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1. Modeling of ac dielectric barrier discharge
J. S. Shang and P. G. Huang
Citation: J. Appl. Phys. 107, 113302 (2010); doi: 10.1063/1.3415526
View online: http://dx.doi.org/10.1063/1.3415526
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Published by the American Institute of Physics.
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2. Modeling of ac dielectric barrier discharge
J. S. Shanga兲
and P. G. Huang
Department of Mechanical and Materials Engineering, Wright State University, Dayton Ohio 45435, USA
共Received 19 February 2010; accepted 27 March 2010; published online 2 June 2010兲
The qualitative electrodynamic field of the dielectric barrier discharge in air is studied by a
three-component, drift-diffusion plasma model including the Poisson equation of plasmadynamics.
The critical media interface boundary conditions independent of the detailed mechanisms of surface
absorption, diffusion, recombination, and charge accumulation on electrode or dielectrics are
developed from the theory of electromagnetics. The computational simulation duplicates the
self-limiting feature of dielectric barrier discharge for preventing corona-to-spark transition, and the
numerical results of the breakdown voltage are compared very well with data. According to the
present modeling, the periodic electrodynamic force due to charge separation over the electrodes
also exerts on alternative directions from the exposed to encapsulated electrodes over a complete ac
cycle as experimental observations. © 2010 American Institute of Physics. 关doi:10.1063/1.3415526兴
I. INTRODUCTION
The viable flow controls at atmospheric condition have
been shown by using the dielectric barrier discharge 共DBD兲
and the corona discharge in subsonic and transonic flow
regimes.1–3
The electrofluid-dynamic interaction through the
inelastic collision between ions and neutral particles pro-
duces a wall-jetlike stream known as electric wind; the maxi-
mum speed of the wall jet can be as high as a few meters per
second.1,2
This electric wind can be effective for flow control
at the aerodynamic bifurcation point.1,4
The ionizing process
of DBD via electronic collision is also known as the silent
discharge and has been applied to ozone production since the
mid 19th century.5
In contrast to DCD, the DBD is main-
tained by an alternating electric current. The DBD also op-
erates on a self-limiting process by the reduced electric field
potential through the surface charge accumulation, thus pre-
vents the corona-to-spark transition. Despite numerous com-
putational simulations, most computational simulations have
not imposed the correct media interface boundary condition
for describing this key physical phenomenon of the DBD.6–11
At atmospheric pressure, the DBD consists of numerous
microdischarges or streamer which are generated by the ex-
ternally applied electric field potential.3,8,12
These microdis-
charges have a short life span of about a few nanoseconds
and with the random temporal and spatial structures.3
The
discharge pattern over the dielectric surface depends on the
polarity and amplitude of the applied electric field, as well
as, the electric permittivity of the electrode.1
Nevertheless,
the discharge phases still can be identified as avalanche,
streamer formation, a subsequent glow discharge and final
quenching of the microdischarge on the electrodes.12
A com-
plex physical phenomenon of DBD emerges; a wide range of
discharge patterns are observed depending on the gas mix-
ture, pressure, electrode arrangement, and other parameters.
However, the global structure always consists of the continu-
ous diffusive and random distributed pulsing microdis-
charges of short duration.
The nonequilibrium chemical kinetics associated with
the DBD is well known because it has been applied as an
ozone generator for years. The plasma chemical kinetics in
atmospheric gas consists of 576 chemical reactions involving
vibrationally excited states of nitrogen and oxygen, ozone,
positive and negative ions, besides oxide-nitrides.13
Again,
DBD is a nonequilibrium transient discharge. The mean en-
ergy state of the electrons and the heavy particles is consid-
erably different. For this reason the energy of charged par-
ticles can be effectively transferred into the internal states of
molecule or atom. Important information provided by the
work of Bogdanov et al.9
is that the influence of the nega-
tively charged ions is not essential for flow control. There-
fore, the three-component 共electron, positively charged ion,
and neutral兲 gas discharge formulation by Surzhikov and
Shang14
can be considered as a qualitatively modeling for
ionized air.
For DBD applications the interaction of charged par-
ticles and the dielectrics is important. According to Gol-
ubovskii et al.,8
the photoemission is negligibly small for
nitrogen because the energy of photons in the visible range is
too small to cause the emission of electrons. Other important
processes are desorption of electrons and surface recombina-
tion. However, the secondary electrons emission of electrons
from the surface during an ac cycle leading to the charge
separation in the cathode layer is a dominant mechanism.
