22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Addressing plasma-liquid interactions in a global model
A.M. Lietz1 and M.J. Kushner2
1
2
University of Michigan, Department of Nuclear Engineering and Radiological Sciences, US-48109 Ann Arbor, MI, U.S.A.
University of Michigan, Department of Electrical Engineering and Computer Science, US-48109 Ann Arbor, MI, U.S.A.
Abstract: Modeling of plasma liquid interactions is challenging due to the geometrical and
chemical complexities. GlobalKIN, a global plasma model, has been modified to address
plasma-liquid interactions in order to rapidly address a large parameter space when
developing reaction mechanisms. Conceptual comparisons of different plasma sources can
also be made. Development and demonstration of the model are discussed.
Keywords: atmospheric pressure plasma, plasma model, plasma-liquid interactions
1. Introduction
Plasma-liquid interactions have become increasingly
important for emerging applications such as water
treatment [1], plasma cancer treatment [2] and wound
healing [3].
Quantitative understanding of these
interactions would greatly benefit experimental design
and provide a context for interpreting results. In
designing a plasma source, many parameters must be
selected, including the geometry, gas flow rate, power,
and treatment time. Typical design requirements include
production of specific radical species, gas temperatures
below a maximum value, and a device size that is
appropriate to the substrate size. For example, devices
with a range of gas residence time from no applied flow,
such as a floating electrode dielectric barrier discharge
(DBD) [3] or surface microdischarge [4], to flows of
several standard liters per minute (slpm) through a
microdischarge jet [5]. The discharge gases range from
rare gases and rare gas with reactive additives, to ambient
air. Applied power can be continuous, as in a microwave
discharge, but is often pulsed, as in a DBD.
The liquid and plasma dynamics are coupled, because
the plasma electron temperature, density, and chemistry
are affected by the humidity, and the liquid chemistry is
influenced by the fluxes of reactive species from the
plasma. In order to narrow the parameter space during
the design process, it would be beneficial to use a rapidly
executing model that addresses both the gas phase and
liquid phase properties. In this paper, we report on the
development and implementation of a 2-zone
global-model that couples gas phase plasma with liquid
phase chemistry.
2. Description of Model
GlobalKIN is a global plasma chemistry model [6],
which has been expanded to include interactions with
liquids. The base GlobalKIN addresses gas phase
plasmas and surface chemistry using well-stirred-reactor
or plug flow approximations.
Rate equations are
integrated for electron, ion and neutral species densities,
electron, gas and ion temperatures and surface kinetics.
The surface kinetics are addressed using a site-balance
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model. Electron transport and rate coefficients are
derived from electron energy distributions produced by a
stationary two-term spherical harmonic expansion
solution of Boltzmann’s equation for a range of values of
reduced electric field (E/N).
To address the coupled plasma-liquid system, the
simulation is divided into two zones, one gas plasma and
one liquid. The relative volumes and interfacial area
between the two zones are specified. Power is applied to
generate the gas phase plasma by electric fields produced
by a circuit module, or by specifying the power deposition
as a function of time. Gas flow through the plasma zone
is also addressed.
Volume averaged diffusion from the gas plasma
interacts with different wall materials according to their
fractional area and a surface-dependent reaction
mechanism. One of the wall materials is the surface of
the liquid. Neutral species diffuse across the interface
according to Henry’s law which specifies that solubility
of a species in a liquid is proportional to its density in the
gas phase. At the liquid surface,
Γi ,solvate =
Di ni , gas  hni , gas − ni ,liquid

hni , gas
Λ 




where Γ i,solvate is the flux of species i from the gas phase
which is solvated into the liquid, D i is the gas phase
diffusion constant, Λ is the diffusion length of the plasma
region, and n i,gas and n i,liquid are the number density of
species i in the gas and liquid zones respectively. h is the
dimensionless Henry’s law constant. This means that the
loss fraction of the flux of a neutral species at the water
layer depends on the density of that species both in the
gas phase and in the water. A larger Henry’s law constant
enables a larger portion of the diffusion flux towards the
interface to solvate. Given that the potential energy of all
positively charged species exceeds any surface activation
energy barrier, the entire diffusion flux of ions reaching
the interface is assumed to enter the liquid. Photons also
enter the liquid without a barrier. The liquid is assumed
to be well stirred, and reactions between solvated species
are addressed by a separate liquid reaction mechanism.
