22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Concentration profiles of chemical species in water exposed to an
atmospheric-pressure plasma: numerical study
K. Ikuse and S. Hamaguchi
Center for Atomic and Molecular Technologies, Graduate School of Engineering, Osaka University, Osaka, Japan
Abstract: A one-dimensional simulation model has been developed to analyze the
generation and transport processes of chemical species in water that are generated by an
atmospheric-pressure plasma in contact with the water surface. It has been found that
highly reactive species form a thin layer underneath the gas-liquid surface, where highly
reactive species are converted to less reactive chemical species.
Keywords:
atmospheric-pressure plasma, ROS/RNS, reaction-diffusion
1. Introduction
Biomedical applications of atmospheric-pressure
plasmas (APPs) in ambient air at room temperature have
been widely studied. One of the goals for such study is
to develop plasma systems that have therapeutic effects
on some types of diseases and wounds. Therapeutic
and/or sterilizing effects on living tissues and cells are
considered to be caused by direct exposure of APPs that
emit plasma-generated reactive species such as ions and
radicals. Among various chemically reactive species
generated by plasmas, reactive oxygen species (ROS)
and reactive nitrogen species (RNS) play key roles for
plasma-based therapies.
When an APP is applied to a living body for a
therapeutic purpose, gaseous species generated by the
plasma do not interact directly with the tissues and cells
in general. In many cases, a thin layer of liquid such as
blood and/or lymph covers a wound or tissue requiring a
therapeutic treatment and therefore chemically reactive
species generated by the plasma need to be transported
through such liquid. During this transport process,
some of these species may react with other chemical
species and/or converted to different types of reactive
species. Therefore, the observation of species in the gas
phase does not directly convey information on abundant
chemically reactive species in the vicinity of the tissue.
In this study the numerical simulations have been
performed to investigate the time evolution of the
concentration distributions of such species in water
exposed to an APP.
2. Numerical simulations
A one-dimensional simulation model that governs
reactions and transport of various chemical species in
water facing a gas-phase plasma has been developed. In
this model the influx of the gaseous species to the water
surface is given as the boundary condition with the
assumption that the plasma is in steady state (i.e., the
composition is constant in time and uniform in space at
the plasma-water interface). The gas phase species are
assumed to enter water at their thermal velocities and the
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outward flux of reactive species from water to the gas
phase is determined from Henry’s law. Typically the
concentrations of the gaseous species which is used in
this model are selected from the experimental data
available in published literatures [1-3]. The initial
condition of the liquid is pure water (pH = 7) with
dissolved oxygen and nitrogen in equilibrium with air at
1 atm. The model incorporates 37 species and 111
chemical reactions in water at room temperature.
The simulations have been performed as a
one-dimensional model in the direction from the liquid
surface to the bottom. The governing equations of the
simulation model for N chemical species have been
derived as in the following manner. Equations of the
mass and momentum conservations of species 𝑖 are
given by:
𝜕𝑛𝑖
𝜕𝜕
𝑚𝑖 𝑛𝑖
+ ∇ ∙ (𝑛𝑖 𝐯𝑖 ) = 𝑅�𝑖
𝑑𝐯𝑖
= −𝑘𝐵 𝑇∇𝑛𝑖 + 𝑞𝑖 𝑛𝑖 𝐄 − 𝜈𝑖 𝑚𝑖 𝑛𝑖 (𝐯𝑖 − 𝐯𝐶 )
𝑑𝑑
with 𝑖 = 1,2, ⋯ , 𝑁, where 𝑛𝑖 , 𝑡 and 𝐯𝑖 represent the
concentration of species 𝑖 , time and fluid velocity.
Here 𝑅�𝑖 is the chemical reaction term determined from
the rate equations [4]. Other parameters 𝑚𝑖 , 𝑘𝐵 , 𝑇,
𝑞𝑖 , 𝐄, 𝜈𝑖 and 𝐯𝐶 denote the atomic or molecular mass
of species 𝑖 , Boltzmann constant, water temperature,
electrical charge of species 𝑖, electric field, collision
frequency of species 𝑖 with water molecules and the
convective flow velocity of water, respectively. The
electric field 𝐄 is calculated from Poisson’s equation:
∇∙𝐄=
𝜌
𝜀
where 𝜌 is the total charge density and 𝜀 is the
permittivity of pure water. If collisions of chemical
species with water molecules are sufficiently frequent,
inertia of the momentum conservation 𝑚𝑖 (𝑑𝐯𝑖 ⁄𝑑𝑑) can
be ignored. Therefore the fluid velocity of the chemical
1
species 𝑖 can be written as:
with
𝐯𝑖 = 𝐯𝐶 + 𝜇𝑖 𝐄 −
𝜇𝑖 =
𝐷𝑖 =
𝑞𝑖
𝐷𝑖
𝑛𝑖
𝜕𝑛𝑖
𝜕𝜕
∇𝑛𝑖
= 𝑅�𝑖 − 𝐯𝐶 ∇𝑛𝑖 − 𝜇𝑖 ∇ ∙ (𝑛𝑖 𝐄) + 𝐷𝑖 ∆𝑛𝑖 .
The simulation has been parallelized based on the
domain decomposition with Message Passing Interface
(MPI), which allows the computation for many seconds
of physical time to be completed within reasonable
computational time.
