st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Numerical Simulation of Spatiotemporal Behavior of Electric Double Layer
in Aqueous Solution in contact with Gas-phase Plasma Sheath
T. Shirafuji1 and A. Nakamura2
1
Dept. Physical Electronics and Informatics, Osaka City University, Osaka 558-8585 Japan
Abstract: Numerical simulation of electric double layer in contact with a dielectric barrier
discharge has been performed. Preferential appearance of positive or negative ions has been
observed on the top surface of the liquid. This means that the preferential interaction can be
realized between gas-phase plasma species and liquid phase ions.
Keywords: Plasma, Sheath, Liquid, Electric Double Layer, Simulation
1. Introduction
Plasmas in contact with liquid have attracted much attention because of their potential applications such as
materials syntheses, treatments, and also medical treatments of living tissues [1-3]. In the plasma processing in
contact with liquid media, the most important part is the
plasma-liquid interface, which consists of two
space-charge layers. One is the “sheath” in the gas-phase
plasma. Another is the “electric double layer” (EDL) in
the liquid phase. Both of them are governed by the spatial
profile of charged-particle density around them, and form
local electric fields as predicted from the Poisson equation.
In the plasma processing in contact with liquid media,
particles (electrons, ions, neutrals and photons) impinge
onto the gas-liquid interface to make interactions with the
liquid-phase species. In many cases, however, this phenomenon has been treated only with simple Henry’s law
without considering the EDL, even though the EDL is the
place where the impinging gas-phase species encounter
the primary reactions with liquid-phase species.
Since the chemical species dissolved in the liquid-phase
mostly exist in the form of ions, chemical reactions at the
interface should be affected by existence of the EDL. For
example, the polarity of the EDL must change the lineup
of the liquid-phase ions which are awaiting gas-phase
species at the interface. When we utilize time-varying
applied voltage, we must also pay attention to the fact that
formation of the EDL takes finite time, which is governed
1 mm
Glass(Eps=4)
1 mm
Ar (Atm. Press.)
by the magnitude of mobility and diffusion coefficient of
the liquid-phase ions.
In order to properly design the plasma processing in
contact with liquid phase, we need to understand spatiotemporal behavior of the EDL in contact with the plasma
sheath. In this work, we have performed numerical calculation, and report its preliminary results in this paper.
2. Model Description
The model geometry is shown in Fig. 1, which has a
simple DBD structure being composed of top electrode /
dielectric (glass) / gas (Ar) / liquid / bottom electrode.
Relative dielectric constant of the glass is 4. The difference from a conventional DBD reactor is that the bottom
electrode is covered with liquid, which has both conductive and dielectric characteristics. Relative dielectric constant of the liquid is 80, which corresponds to H2O. Electrical conductivity of the liquid is governed by transport
parameters of positive and negative ions in the liquid,
which are listed in Table 1 together with those of
gas-phase electrons and Ar ions [4]. The values of
transport parameters of ions in the liquid are slightly
modified from those for H+ and OH- [5] for investigating
effects of magnitude of transport parameters of ions in the
Table 1. Transport parameters (mobility μ and diffusion
coefficient D) of liquid-phase ions, and those of
gas-phase positive ion and electron.
μ+ = kPos×50×10−8 m2/Vs
μ− = kneg×50×10−8 m2/Vs
μAr+ = approx.10−4 m2/Vs
μe = approx.10−2 m2/Vs
D+ = kPos×10×10−9 m2/s
D− = kneg×10×10−8 m2/s
DAr+ = approx. 10−6 m2/s
De = approx. 10−1 m2/s
Vapp = 500 V
Freq = 20 kHz
liquid.
Table 2. Gas-phase reactions.
0.5 mm
Liquid(Eps=80)
Fig. 1 Model geometry for the simulation of the DBD
in contact with liquid.
Reactants
e + Ar
e + Ar
e + Ar*
Ar* + Ar*




Products
2e + Ar+
e + Ar*(3P)
2e + Ar+
e + Ar + Ar+
Rate Const.
Cross Section
Cross Section
Cross Section
3.37x108 m3/(s mol)
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
2.1 Gas-phase model (DBD)
The gas employed in the DBD is Ar, and gas-discharge
simulation has been performed by using local field approximation.
The gas-phase reactions used in this work are listed in
Table 2, in which only major reactions are taken into account. Regarding the electron impact ionization and excitation (to Ar(3P) metastable states), their reaction rates are
calculated with their cross-section data together with
electron energy distribution function determined by solving Boltzmann transport equation with a given E/N. Electric field is determined through Poisson’s equation and
spatial profile of charged particles.
Regarding loss processes, charged particles and Ar* are
assumed to be lost only at the wall surface with sticking
probability of unity. Sticking probability of Ar is assumed
to be zero.
2.2 Liquid-phase model (EDL)
In this study, we have adopted the model by Morrow et
al [5]. The liquid medium employed in this work is ideal
de-ionized (DI) water under normal temperature and
pressure for simplicity. Although the concentration of ions
in the DI water is small, it is governed by following equilibrium reactions;
Generation:
H2O  H+ (H3O+) + OH−,
Recombination:
H+ (H3O+) + OH−  H2O.
