Environmental Engineering Reference
In-Depth Information
Fig. 14.17 The magnitude
of the DEP dimensionless
force
h
F
DEP
i
/
F
0DEP
plotted
along five vertical lines:
x
/
d
¼
0, 0.25, 0.5, 0.75,
1 (Logarithmic scale)
force reaches its maximum near the electrodes
margins (a difference of at least two
orders of magnitude), and diminishes rapidly with the height. Practically, at heights
y
'
d
the dielectrophoretic effect is negligible. On the other hand, the results obtained
by solving the problem (
14.26
)-(
14.27
) reveal that the nanoparticles subjected to the
calculated pDEP force are strongly attracted to the electrodes edges, while their
volume concentration in fluid diminishes, as showed in Fig.
14.16b
.
The variation of magnitude of the DEP dimensionless force
>
h
F
DEP
i
/
F
0DEP
plotted in Fig.
14.17
along five vertical lines,
x
/
d
¼
0,0.25,0.5,0.75, and 1, respec-
tively, shows that above the value
y
/
d
1 this quantity decreases exponentially and
remains constant with
x
across the array, independent of the shape of electrodes.
One observes that for values
y
/
d
¼
>
1 the force practically not depends on the
x
coordinate, and decreases exponentially with
y
. For
y
>
d
it holds very well the
approximation:
h
i=
F
0DEP
¼
:
ð
:
685
y
=
d
Þ
ð
:
Þ
F
DEP
0
195exp
0
14
30
which allows the evaluation of the levitation height in the case of negative
dielectrophoresis.
The analysis of the effect of the height of electrodes on DEP force variation
shows that the dependence on
y
is quite the same, only slightly translated with a
value corresponding to electrode height, as revealed by the results from Fig.
14.18
.
After this analysis of dielectrophoretic forces distribution inside the separation
device, we move to the evaluation of the efficiency of the device.
The efficiency of the filtration process can be evaluated by calculating the
Filtration rate
(
14.28
) for different values of problem
s parameters. The computa-
tion is performed using an iterative procedure: the output concentration in one unit
cell is considered the input concentration for the next unit cell, in order to describe
the cumulative effect of the filtration inside the dielectrophoretic device. This type of
'