Meanwhile, the surface charge accumulation also alters the
electrical potential within the discharge domain. In view of
the relatively short duration of microdischarge versus the mi-
crosecond time scale of the DBD cycle; the instantaneous
surface recombination is a plausible and acceptable approxi-
mation. Finally and most importantly, the ionization of DBD
is still a basic Townsend process.12
This observation be-
comes a corner stone of the present formulation for ioniza-
tion.
II. GOVERNING EQUATIONS
The pioneering effort by Massines et al.6
has provided
helpful insights for understand the DBD behavior. Their two-
a兲
Electronic mail: joseph.shang@wright.edu.
JOURNAL OF APPLIED PHYSICS 107, 113302 共2010兲
0021-8979/2010/107共11兲/113302/7/$30.00 © 2010 American Institute of Physics
107, 113302-1
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3. dimensional analysis was conducted for a parallel-electrode
configuration which is unsuitable for flow control applica-
tion. Therefore, all investigations of plasma actuator adopt
the asymmetric electrodes arrangement and include the key
element of the discharge; the physics must be analyzed as a
time-dependent phenomenon.7–11
From more recent investigations, it becomes clear that a
direct simulation of multiple microdischarges in temporal
and spatial dimensions is beyond the present computational
capability.11
Therefore, all numerical simulations, including
the present effort, can only describe a series of multiple mi-
crodischarges as a globally diffusive discharge and capture
the essential physics produced by the fundamental mecha-
nisms of the DBD.
The ionization of the DBD is mainly the result of ava-
lanche growth of electrons produced by the secondary emis-
sion on the cathode.12
The temporal and spatial development
of nonequilibrium partially ionized gas that consists of elec-
trons and positively charged ions can be described by the
classic drift-diffusion theory.12,14,15
In the absence of the en-
ergy conservation equations, the electron temperature, Te can
only be estimated by empirical means and is assumed to
have a constant value less than two. A consistent electrical
field is obtained by solving simultaneously the Poisson equa-
tion of plasmadynamics as follows:
⳵ne
⳵t
+ ⵜ · ⌫
ជe = ␣共兩E
ជ兩,p兲兩⌫
ជe兩 − ␤nen+, 共2.1兲
⳵n+
⳵t
+ ⵜ · ⌫
ជ+ = ␣共兩E
ជ兩,p兲兩⌫
ជe兩 − ␤nen+, 共2.2兲
ⵜ2
␸ =
e
␧
共ne − n+兲. 共2.3兲
In which, ⌫
ជe=−Deⵜne−ne␮eE
ជ and ⌫
ជ+=−D+ⵜn++n+␮+E
ជ are
the electron and ion number density fluxes. In the above
formulation, ␣共E,p兲 and ␤ are the first Townsend ionization
coefficient and recombination coefficient, respectively. The
␮e and ␮+ are the electron and ion mobility, De and D+ are
the electron and ion diffusion coefficients.14,15
The formula
for the coefficients of mobility and diffusion is the well-
known Einstein relationship.12
In Eq. 共2.3兲, e is the elemen-
tary charge and ␧ is the electrical permittivity which is dif-
ferent for the weakly ionized gas and dielectrics. A typical
relative dielectric permittivity of the dielectric material has a
range from 2.7 共polystyrene兲 to 6.0 共lead glass兲.
III. BOUNDARY CONDITIONS
The dielectric barrier is defined as an impermeable inter-
face of media. All charged particles reached this boundary
are collected on the surface after interactions in molecular
and atomic scales. The boundary conditions on the interface
shall be imposed according to Maxwell equations in the time
domain.16
These boundary conditions stipulate the necessary
relationships for the normal and tangential components of
electromagnetic field variables across a media interface. For
DBD simulation, the only pertinent interface boundary con-
ditions are the tangential component of the electric field in-
tensity, E, and normal component of the electric displace-
ment, D.
The media interface boundary conditions for DBD con-
sist of two principal locations; on the exposed electrode and
the dielectric barrier that encapsulates the other electrode.
