22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Gas dynamics and afterglow chemistry of a helium jet against a flat surface
A. Obrusník1, K. P. Arjunan2, L. Zajíčková3 and S. Ptasinska2
1
2
Department of Physical Electronics, Faculty of Science, Masaryk University, Brno, Czech Republic
Radiation Laboratory and Department of Physics, University of Notre Dame, Notre Dame, 46556 IN, U.S.A.
3
Plasma Technologies at CEITEC, Masaryk University, Brno, Czech Republic
Abstract: This contribution presents a numerical model of the gas dynamics, gas mixing
and afterglow chemistry in a high-frequency atmospheric-pressure plasma jet discharged
into ambient atmosphere. The model allows obtaining spatially-resolved gas velocity,
composition and concentrations of selected radicals.
Keywords: APPJ, helium plasma, DBD jet, plasma medicine, plasma sterilization
1. Introduction
Atmospheric-pressure plasma jets (APPJs) have been
utilized in the past years in a number of promising
biomedical applications such as surface sterilization and
wound healing [1]. Very recently, they have also been
used in cancer research [2], showing that under some
conditions, they are capable of inducing apoptosis in
cancer cells.
When living tissue is exposed to plasma, it can be
altered by elevated temperatures, ultraviolet light
emission from the plasma or by radicals that are
produced there. This contribution describes a numerical
model capable of calculating spatially-resolved
concentrations and fluxes of selected radicals in a helium
jet operating against a flat surface of a Petri dish. This
work differs from most works simulating the afterglow
chemistry (the most advanced possibly published by
Murakami et al. [3]) by including only a simplified set of
reactions. On the other hand, the particle balance
equations are not solved in 1D but in 2D axially
symmetrical geometry, which provides valuable insight
for biomedical applications of such plasmas.
The spatially-resolved fluxes of various radicals to the
substrate are correlated with experimental conditions, in
which E.coli bacteria were exposed to this helium plasma
and the relative importance of individual radicals is
assessed.
The whole model is implemented using the COMSOL
Multiphysics simulation platform, which discretizes
differential equations using the finite element method.
2. The model
The model consists of two parts, the background gas
dynamics part describes the gas flow and mixing of the
background gases (i.e., helium and air) and the afterglow
chemistry part which describes the production and loss of
selected radicals and their transport through the effluent.
All the equations are solved in two-dimensional axially
symmetrical geometry, therefore the model is capable of
providing spatially-resolved fluxes of radicals to the
surface. The computational geometry consists of a
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capillary tube with a diameter of 5 mm and a Petri dish
with a diameter of 10 cm. The distance of the Petri dish
Fig. 1. The computational geometry. The gas dynamics is
solved for both inside and outside the capillary, the
afterglow chemistry only outside.
from the jet outlet varies from 0.5 to 2.5 cm. The
geometry, in which the equations are solved, is shown in
figure 1. It should be stressed that the gas dynamics
equations are solved both inside the quartz capillary and
in the region around it while the afterglow chemistry is
solved only in the region around the APPJ.
The computational geometry reflects the actual
experimental setup previously used in biomedical
research [4]. It is a dielectric barrier discharge (DBD)jet
driven by pulsed DC voltage with a driven electrode
located in the lower part of the capillary and the grounded
electrode located in the upper part.
2.1 Background gas dynamics
The gas dynamics part of the model describes the flow
and mixing of the background gases – helium and
ambient air – with air being considered a single
component. The model solves the Navier-Stokes
equations in the form
∇ ∙ (𝜌m u) = 0,
(1)
2
𝜌m (u ∙ ∇)u = ∇ ∙ �𝜇m (∇𝐮 + (∇𝐮)T ) − 𝜇m (∇ ∙ 𝐮)� +
𝜌m 𝐠..
