Environmental Engineering Reference
In-Depth Information
14.3.2.2 Numerical Results
For the computation of the pDEP force, we first solved the Laplace equation for the
real and imaginary components of the electric potential, together with the associ-
ated boundary conditions presented in Fig.
14.13
. The computational domain
consists of a unit cell described by the following set of geometric parameters:
l
¼
d
¼
100
ʼ
m,
H
¼
500
ʼ
m, and
w
¼
100
ʼ
m. The simulations were performed for
particles with characteristic sizes
a
200 nm, respec-
tively, suspended in air. The dielectric response of the particles is characterized by
the real part of the CM factor
K
R
¼
¼
50 nm,
a
¼
100 nm, and
a
¼
1 and we considered the amplitude of the
electric potential applied on the electrodes varying in the range
V
0
¼
24 V.
In order to avoid numerical difficulties, due mainly to the extremely wide range
of variation of the DEP force inside the computational domain, we chose to solve
the model equations in the dimensionless form. If the electric potential is scaled
with the applied electrode voltage
V
0
, the distances with the electrode width
d
, the
time with
d
2
/
D
, the velocities with
D
/
d
, and the particle volume fraction with the
initial average volume fraction
C
0
, the corresponding dimensionless form of the
DEP force (
14.11
) is:
12
2
2
0
0
V
0
R
0
V
0
I
h
F
DEP
i
¼
F
0DEP
∇
þ
∇
:
ð
14
:
29
Þ
∇
ε
m
K
R
(
V
0
2
/
d
3
) a quantity that mea-
sures the intensity of the external field. The prime symbol above denotes the
dimensionless quantities.
The magnitude of the vector
a
3
We noted in the above equation
F
0DEP
¼
2
ˀ
∇
0
V
0
I
|
2
), proportional to the dimen-
sionless DEP force given by Eq. (
14.29
), calculated in the vicinity of the electrodes, is
presented in Fig.
14.16a
in logarithmic scale. The results clearly show that the pDEP
∇
0
(|
∇
0
V
0
R
|
2
+|
Fig. 14.16 (a) Spatial distribution of the calculated magnitude of the vector
/
F
0DEP
in
logarithmic scale, and (b) Calculated particle concentration distribution for a typical separation
h
F
DEP
i