The physical meaningful boundary conditions are straightfor-
ward. The key physical phenomena are the secondary emis-
sion of electrons from the cathode, the surface charge accu-
mulation on the electrodes, and the repulsion of positive ions
from the anode. In an ac field, the exposed electrode acts as
an anode when the applied electric potential is positive. And
its role reversed as the cathode when the electric potential is
beneath the grounded state. The discharge breakdown occurs
only when the field potential has exceeded the threshold de-
fined by the Pachen’s law.12
According to the theory of electromagnetics, the electric
field across the dielectric and plasma interface must satisfy
the following conditions:16
n
ជ ⫻ 共Ed − Ep兲 = 0, 共3.1兲
n
ជ · 共Dd − Dp兲 = ␳e,s. 共3.2兲
In the above equations, the subscripts d and p designating the
variable either resides in the dielectrics or plasma medium.
The local surface charge density is defined as ␳e,s=e兰共ni
−ne兲dx which has a dimension of coulombs per metre
square.
Equation 共3.1兲 simply states that the tangential electrical
field strength is continuously across the media interface. It
can be shown on Cartesian frame, the rate of change for
electric potential in z, ⳵␸/⳵z, must be identical across the
interface along the x coordinate. Similarly, the rate of change
in electrical potential in x, ⳵␸/⳵x, must be equal along the z
coordinate across the media interface. For the present simu-
lation, this requirement is automatic satisfied by the defini-
tion of two-dimensionality.
The discontinuity of the normal component of the elec-
tric displacement, D, across different media must be bal-
anced by the net surface charge on the interface by emission,
desorption, and accumulation. In fact, the condition defined
by Eq. 共3.2兲 is independent of all chemical-physics processes
on the medium interface. And this equation is further devel-
oped by introducing the electric potential for the partially
ionized plasma, E=−ⵜ␸ to become;
␧p
⳵␸p
⳵n
− ␧d
⳵␸d
⳵n
= ␳e,s. 共3.3兲
On the dielectric barrier, the surface diffusion and desorption
can be modeled by the collisions of excited molecules and
atoms by their collision frequency and the binding energy.8
However for the present purpose, the added sophistication is
unwarranted. Therefore, the charge accumulation on surface
is the result from the instantaneous recombination of the
charge particles, and Eq. 共3.3兲 reduces to the following for
the two-dimensional formulation:
113302-2 J. S. Shang and P. G. Huang J. Appl. Phys. 107, 113302 共2010兲
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4. ⳵␸p
⳵y
=
␧d
␧p
⳵␸d
⳵y
+
e
␧p
冕共ni − ne兲dx. 共3.4兲
Equation 共3.4兲 is one of the key boundary conditions to be
imposed on the medium interface whether it is the exposed
electrode or the dielectrics. All other physics meaningful
boundary conditions on the interface have been demonstrated
to be robust and accurately described the behavior of weakly
ionized gas generated by electrons collision.11,14,15
When ␸共t兲⬎0, the exposed electrode performs as the
anode on which the electrical potential is prescribed by the
externally applied ac current source, and all positively
charged ions are repulsed. The imposed boundary condition
on the anode are;
␸共t兲 = EMF sin共␼t兲, 共3.5兲
ni = 0, 共3.6兲
⳵ne
⳵y
= 0. 共3.7兲
where the electromotive force 共EMF兲 is the external voltage
applied to the DBD circuit and the electric field potential
across the exposed and the dielectric barrier after the break-
down is determined by the external circuit equation; EMF
=␸+R兰J̄dv,11,14,15
where the electric current density of the
discharge is simply, J
ជ=e共⌫
ជi−⌫
ជe兲.
At this same instant, the dielectric barrier surface acts as
the cathode which must satisfy the following boundary con-
ditions; the secondary electron emission leads to an exces-
sive accumulation of ions over the dielectric barrier to reduce
the effective electric potential difference. The secondary
electronic emission from the cathode is described by the nor-
mal component of the ion number density flux, ⌫
ជe=−␥⌫
ជ+.12
However, an approximation has been proven accurate by re-
taining only the diffusive contribution on the emissive sur-
face to become, ␮ene=␥␮+n+.14,15
The coefficient of second-
ary emission, ␥, is depended on surface material and electric
field intensity and has been extensively studied by Raizer.12
A range of ␥ values from 10−2
to 10−1
were recommended
for numerical study of glow discharge and widely adopted
for computational gas discharge simulations. In this ac phase,
the imposed boundary conditions on the cathode are;
⳵␸p
⳵y
=
␧d
␧p
⳵␸d
⳵y
+
e
␧p
冕共ni − ne兲dx, 共3.8兲
⳵ni
⳵y
= 0, 共3.9兲
ne = ␥d冉␮i
␮e
冊ni. 共3.10兲
Equation 共3.8兲 ensures a diminishing electric intensity across
the electrodes through the surface charge accumulation dur-
ing an ac cycle. It is also the fundamental mechanism of the
self-limiting characteristic in preventing DBD transition to
spark.