Although H+ in the water should be treated as H3O+, we
refer to positive ions in water as simply H +. The rate constants for the generation and recombination reaction are as
follows;
G = 8.41×1023 m−3 s−1,
k = 2.32×10−16 m3 s−1.
The equations to be solved for obtaining spatial profile
of the H+ and OH- are as follows;
N
t
N
t
x
x
D
N
x
x
D
N
x
x
N v
G kN N ,
N v
G kN N ,
where positive and negative subscript represents that the
parameter is for H+ and OH-, respectively. Drift velocity
of the ions is calculated with their mobility. Electric field
in the liquid is calculated through Poisson’s equation with
spatial profile of the ions.
In our model, the liquid is in contact with plasma, while
the liquid in the Morrow’s model is sandwiched by insulating electrodes, which is employed for the purpose of
simply applying potential without external charge injection into liquid phase. Since we have plasma-liquid interface, we must pay attention to the charge injection due to
electron and ion flux onto the surface of liquid.
In our model, the boundary condition at the liquid surface and at the bottom electrode is assumed to have symmetric concentration profile. Regarding the liquid surface,
electrons and ions impinge onto it. In order to keep current conservation law, we have employed very simple
boundary condition where all the charges brought from
gas-phase are consumed to produce same amount of ions
with same polarity in the liquid. If the impinging
gas-phase ions and liquid phase ions have different charge
polarity, we have employed neutralization of the ions on
the top surface of liquid. Although we must pay attention
to the depth which is affected by the impinging gas-phase
ions, it is assumed to be zero for simplicity at present.
3. Results and Discussion
3.1 Spatial Profile
Figure 1 shows spatial profile of potential, concentration of gas-phase electrons and ions, concentration of liquid-phase positive and negative ions around the top and
bottom of liquid. Figure 1(a) and 1(b) is the results at the
phase when the electron and ion flux onto the liquid becomes maximum value, respectively. We refer these two
phases as “electron flux” phase and “ions flux” phase,
respectively.
When the voltage of the top electrode is negative as in
Fig. 1(a), electrons move toward the liquid surface. The
electron flux induces negative ions at the top surface of
the liquid. Concentration of the induced negative ions is
much larger than that around the bottom electrode. At the
bottom electrode with no charge injection, the EDL is
formed as a result of only potential drop from the top to
the bottom of the liquid, which is 7.7 V in this case.
When the voltage of the top electrode is positive as in
Fig. 1(b), positive Ar ions move toward the liquid surface.
The ion flux induces positive ions at the top surface of
liquid. Concentration of the positive ions at this “ion flux”
phase is lower than that of the negative ions at the “electron flux” phase described above. This is due to difference
in the flux of electrons and ions, which is caused by the
difference in the mobility of them. Electrons flux is very
high but soon disappears, while ion flux is not so high but
duration is longer than electron flux.
3.2 Effects of Transport-Parameter Magnitude
In order to investigate effects of transport-parameter
magnitude of liquid-phase ions, we have performed simulation under the following conditions; (a) positive ions
are slower than negative ions, (b) positive and negative
st
0.4
t = 8 us
Elec. Flux on Liq. Top
N-
0.2
N+
0.6
0.4
Liquid Bottom=>
t = 8 us
N+
N-
0.2
0.0
1.4980 1.4990 1.5000
-3
Postion (x10 m)
(a) “Electron Flux” Phase (t=8 us)
0
-2
-4
2.4V
t = 30 us
Ion Flux to Liq. =>
-1.0
0.0
1.0
-3
Position (x10 m)
1.0
0.8
0.6
0.4
0.2
<=Liquid Top
t = 30 us
Ion Flux on Liq. Top
N+
N-
0V
Conc. (x10
17
2
2.0
-3
m )
2
Liq.
-3
0.8
Gas
0.0
1.0000 1.0010 1.0020
-3
Position (x10 m)
1.5
<=Dielec. Gas Liquid=>
Ion Flux to Liq. =>
1.0
0.5
Ar+
e
0.0
0.0
0.5
1.0
-3
Position (x10 m)
100
m )
0.0
0.0
0.5
1.0
-3
Position (x10 m)
1.0
Potential (x10 V)
17
0.0
1.0000 1.0010 1.0020
-3
Position (x10 m)
e
Dielec.
18
0.6
<=Liquid Top
0.5
4
Conc. (x10
0.8
Ar+
-3
-1.0
0.0
1.0
-3
Position (x10 m)
1.0
1.0
m )
-4
-3
-7.7V
m )
-2
<=Dielec. Gas Liquid=>
Elec. Flux to Liq. =>
1.5
21
0
0V
20
-3
m )
21
Conc. (x10
t = 8 us
2
Elec. Flux to Liq. =>
2.0
Conc. (x10
-3
Liq.
m )
Gas
Conc. (x10
Dielec.