𝜈𝑖 𝑚𝑖
𝑘𝐵 𝑇
𝜈𝑖 𝑚𝑖
where 𝜇𝑖 and 𝐷𝑖 denote the mobility and diffusion
coefficient. If the water flow is incompressible, the
divergence of the convective water flow velocity can be
ignored, i.e.,
∇ ∙ 𝐯𝐶 = 0.
Thus the governing equation of our simulation model can
be obtained from combining the mass conservation
equation with the expression of velocity 𝐯𝑖 ,
3. Results
Fig. 1 shows the concentration distributions of
chemical species in liquid at 1 second after plasma
irradiation that supplies (a) OH only, (b) OH and NO, or
(c) 6 species, i.e., H 2 O 2 , HO 2 , NO, NO 2 , NO 3 and O 3 ,
respectively. The gas-phase densities and dissolving
rates of these species are summarized in Table 1. It is
assumed that there is no water convection or no external
electric field.
axis
(a)
(c)
Fig. 1. The concentration distributions of the chemical
species at 1 second after starting irradiation. The
supplied species are (a) OH only, (b) OH and NO, (c)
H 2 O 2 , HO 2 , NO, NO 2 , NO 3 and O 3 . The horizontal
2
(b)
represents the depth from the liquid surface in liner scale
and the vertical axis represents density in log scale.
The dissolving rates of supplied species are summarized
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in Table 1.
Table 1.
Gas densities and dissolving rates.
Gas density
Dissolving rate
(𝑚𝑚𝑚 ∙ 𝑐𝑐−2 ∙
𝑠 −1 )
1.8×10-6
𝐿−1 )
Ref.
1.7×10-7
[1]
HO 2
-12
5.0×10
[2]
OH
1.7×10-6
[1]
2.5×10-5
NO
-8
1.7×10
[1]
1.9×10-7
NO 2
1.3×10-8
[3]
1.2×10-7
NO 3
1.7×10-8
[3]
1.3×10-7
-6
[1]
1.5×10-5
H2O2
O3
(𝑚𝑚𝑚 ∙
1.7×10
5.5×10-7
It is seen that a variety of species are generated in
water and one of the most dominant species among them
is hydrogen peroxide (H 2 O 2 ) in all cases. In the cases
of (b) and (c), solution becomes acidic due to the
generation of nitric acid (H+ and NO 3 -) which is
consistent with experimental observations [5]. Ions and
aqueous electrons diffuse as ambipolar diffusion due to
their charges. It is found that highly reactive species
such as hydroxyl radicals (OH) and NO 3 are confined
near the liquid surface and form a boundary layer which
strongly affects the generation of chemical species in
water. More stable (i.e., less reactive and long-lifetime)
species are generated in this layer and diffuse into the
bulk water. The concentrations of NO and NO 2 are
very low at the interface between plasma and water
although they are supplied from an APP in the gas phase
and then rise along depth. The results of (b) and (c) in
Fig. 1 suggest that these NO and NO 2 are formed in the
water due to some chemical reactions and the profile of
pH (concentration of H+) affects those reactions.
It has been found that a variety of species are
generated from the chemical reactions especially in a
thin liquid layer at the gas-liquid interface. Highly
reactive species that are supplied to water from an APP
are confined to this thin layer due to their high-rate
reactions whereas less reactive and therefore more stable
species such as H 2 O 2 diffuse into water. This thin
liquid layer may be called “reaction boundary layer,”
which acts as the source of reactive species observed in
the liquid bulk.
5. References
[1] R. Sensenig, S. Kalghatgi, E. Cerchar, G. Fridman,
A. Shershevsky, B. Torabi, K. P. Arjunan,
E. Podolsky,
A.
Fridman,
G.
Friedman,
J.A. Clifford and A.D. Brooks. Ann. Biomed.
Engng., 39, 674 (2011)
[2] D.X. Liu, P. Bruggeman, F. Iza, M.Z. Rong and
M.G. Kong. Plasma Sources Sci. Technol., 19,
025018 (2010)
[3] T. Murakami, K. Niemi, T. Gans, D. O'Connell and
W.G Graham. Plasma Sources Sci. Technol., 22,
015003 (2013)
[4] S. Hamaguchi.
in: AIP Conf. Proc. 1542 Eighth
International Conference on Atomic and Molecular
Data and Their Applications ICAMDATA-2012.
(J.D. Gillaspy, W.L. Wiese and Y.A. Podpaly; Eds.)
214 (2013)
[5] S. Ikawa, K. Kitano and S. Hamaguchi. Plasma
Process. Polymers, 7, 33 (2010)
4. Summary
The numerical simulations of chemical reactions and
diffusion of reactive species in water exposed to an
low-temperature APP have been performed based on
reaction-diffusion equations coupled with Poisson
equations. When a living tissue is exposed to an APP,
there is almost always a liquid layer, such as blood,
lymph, or other body fluids, that separates the gas phase
and the tissue. Therefore chemically reactive species
such as OH, NO and O 3 generated by the plasma in the
gas phase need to be transported through the liquid layer
before reacting with the tissue surfaces. Thus the aim
of this study is to reveal what species are generated in
liquid due to the supplied radicals from plasma and how
deeply they can diffuse into the bulk water. The
simulations have been performed based on a
one-dimensional model in the direction from the liquid
surface to the bottom. The model incorporates 37
species and 111 chemical reactions in water at room
temperature.
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