The role of the exposed electrode and the dielectric bar-
rier surface reverses when the polarity of the ac field
switches to ␸共t兲⬍0. The exposed electrode now functions as
the cathode, the secondary emission by electron collision oc-
curs over it and the coefficient of the emission on the metal
surface, ␥m, is different from that of the dielectrics.
To complete the boundary conditions specification for
the DBD simulation, the vanishing gradient condition is im-
posed uniformly for all three dependent variables at the far-
field boundary of the computational domain. For the multiple
length- and time-scales phenomenon; the ionization and re-
combination of charge particles is considered to be instanta-
neous in comparison with the time scale of the alternative
electric field. Therefore, no separate boundary condition
treatment at the switching instant is imposed.
IV. NUMERICAL PROCEDURE
For the present investigation, the temporal accuracy in a
relatively short duration is essential; therefore, a greater
stability-bound implicit scheme for a larger time step is not
necessary. Instead a successful iterative relaxation procedure
is selected. As a consequence, the distinction between tem-
poral and iterative accuracy is diminished. By this formula-
tion all electrodynamics equations, including the Poisson
equation of plasmadynamics, can be cast in the flux vector
form. The governing equations; Eqs. 共2.1兲–共2.3兲 in the flux
vector form are;
⳵U
⳵t
+
⳵Fx共U兲
⳵x
+
⳵Fy共U兲
⳵y
= S. 共4.1兲
Where the dependent variable is U
ជ =U
ជ 共ne,n+,␸兲, the flux
vector is given as F
ជ =F
ជ共⌫e,⌫+,␸兲, and the inhomogeneous
right-hand-side terms become S
ជ =关␣共E,p兲兩⌫e兩
−␤n+ne,␣共E,p兲兩⌫e兩−␤n+ne,−␳e/␧,兴.11,15
The specific ex-
pressions can be easily obtained from Eqs. 共2.1兲–共2.3兲 thus
are not repeated at here. The basic formulation in delta form
is achieved by taking the difference of dependent variables in
consecutive time levels, ⌬U=Un+1
−Un
, which is achieved
by flux vector linearization as an approximate Riemann
problem.11
The governing equation in diagonal dominant, alternat-
ing direction implicit 共DDADI兲 delta form acquires follow-
ing expression:11,15
⳵共⌬U兲
⳵t
+ 冋⳵
⳵x
共⌬Fx兲 +
⳵
⳵y
共⌬Fy兲册Diag
= − 冋⳵
⳵x
共Fx
n
兲 +
⳵
⳵y
共Fy
n
兲册+ Sn
. 共4.2兲
In the above formulation, all off-diagonal terms of the dis-
critization are moved to the right-hand-side of the finite-
difference approximation to maintain diagonal dominance
for enhancing the computational stability.11,15
By so doing,
an axiom of the optimal numerical simulation is fully real-
ized in that the physical fidelity is controlled by the right-
hand-side of the approximation. The left-hand-side of the
approximation is pure numerical and is constructed to main-
tain the computational stability. The temporal accuracy is
113302-3 J. S. Shang and P. G. Huang J. Appl. Phys. 107, 113302 共2010兲
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5. ensured by adopting the third-order Runge–Kutta scheme for
the internal iterations to resolve the dynamic event of 10 kHz
range, thus the flux limiter of the split flux vectors is not
required.
For two-dimensional computations, the electromagnetic
field is maintained by the applied ac electrical potential up to
4.0 kV and at a frequency of 10 kHz; it is a time dependent
phenomenon. For the DBD configuration, the high grid-point
density is required in the contiguous regions between elec-
trodes. Three mesh systems of 共192⫻302兲, 共382⫻602兲, and
共762⫻1302兲 were used for numerical resolution study.11
The
grid system of 共382⫻602兲 has been shown to be sufficient in
describing the physics thus was chosen for the bulk of the
present numerical simulations.
