22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Numerical study on the interaction between surface micro-discharge and
deionized water
Z.C. Liu1, D.X. Liu1, C. Chen1, D. Li1 and M.G. Kong1,2
1
Center for Plasma Biomedicine, State Key Lab of Electrical Insulation and Power Equipment, Xi’an Jiaotong
University, Shaanxi, P.R. China
2
Frank Reidy Center for Bioelectrics, Old Dominion University, Norfolk, Virginia, U.S.A.
Abstract: Cold atmospheric-pressure plasmas have great prospects in diverse applications
like environmental protection, biomedicine, nanotechnology, etc. In such applications the
targets to be treated are often humidor even in aqueous solution. Reactive species
generated by plasma should pass through a water layer before acting on the targets. In this
paper, a hybrid model is developed to investigate the mass transfer and chemical processes
between a surface micro-discharge in humid air and the downstream deionized water. This
model includes three sub-models, namely zero-dimensional chemical kinetic model for the
surface plasma, one-dimensional diffusion model for the air gap region, and onedimensional drift-diffusion model for the liquid region. A total of 56 species and 756
reactions are incorporated.
The distributions of reactive species in liquid are obtained and the underlying mechanism is
discussed. It is found that only HNO 2 , HNO 3 , O 3 , H 2 O 2 , N 2 O and N 2 O 5 can pass though
the 1 cm air gap and reach the surface of liquid, but more short-lived species exist in the
liquid. The short-lived species are generated in-situ in the liquid, and they can transform
reciprocally with the participation of ozone and hydrion. The penetration speed of species
in liquid decreases modestly as the growing of plasma-on time, and hence no species can
arrive to the liquid bottom, 1 cm in depth, after 10 minutes of treatment. The density of
reactive species increases with plasma-on time, and the densities of H 2 O 2 , O 3 , nitrite and
nitrate are above 1nM after 10 minutes of treatment.
Keywords: surface micro-discharge, mass transfer, penetration, chemical process
1. Introduction
Cold atmospheric-pressure plasmas have a great future
in diverse application fields, such as environmental
protection and biomedicine [1-2]. However, most of
these applications are in humid circumstance, and reactive
species from gas plasmas have to dissolve in liquids
before finally acting on the targets. The mass transfer and
chemical processes in both gaseous and aqueous phases
are complex thus imperfectly understood. In recent years,
numerical models were developed for studying the
interaction between gas plasma and aqueous solution, but
most of the models are zero dimensional, only 2 - 3
models have space resolution ability [3-4]. The models
presented in ref. [3-4] are for direct plasma-water
interactions for which the fundamental mechanism in the
gas-liquid interface is not well known [5], and hence
many assumptions have to be made for the model
development.
In this paper, surface micro-discharge (SMD) in air is
selected to be the plasma source, and deionized water is
put in the downstream region 1 cm from the plasma. The
ions generated by plasma cannot pass through this air gap
in the reason of that their effective diffusion distances are
no more than tens of microns. This indirect plasma-liquid
interaction is beneficial to modelling study because many
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physicochemical processes can be neglected.
The surface micro-discharge generates reactive species,
and then they transfer into the air gap. Some reactive
species are able to transfer though the air gap and dissolve
in liquid. For plasma, zero-dimensional chemical kinetic
model is selected to calculate the chemical process. And
one-dimensional drift-diffusion model is established for
transfer and chemical kinetic in air gap. The mass
transfer between the air gap and liquid is described by
Henry' Law. One-dimensional drift-diffusion model is
chosen to describe the drift motion, the diffusion motion
and the aqueous chemistry of species in liquid region.
These three sub-models are calculated simultaneously,
and reaction rates as well as density of species in three
regions are obtained.
2. Description of the computational model
This hybrid model consists of three sub-models, namely
zero-dimensional chemical kinetic model for microdischarge, one-dimensional diffusion model to describe
the dynamics and chemical kinetic in air gas region, and
one-dimensional drift-diffusion model for species in
liquid region. And the model is structured by 56 species
and 756 chemical reactions. The species in different
regions are listed in Table 1, and the detail information
1
about reactions can be gotten in ref. [6-7].
Table 1. Species considered in the model.
Plas
ma
regio
n
Cation N+ , N+2 , N+3 , N+4 , NO+ , N2 O+ , NO+2 , H+
s
H+2 ,H+3 ,O+ , O+2 , O+4 , OH+ , H2 O+ , H3 O+
Anions e, O- , O-2 , O-3 , O-4 , NO- , NO-3 , H- , OH- ,
N2 O- ,NO-2
∂ng ,i
∂t
Neutra N(2 D), N2 �A3 Σ�, N2 �B3 Π�, H, N, H2 ,
ls
N2 , H2 O, O(1 D), O, O2 (a1 Δ), O3 , OH
HO2 , H2 O2 ,O2 , NO, NO2 , NO3 , N2 O3
N2 O4 , N2 O5 ,HNO2 , HNO3 , N2 O, HN
Air
NO, N2 O, NO2 , NO3 , N2 O3 ,N2 O4 , N2 O5 , HNO
gap
HNO2 ,HNO3 , N, N2 , O2 , O, O2 (a1 Δ), O3 , OH
regio HO , H O , H , H O
2
2 2
2
2
n
Liqui O, O3 , OH, HO2 , HO3 , H2 O2 , N2 , O2 , H2 O, H
d
N2 O3 ,NO, NO2 , NO3 , N2 O4 , N2 O5 , HNO2 , H+
regio HO-2 , OH- , O- , O-2 , O-3 , NO-2 , NO-3 , O2 NOOH,
n
O2 NOO- , ONOO- , ONOOH, HNO3 , N2 O
The process of SMD generated in humid air is
described by zero-dimensional chemical kinetic model,
which is made up of 53 species and 624 reactions, based
on SMD model of Sakiyama[6]. Clearly, the mass
conservation equation is as follows:
∂n p ,i
Γ pg ,i
= R p ,i −
∂t
dp
(1)
where n p represents the number density of species in the
plasma, R p the reaction rate, Γ pg the particle flux between
the plasma region and the air gap region, and d p the
thickness of the plasma region. The d p is set to be 100μm,
according to the typical radius of discharge filaments.
The subscript i represents the ith species.
The energy conservation equation and the estimated
equation of electric field strength are provided below,
respectively:
2

