Biomedical Engineering Reference
In-Depth Information
Fig. 8.41 Arrangement of rings
The main parameters of the filters are the following: the size of arrested particles,
the relation of throughput to pressure drop, and the size (or the weight) of the
filter. We have used a numerical model of the filtration process to calculate these
properties.
To calculate the filter parameters, it is necessary to know the hydraulic resistance
of one slit between two microrings:
G
¼
P
=
Q
;
(8.118)
where
G
is the hydraulic resistance of one slit between two microrings,
P
is the
pressure drop in the slit, and
Q
is the flow rate in the slit.
The hydraulic resistance of the section between radius
r
and
r
+
dr
can be
calculated as
6
m
dG
¼
dr
;
(8.119)
p
r
x
3
ð
r
Þ
where
dG
is the hydraulic resistance,
is the viscosity coefficient,
r
is the current
radius (Fig.
8.41
), and
x
(
r
) is the current width of the slit at the radius
r
.
x
(
r
)is
calculated by expressions (8.115) - (8.117), and then
m
Z
r
1
G
¼
dG
:
(8.120)
r
4
We have determined
G
by numerical integration in equation (8.120). Hydraulic
resistance of the slit depends on the shape of the microrings and on the distance