A typical DBD configuration for flow control is modeled
and the schematic is depicted in Fig. 1. The exposed and
encapsulated electrodes have the same dimension of 10 mm
long and a thickness of 0.102 mm. The maximum horizontal
separation distance between electrodes is 3 mm and the en-
capsulated electrode is embedded in polystyrene by a vertical
recess of 0.127 mm. The grid spacing is highly clustered
over the electrodes, the adjacent domain between electrodes,
and is gradually stretched toward the far field. The minimum
grid spacing in x is 10−3
mm, so the electrode is defined by
100 mesh points with grid density clustering at the edges.
The minimum grid spacing in the y direction is less than
3.0⫻10−4
mm immediately adjacent to the electrodes.
The temporal sequential computations have been initi-
ated from the zero electric potential difference state, thus the
initial value prescription is straightforward. The time-
dependent solution is driven by the externally applied ac
field. The time advancement is regulated by satisfying the
internal iterative convergence tolerance defined by a normal-
ized global norm of 10−6
. A large amount of effort is devoted
to maintain the computational stability which has offered a
significant challenge to the DDADI scheme.
V. CYCLIC DISCHARGE STRUCTURES
As it has been previously discussed, the DBD structure
consists of numerous microdischarges with different charac-
teristics during an ac cycle.3,8
The spatial and temporal scales
of individual microdischarge are numerically irresolvable at
present. Therefore, all current numerical simulations can
only be considered as a global description of DBD.
In Fig. 2, the fundamental self-limiting characteristic of
the DBD is convincingly captured by the present results at
the externally applied electrical potential of 3.0 and 4.0 kV
across the overlapped electrodes. At the quiescent atmo-
spheric condition, the discharge breakdown takes place at a
voltage of 2.8 kV before the externally applied electrical
field reaches its peak values for both polarities. Then a lower
and constant electric potential is maintained by the conduc-
tive current and the surface charge accumulation on the elec-
trodes within the discharge. In the positive polarity phase,
the discharge occurs when the positive-going potential ex-
ceeded the breakdown voltage and continues until the
negative-going external field falls beneath the breakdown
threshold. The identical behavior is also observed for the
negative polarity phase. During the initial breakdown pro-
cess, a sudden drop of the electric potential with respect to
time induces a surge of the displacement current in the dis-
charge. In experimental measurements, this surge indicates
the existence of multiple microdischarges and also knows to
lead to a train of pulsations in the electrical circuit.1–3,17
Similarly the sudden drop of the electrical potential has also
generated nonphysical oscillations known as the Gibbs phe-
nomenon in some numerical simulations.7–11
Figure 3 summarizes the relationship of the breakdown
voltages and the gap distances between the exposed elec-
trode and the encapsulated electrode. The gap distances be-
tween electrodes increase from a contagiously overlapping
position to the distances from 1 to 3 mm. The breakdown
voltages of different gap distances increase as the gap dis-
tance is widened. The lowest breakdown voltage is 2.8 kV
when the horizontal gap distance vanishes, and the highest
voltage is around 2.98 kV when the gap distance is raised to
3.0 mm. These observations are identical for both the posi-
tive and negative polarities in the ac cycle and agree with
experimental data.17
In essence, the computational results
based on the electrodynamic equations honor Paschen’s
law.12
The important comparison of the periodic voltage-
current characteristic of computational results with experi-
mental data over 1000 microseconds 共five ac cycles兲 is de-
picted in Figs. 4. The comparison with data at the externally
FIG. 1. 共Color online兲 Schematic of asymmetric DBD configuration for flow
control.
FIG. 2. 共Color online兲 Self-limiting characteristic and breakdown voltage of
DBD.
113302-4 J. S. Shang and P. G. Huang J. Appl. Phys. 107, 113302 共2010兲
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6. applied electrode potential of 4.0 kV reveals a good overall
affinity between data and computational results at the instant
of breakdowns. Prior to the breakdown, the electrical current
consists only of the displacement component. After the
plasma ignition, the electrical current has an additional con-
ductive component of the DBD. The magnitude of this com-
ponent is relatively minuscule and indicates a current density
less than 0.008 mA/cm. This calculated value agrees well
with data collected over a wide group of experiments.1,17
The only discrepancy between results around the break-
down is that the data indicates the multiple oscillations in the
electric current but only appears as a single spike in the
computational simulation. It is understandable because the
randomly distributed, highly luminous, and concentrated mi-
crodischarges propagating from the electrode are not resolv-
able by any state-of-the-art numerical procedures.8–11
In
computational simulations, the Gibb phenomenon at the
breakdown has often been incorrectly identified as the micro-
discharges but is completely eliminated from the present
computation. In short, the present computational simulation
has correctly captured the onset of breakdown and the self-
limiting behavior of DBD.