Conc. (x10
4
2
Potential (x10 V)
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
80
60
Liquid Bottom=>
Nt = 30 us
40
N+
20
0
1.4980 1.4990 1.5000
-3
Position (x10 m)
(b) “Ion Flux” Phase (t=30 us)
Fig. 2 Spatial profile of potential, gas-phase electrons and ions, liquid-phase positive and negative ions around the top
and bottom of liquid. (a) and (b) is the results at the phase when dominant flux onto the liquid is electron flux and ion
flux, respectively.
ions are identical, and (c) negative ions are slower than
positive ions.
In order to investigate how the gas-phase species interact with the species in the EDL, we have plotted
gas-phase flux on the liquid surface and concentration of
ions on the top surface of liquid.
Figure 2 shows the results. Fig. 2(a) shows the flux of
electrons and ions onto the liquid surface as a function of
time. Since the feature of the flux was not affected by the
transport parameters of liquid, only one figure is presented in the figure.
Figure 2(b), 2(c) and 2(d) show the concentration of
positive and negative ions in the case of (b) positive ions
are slower than negative ions (kPos=0.1, kNeg=1.0), (c) positive and negative ions are identical and (d) negative ions
are slower than positive ions (kPos=1.0, kNeg=0.1).
As can be understood from Figs. 2(b), 2(c) and 2(d),
concentration of positive and negative ions increases on
the top surface of liquid when positive and negative
charge is supplied from gas-phase plasma, respectively.
Then, it decreases due to drift, diffusion and/or recombination reaction. In the case of 2(c), where the positive and
negative ions are identical, the rate of increment and decrement is also identical. In the case of 2(b) and 2(d), they
are different because of the difference in the transport
parameters. Slower ions remain on the top surface while
faster ions are extracted from the top surface.
Since the duration of contribution of the neutral radical
species onto the liquid surface is considered to be longer
than that of electrons and ions, the time-dependency of
the neutral radicals is broad, and is not like the electrons
and ions shown in Fig. 2(a). This implies that there is a
possibility of semi-preferential reaction between the
gas-phase chemical species and liquid phase ions. In the
case of gold nanoparticle synthesis, positive and negative
ions are H+ (m/z = 1) and AuCl4- (m/z = 339), respectively,
in which negative ions is slower than positive ions because of difference in their molecular weight. Thus, we
can expect that there are preferential reactions between
AuCl4- and gas-phase radicals.
3.3 Effects of Frequency
The effect of difference in the transport parameters is
considered to be pronounced if we employ different frequency. Thus, we have investigated effects of frequency.
Fig. 3 shows concentration of positive and negative ions
in the liquid top surface in contact with Ar-DBD operated
with 2, 20 and 200 kHz. In this calculation, negative ions
are slower than positive ions (kPos=1.0, kNeg=0.1). The
characteristics of the flux of charged particles from the
gas-phase plasma are similar to that of Fig. 2(a) although
it is not shown in the Fig. 3.
As can be understood from Fig. 3, in the case of low
frequency of 2 kHz, concentration of both of positive and
negative ions returns to equilibrium value for them because enough time is given for the ions to reduce their
concentration. With increasing frequency, slower ions are
surely left on the top surface. In the case of 200 kHz,
concentration of slower negative ions is always greater
than that of faster positive ions. Although their concentration ratio is not high in this calculation, this implies that
preferential reaction between liquid-phase ions and
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Fig. 4 Ion concentration in the liquid top surface in
contact with DBD operated with different frequency.
Fig. 3 (a) Flux of ions and electrons from gas-phase
plasma, and concentration of ions on the top surface of
liquid in the case of (b) positive ions are slower than
negative ions, (c) positive ions and negative ions has
the same transport parameters and (d) negative ions
are slower than positive ions.
gas-phase radicals can be pronounced by employing
higher frequency.
4. Conclusion
Numerical simulation of Ar-AP-DBD in contact with
liquid has been performed, and effects of transport parameters of ions in liquid medium have been investigated.
The results of numerical calculation predict that there are
possibility of preferential reactions between gas-phase
radicals and liquid-phase ions, in which slower ions preferentially appear on the top surface of liquid and interact
with gas-phase species. Since this is only numerical prediction without experimental proofs, we are planning to
perform experiments for proving the prediction obtained
in this work.
5. Acknowledgements
This work has been partly supported by the
Grant-in-Aid for Scientific Research on Priority Area
"Frontier science of interactions between plasmas and
nano-interfaces" by MEXT, Japan.
6. References
[1] B. R. Locke, M. Sato, P. Sunka, M. R. Hoffmann and
J. S .Chang: Ind. Eng. Chem. Res. 45, 882 (2006).
[2] O. Takai: Pure Appl. Chem. 80, 2003 (2008).
[3] P. Bruggemann and C. Leys: J. Phys. D: Appl. Phys.
42, 053001 (2009).
[4] S. C. Brown, Basic Data of Plasma Physics (MIT
Press, 1959).
[5] R. Morrow and D. R. McKenzie: Proc. Royal Soc. A
468, 18 (2012).