The system is now fully known. Note that we have not taken into account the
pressure drop at the intersections. It should be treated as in the preceding section.
We insist that the dimensioning we have done corresponds to a Newtonian fluid,
such as diluted blood, not whole blood.
2.2.11 Hydrodynamic Entrance Length: Establishment of the Flow
2.2.11.1
Theory
When a fluid enters a tube, at the entrance of a tube, there is a length where the flow
in not yet established. The shape of the velocity profile evolves until it reaches the
established profile (Hagen-Poiseuille profile for a laminar flow), as shown in Figure
2.43. The evolution of the profile is due to the progressive increase of the boundary
layers at the wall. When the boundary layers merge at the center axis, the flow is
established.
The length of the establishment region may be approximated by using the
boundary layer theory. If we suppose that the entrance length corresponds to the