In Fig. 5, the reduced electrical field potential within the
DBD field is made evident by the charge number density
concentration over the dielectrics or the exposed electrode.
The time-dependent computational results are depicted at the
instants when the peak values of the EMF of ⫾3.0 kV are
applied. At this instant in time, when the exposed electrode
carries a positive voltage, the secondary electrons emission
from the dielectrics creates an overwhelming positively
charged particles accumulation over the barrier surface to
reduce the electrical potential of the DBD field. At the same
instant, the electron propagation is restrained by the anode
and most electrons are concentrates over the edge of the
anode. When the electrical polarity is reversed on the ex-
posed electrode, all positively charged ions are now expelled
from the dielectrics and concentrate near the lower edge of
the exposed electrode. At the same time, the electrons are
accelerated from the exposed electrode toward the dielec-
trics. The accumulated electrons over the dielectrics diminish
the electrical intensity within the DBD field. The propaga-
tions of the positively charged ions and electrons within an
ac cycle are clearly illustrated by the computational simula-
tion.
VI. CHARGE SEPARATION AND ELECTRODYNAMIC
FORCE
For flow control, the basic mechanism is the well-known
electric wind, which is associated with the electrodynamic
force of the DBD. The movement of neutral medium is the
results of momentum transfer between the positive charged
ions and neutrals.1,3,12
The force acts on the ion in DBD is of
the same nature as in a corona discharge. In fact, the
FIG. 3. Breakdown voltage vs electrodes gap distance.
FIG. 4. 共Color online兲 Comparison of voltage and current with experimental
data at EMF=4.0 kV, 10 kHz.
FIG. 5. 共Color online兲 Space charge contours during an ac cycle, EMF
=3.0 kV, 10 kHz.
113302-5 J. S. Shang and P. G. Huang J. Appl. Phys. 107, 113302 共2010兲
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7. electrode-directed corona discharge is a component of the
DBD.3,7
The force due to space charge separation can be
given as
F
ជ ⬇ e共n+ − ne兲E
ជ + O冉eD+
␮+
ⵜ n+,
eDe
␮e
ⵜ ne冊. 共6.1兲
By a simple order of magnitude analysis, the force generated
by the electric field intensity is by far the dominant mecha-
nism over the diffusion. The electrodynamic force in electric
potential becomes;
F
ជ = e共ne − n+兲 ⵜ ␸. 共6.2兲
Based on the Eq. 共6.2兲, the orientation of the electrodynamic
force is determined by the combined signs of the gradient of
electric potential and the relative magnitude of electron and
ion number densities.
In other words, the magnitude of the electrodynamic
force is controlled by the electrical field intensity and the
charge separation of the DBD field. The latter can be ob-
tained from the instantaneous electron and ion number den-
sity computations. Figure 6 displays this information at the
instant after the externally applied electrical potential ex-
ceeds the breakdown voltage and the discharge reaches its
steady state. The magnitude of the applied EMF is 4.0 kV
across the overlapping electrodes. First of all, the effective
electrical potential within the DBD field is consistently lower
than the externally applied field due to the conductive current
of the discharge. The instantaneous and maximum value of
共n+−ne兲 over the dielectric barrier attains a value of 6.11
⫻1011
cm−3
. The resultant force according to Eq. 共6.2兲 is
uniformly directed from the exposed electrode to the dielec-
tric barrier and has a magnitude of 9.15⫻105
dyne/cm3
.
This result reaches an order of magnitude agreement with the
estimates of Beouf et al.7
and is greater than the maximum
force of 5.96⫻105
dyne/cm3
generated by the EMF of 3
kV.11
However, it needs to be reminded that the maximum
electrodynamic force only exists within the thin plasma
sheath and for a very short time span.
