Biomedical Engineering Reference
In-Depth Information
Figure 2.38
Viewofamicroneedle.
2.2.10 Microfluidic Networks: Worked Example 2—Plasma Extraction
from Blood
Separating plasma from blood is the first step of blood analysis. A promising
method is based on the Zweifach-Fung bifurcation effect [44, 45]. The bifurca-
tion law describes that, in the microcirculation, when erythrocytes (red blood cells)
flow through a bifurcating region of a capillary blood vessel, they have a tendency
to travel into the daughter vessel, which has the higher flow rate, leaving very few
cells flowing into the lower flow rate vessel. The critical flow rate ratio between the
daughter vessels for this cell separation is approximately 2.5:1 when the cell-to-ves-
sel diameter ratio is of the order of 1. This effect will be investigated in more detail
in Chapter 6.
The principle is to design a network having the form of a tree where a fixed
fraction of the main flow is diverted into side branches [46] (Figure 2.42). Let us
note
α
this fixed fraction. The problem is to find the hydraulic resistances of all the
side branches.
2.2.10.1
FlowRates
Consider first the flow rates. At the first intersect,
(2.86)
Q
=
2
B
Q
+
Q
0
1
M
1
and, dividing by
Q
M
1
, we find
Q
0
/
Q
M
1
= 2
α
+ 1.
Then
Q
0
Q
=
M
1
2
α
α
α
+
1
(2.87)
Q
0
Q
=
B
1
2
+
1
Figure 2.39
Detailedviewofthemicroneedle:mainchannelandobliquesidechannels.(Courtesy
ofF.Rivera,CEA/LETI.)