1
Temperature changes in the liquid as well as evaporation
are also addressed in the model.
3. Argon Discharge
For proof of principle, the model was applied to a
simple case of a pure argon plasma over pure water. The
plasma was generated with a 5 ns pulse of power
repeating at 1 kHz. This profile of power deposition is
analogous to a dielectric barrier discharge. An argon
reaction mechanism including 6 species was used in the
discharge. Only Ar, Ar+, and electrons were allowed to
diffuse into the liquid zone. The reactions within the
liquid water were limited to:
Ar+ + H 2 O → H 2 O+ + Ar
H 2 O+ + H 2 O → H 3 O+ + OH
OH + OH + M → H 2 O 2 + M
The results of this demonstration are shown in Fig. 1.
The electron density rises with each pulse to a volume
averaged maximum of 4.3 × 1012 cm-3 and decays
between pulses, to 9.2 × 109 cm-3. The argon, with a
dimensionless Henry’s law constant of 2.1 × 10-2,
continually and smoothly diffuses into the liquid water. It
does not reach its saturation level in this time scale. In the
liquid zone, Ar+ enters from the plasma during each pulse
at low levels, and rapidly charge exchanges with H 2 O to
form H 2 O+. In this mechanism, OH and H 3 O+ are formed
only while the H 2 O+ density is nonzero, which is for
about 25 ns after the start of each the pulse. The H 3 O+
and OH are approximately the same densities because
they are formed by the same reaction, and the OH
consumed to form H 2 O 2 is two orders of magnitude lower
than the OH density. H 2 O 2 is a terminal species in this
mechanism, and it continues to accumulate.
The verification of the modified model on several proof
of principle cases, as well as the comparison with a more
advanced, 2-dimensional model, nonPDPsim, will be
discussed. It will be tested on cases such as DC-pulsed
plasma jets and discharges in bubbles of various gases.
The model is most effective when representing a
plasma interacting with a thin liquid layer, or a stirred
liquid, where the concentration gradient of solvated
species is less significant. Additionally, large spatial
non-uniformities within the plasma are not addressed in
global models.
4. Concluding Remarks
Gas phase plasma - liquid interactions are being
investigated for biomedical and water treatment
applications. The very large parameter space available
for design of devices emphasizes the need for a rapidly
executing model to help narrow this parameter space.
GlobalKin, a global model for gas phase plasmas has been
expanded to include these interactions and liquid
chemistry. The transport of species between the liquid
and the plasma is modelled using Henry’s Law and the
volume averaged diffusion losses from the plasma. The
2
Fig. 1. A pulsed argon DBD over liquid water. Argon
diffuses into the liquid zone, and Ar+ entering the liquid
zone produces OH.
model has been tested using simple chemistries. Results
will be discussed for activation of water discharges
sustained in a variety of gas mixtures (noble gases to air).
5. Acknowledgements
This work was supported by the DOE Office of Fusion
Energy Science (DE-SC0001319) and the National
Science Foundation (CHE-1124724).
6. References
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S. Lerondel, A. Le Pape and J.-M. Pouvesle.
Plasma Med., 1, 1 (2011)
[3] D. Dobrynin, A. Wu, S. Kalghatgi, S. Park,
N. Shainsky, K. Wasko, E. Dumani, R. Ownbey,
S. Joshi, R. Sensenig and A.D. Brooks. Plasma
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[4] T. Shimizu, J.L. Zimmermann and G.E. Morfill.
New J. Phys., 13 (2011)
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[6] R. Dorai, K. Hassouni and M.J. Kushner. J. Appl.
Phys., 88, 10 (2000)
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