Vg 
av 
P
Z i µi n p ,i  EG +
dt
=
∑
∫

T 0 i
dg 


 1  t − 5τ pls   (3)
=
EG Em exp  − 

 2  τ pls  



dp
T
(2)
where P represents the cycle-average power density, set
to be 0.05 W/cm2, and T = 100 μs is the period of a
discharge cycle. μ is the mobility and Z is the absolute
value of charge. E g is the electric field which is assumed
to have a Gaussian-like pulsed profile, and more detail
information about this assumption in ref. [6]. V g (= 1 kV)
is the discharge gap voltage, calculated by means of the
2
V-Q Lissajous figure. And d g (=1mm) stands for the
average length of discharge filaments.
Between the deionized water and plasma region, there
is 1cm air gap. In this region, the one-dimensional
diffusion model is adopted to calculate reactions and
diffusion, consisting of 21 species and 63 reactions. The
governing equation is as follows:
− Dg ,i ∇ 2 ng ,i =
Rg ,i
(5)
where n g,i stands for the density of ith specie, D g,i is its
diffusion coefficient in air, and R g,i is the sum of reaction
rates of ith specie. In addition, the value of D g,i is listed
in ref. [6].
Not all species calculated in air region have the ability
to penetrate into the liquid region. Most of species cannot
go through the air gap, like short-lived oxygen and
nitrogen species, some low concentration species. The
density relationship of these species is described by the
Henry' Law, and the Henry's coefficients can be found in
ref. [3, 7]. For the liquid region, a one-dimensional submodel is constructed, with a view to the drift motion, the
diffusion motion and the aqueous chemistry, and made up
of 32 species and 103 reactions. The more details are
revealed in ref. [3, 7]. Considering that the uneven
distributions of ions in liquid could cause the eigen field,
the governing equations contain the Possion's equation for
the electric field and the drift-diffusion equation for the
mass conservation, as follows:
∂nl ,i
+ ∇ ⋅ ( − Dl ,i ∇nl ,i + Z i ul ,i nl ,i E ) = Rl ,i
∂t
∂E
= ∑ Z i nl ,i / ε
∂x
(6)
(7)
where n l represents the number density of species in the
liquid region, D l the diffusion coefficient in water, μ l the
mobility of the charged species in water, R l the aqueous
reaction rate, and ε the dielectric constant. And, the value
of D g,i is listed in ref. [3].
Considering the water vapour in air, the initial gas
composition is 76.63% N 2 , 20.37% O 2 and 3% H 2 O [3].
Because the initial pH value of the deionized water is 7 at
25 °C, the concentration of H+ and OH- is set to be
100 nM. And the concentration of other species in the
plasma, air gap and water is set to be 105 m-3. In addition,
the boundary condition of the liquid bottom is Γ = 0, with
an assumption that the bottom have no ability to absorb
species of liquid. This hybrid model is constructed using
COMSOL Multiphysics@, a commercial software, and
three sub-models are calculated simultaneously.
3. Result and discussions
In the air gap, only HNO 2 , HNO 3 , O 3 , H 2 O 2 , N 2 O, and
N 2 O 5 can pass through this gap to reach the liquid surface.
The diffusion length (the minimum density is 1017 m-3) of
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short-lived species in the air gap, such as OH, O2 (a1 Δ),
and HO 2 , is just about 1 – 5 mm. For reactive species, the
density of ozone is most about 23 orders of magnitude per
cubic meter, followed by HNO 3 , H 2 O 2 , N 2 O 5 and N 2 O
about 20 orders of magnitude, and HNO 2 about 19 orders
of magnitude. Most of HNO 3 and N 2 O 5 hydrolyze, when
arriving to the liquid surface. And H+ in liquid is
produced mainly by this process.
Fig. 1 illustrates that the main aqueous ROS are O 3 and
H 2 O 2 . The initial density of OH- is 100 nM, and its
declines rapidly as other species penetrate into deeper
liquid. Therefore the decreasing point of the density
curve of OH- displays the penetration depth of species
generated by other two regions. Based on this point, the
velocity of penetration can be estimated. From 5 to
10mins, the velocity of penetration is 0.008 mm/s,
whereas this velocity is 0.02 mm/s from 40 to 80 s.
Obviously, the velocity is time nonlinearly, and shows a