When the polarity the ac cycle is reversed, the electric
field is vastly different and more complex than that of the
positive EMF of 4.0 kV. Figure 7 displays the electrical po-
tential and charged particle number density distributions of
the instantaneous DBD field. All ions are repulsed from the
dielectric surface and clustered around the lower corner of
the exposed electrode. At the same instant, a large number of
electrons are propagating over the dielectric barrier away
from the corner region of the electrodes. The sign of electric
potential gradient is now positive from the exposed electrode
toward the dielectric barrier. According to the present com-
putation, the plasma sheath is extremely thin 共less than 0.021
mm兲 and its thickness decreases with a lower value of the
electron secondary emission coefficient. The maximum value
of charge separation, 共n+−ne兲 near the intersection of elec-
trodes is 1.01⫻1011
cm−3
, and produces a much smaller
electrodynamic force of 1.45⫻105
dyne/cm3
than the posi-
tive polarity field. This value is greater than that when the
magnitude of EMF of 3.0 kV is simulated 共6.95
⫻104
dyne/cm3
兲.
At a short distance of 0.05 mm away from the intersec-
tion of the exposed electrode and the dielectric barrier 共x
=0.60 cm兲, the near surface electrons concentration exceeds
that of the ions. As the consequence, the electrodynamic
force due to charge separation reverses its direction; now
again is oriented from the exposed electrode toward the di-
electrics. However, the magnitude of this force is generated
by a substantially lower electrical intensity and charged par-
ticles number density. This electrodynamic force is four or-
ders of magnitude lower than that near the intersection of
electrodes to become negligible.
The computational simulation includes only the electron
and ion components; therefore, the trajectory of force vectors
is not altered by collisions with the neutral particles. The
time-average magnitude over an ac cycle is presently unde-
termined but the value is expected to be much lower than the
instantaneous value.
From the present electrodynamic formulation and the ba-
sic physics of discharge separation, the direction of the force
FIG. 6. Electric field and charge number density distribution over dielectric,
EMF=4.0 kV and ␸⬎0.
FIG. 7. Electric field and charge number density distribution over dielectric,
EMF=4.0 kV and ␸⬍0.
113302-6 J. S. Shang and P. G. Huang J. Appl. Phys. 107, 113302 共2010兲
Downloaded 28 Jul 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

8. exerted on the charge particles is alternating from the ex-
posed electrode toward the dielectric barrier and reverse. In
the jargon of DBD operation, the force is a push-pull mode
and with a pulse at the switching of polarity.3
Certainly, there
is the possibility of a dynamic transition in the polarity
switch but the magnitude of the force should be negligible
because the decreasing applied electric potential is beneath
the breakdown threshold.3
Finally, it must be pointed out that
the momentum transfer between the charged and neutral par-
ticles can only be taken into account by solving the electro-
dynamic equations together with the magnetofluid-dynamics
equations.
VII. CONCLUDING REMARKS
The dielectric barrier discharge in air is qualitatively
simulated by solving the drift-diffusion plasma model using
the diagonal-dominant, alternating direction implicit scheme
in the delta formulation. The stiff governing partial differen-
tial equations require an exceptional high numerical reso-
lution for describing the multiple microdischarges that is be-
yond the reach of the state-of-the-art computational
capability. Therefore, only the essential physics of DBD can
be duplicated by using the correct boundary conditions of
electromagnetic theory and allows the self-limiting corona-
to-spark transition to be highlighted.
From computational results of the time-dependent
charge number densities and the electrical field intensity, the
net force acts on the charged particles is found to have an
alternative orientations from the exposed electrode toward
the dielectric barrier and reverse. The maximum and instan-
taneous electrostatic force induced by charge separation is
9.15⫻105
dyne/cm3
. The time-averaged value over a com-
plete alternating current cycle is expected to be much lower
and the integrated electrodynamic force is directed from the
exposed electrode toward the dielectrics.
ACKNOWLEDGMENTS
Authors are thankful for the support from Center of Ad-
vanced Power and Energy Conversion 共CAPEC兲, Wright
State University/Air Force Research Laboratory. The spon-
sorship of Dr. Fariba Fahroo and Dr. John Schmisseur of
AFOSR to the present investigation is sincerely appreciated.
Authors also are in debt to Dr. J. Menart of Wright State
University and Dr. B. Ganguly of Air Force Research Labo-
ratory for their fruitful discussions.
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