Biomedical Engineering Reference
In-Depth Information
Fig. 15
Schematic representation of the pressure drop model used for pressure calculation in the
plasma and ionization chambers
Three pressure stages are relevant to design the capillary lengths and diameters
as shown in Fig.
15
The pressure regimes for stable operation were evaluated by
measurements using pressure sensors and mass flow controllers. They are summa-
rized in Table
1
:
Assuming a constant pressure
p
0
in the chamber, the throughput, which is the flow
out of the chamber into vacuum, or gas flow pressure product
q
pV
at steady state is [
27
] :
q
=
·
Kp
·
;
pV
g
0
where
1
( )
2
2·
κ
RT
·
⎛
⎞
κ−
K
=
⎜
,
⎟
g
⎝
κ+
1
⎠
κ+
1
M
molar
k
,
R
and
M
molar
are the gas dependent isentropic exponent, specific gas constant, and
molar mass, respectively.
The conversion of the throughput
q
pV
into volume flow yields the values listed in
Table
1
. Since in the capillaries laminar fl ow prevails (Reynolds number RE << 2,300),
the pressure drop along the capillaries follows
Hagen-Poiseuille´s equation
:
(
)
2
2
pp
−
π
·
d
4
v
0
q
=
,
pV
128· ·
η
l
2
where
h
,
l
, and
d
are the dynamic viscosity of the gas, length of the capillary, and
the capillary diameter, respectively.