slight downward trend along with the increasing of time.
Fig. 1. The distributions of main ROS in water after the
plasma-on time of 10 mins.
In the liquid the densities of O 3 and H 2 O 2 are far more
than 1 nM, because of massive O 3 and H 2 O 2 in the air
region dissolving, and dissolution is their main way of
supplement in the liquid. The short-lived reactive oxygen
species cannot reach the liquid surface as discussed before,
so they are produced in liquid. And Fig. 2 provides the
close relationship among O 2 -, OH, HO 2 , O 3 - and HO 3
that they can be reciprocal transformation with the help of
ozone and hydrion.
approximate 0.05 mm. And considering 1 nM as the
lowest density, NO 3 - and N 2 O penetrate only about 8 –
9 mm after ten minutes.
Fig. 3. The distributions of main RNS in water after the
plasma-on time of 10 mins.
NO cannot pass through the air gap and arrive into the
liquid, and the point of maximum density is not surface of
liquid discussed before. In the liquid region, NO is
supplied by the reaction: 2HNO 2 → NO + NO 2 + H 2 O;
therefore as the density of HNO 2 declines around 5 mm,
the density of NO has a drop significantly. And as the
densities of HO 2 and NO 2 are falling, the density of NO
reaches a peak. The main removal reactions of it are:
NO 2 + NO → N 2 O 3 and NO + HO 2 → ONOOH. In the
liquid region, ONOOH, the isomer of HNO 3 , is also
considered in the reason of its biological effect [8].
However, the gas phase ONOOH is failed to take account,
because of the lack of its reactions and abundant evidence
of its presence. In liquid region, peroxynitrite is offered
by the reaction of nitric acid and hydrogen peroxide, and
the main removal reactions are its degradation:
ONOOH → NO 2 + OH and ONOOH →H+ + NO 3 -.
As shown by Fig. 4, the average densities of reactive
species are growing up gradually from 1 to 10 mins. The
densities of hydrogen peroxide, ozone, nitrite and nitrate
(Fig. 3), however, are above 1 nM, and others are too low
to be detected.
Fig. 2. The main reactions of some of ROS.
Fig. 3 indicates that there exists no hydrolysis HNO 2
and HNO 3 by the result of low pH after long time
treatment and massive transfer from the air region. The
point of maximum concentration of NO, the well-known
biological reactive species, is not the surface of liquid, but
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Fig. 4. The average density of some reactive species
from1 to 10 mins.
3
4. Conclusion
Based on the hybrid model, only HNO 2 , HNO 3 , O 3 ,
H 2 O 2 , N 2 O and N 2 O 5 can pass though the 1cm air gap
and penetrate into the downstream deionized water.
Although cannot be diffused from the gas phase, some
short-lived reactive species are generated in situ in the
liquid phase. Some short-lived ROS have the ability to
transform reciprocally with the participation of ozone and
hydrion. The penetration speed of reactive species is time
nonlinearly, which decreases modestly with the plasmaon time. After 10 minutes, no species arrive to the liquid
bottom. NO 3 - and N 2 O penetrate the deepest around
8 - 9 mm. The densities of reactive oxygen and nitrogen
species are rising gradually with the plasma-on time from
1 to 10 mins, but only the concentrations of H 2 O 2 , O 3 ,
nitrite and nitrate are above 1 nM, and others are far less
than 1 nM.
5. References
[1] S. Samukawa, M. Hori, S. Rauf, et al. J. Phys. D:
Appl. Phys., 45, 25300 (2012)
[2] M.G. Kong, G. Kroesen, G. Morfill, et al. New J.
Phys., 11, 115012 (2009)
[3] W. Tian and M.J. Kushner. J. Phys. D: Appl. Phys.,
47, 165201 (2014)
[4] C. Chen, D.X. Liu, Z.C. Liu, A.J. Yang, H.L. Chen,
G. Shama and M.G. Kong. Plasma Chem. Plasma
Process., 34, 403 (2014)
[5] M. Witzke, P. Rumbach, D.B. Go and
R.M. Sankaran. J. Phys. D: Appl. Phys., 45, 442001
(2012)
[6] Y. Sakiyama, D.B. Graves, H.W. Chang, T. Shimizu
and G.E. Morfill. J. Phys. D: Appl. Phys., 45,
425201 (2012)
[7] T. Shibata and H. Nishiyama. J. Phys. D: Appl.
Phys., 47, 105203 (2014)
[8] A.W. Girotti. J. Lipid Res., 39, 1529 (1998)
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