3
(2)
1
In the equations above, 𝐮 denotes the mixture velocity,
𝜌m is the mixture density, 𝜇m is the mixture viscosity
calculated from Wilke’s mixture rules [5] and 𝐠 is the
gravitational field.
gas velocity is prescribed based on the flow rate. At the
edges of the whole computational domain, the gas is
allowed to flow out freely by setting p = 1 atm.
As far as the diffusion equation is concerned, the mole
fraction of helium is set to 𝑥He = 1 while at the remote
vertical boundaries, 𝑥He = 0. The helium typically leaves
the computational domain through the upper boundary
due to the buoyant force.
2.2 Afterglow chemistry
The afterglow chemistry includes diffusion equations
that are solved for selected radicals and intermediate
species outside the capillary (see figure 1). The diffusion
equation is, in this case, solved in the form
∇ ∙ (𝐷𝑖 ∇𝑐𝑖 + u𝑐𝑖 ) = 𝑅𝑖
Fig. 2. The velocity magnitude [m/s] and direction for the
helium flow rate of 5.5 slm and the nozzle-dish distance
of 1.5 cm
Fig. 3. The air mole fraction for the helium flow rate of
5.5 slm and the nozzle-dish distance of 1.5 cm
Since the viscosity and the density in equations
(1) and (2) depend on the local gas composition the
Navier-Stokes equations have to be complemented by a
diffusion equation describing the helium-air mixing.
The diffusion model that is utilized is a Fick-like model
with diffusion coefficients calculated from binary
diffusion coefficients using the mixture rules. The binary
diffusion coefficients are calculated from the ChapmanEnskog theory [6]. The gas temperature in the whole
model was assumed constant, T = 300 K.
The gas flow model is constrained by Dirichlet-type
boundary conditions. At the Petri dish and the walls of the
capillary, the gas velocity is set to zero, which is the
standard wall boundary condition. At the helium inlet, the
2
(3)
where 𝑐𝑖 is the molar concentration of species i, 𝐮 is the
mixture velocity obtained from the background gas
dynamics model, 𝑅𝑖 is the source term and 𝐷𝑖 is the
diffusion coefficient. The diffusion coefficients are again
calculated from binary diffusion coefficients using the
mixture rules and are, therefore also a function of the
local gas composition.
The velocity u in the afterglow model is obtained from
the gas dynamics model and it is assumed that the radicals
produced in the afterglow do not change the gas
dynamics. This is a reasonable assumption since the mole
fractions of the radical species do not exceed 10−4 . The
afterglow model currently contains 31 reactions for the
1
+
following species: He* , O+
2 , O2 ( D), O, O3 , H2 O , H,
+
+
HO2 , OH, N2 , N , N, NO, NO2 .
The species and reactions were chosen based on
especially the works of Murakami et al. [3,7] and [8].
These references contain very extensive reaction schemes
of dozens species and thousands reactions. Such complex
reaction schemes would not be feasible in a 2D model but
luckily, the referenced publications also contain
assessment of the importance of individual reactions and
identify the most important ones.
The afterglow model is constrained only by Dirichlettype boundary conditions. At the remote boundaries, it is
assumed that all the radicals and non-ground state species
have recombined and their concentrations are set to zero.
At the inlet, the concentration of the helium metastable is
set to
(4)
𝑐He = 4 ∙ 1015 [m−3 ] ∙ 𝑁A
where 𝑁A is the Avogadro number and the number density
of 4 ∙ 1015 m−3 was estimated based on literature [9].
This choice of boundary conditions follows from an
assumption that ionization and dissociation outside of the
capillary tube is induced exclusively by helium
metastables. Given the configuration of the driven and
grounded electrodes, this assumption is quite reasonable.
In many other setups, the grounded and driven electrodes
are located opposite each other and the field can,
therefore, accelerate electrons also outside the capillary,
making the electron-impact processes non-negligible
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there [10,11]. However, in geometries similar to ours, it
was shown that the electrons lose most of their energy
before exiting the capillary [12].
It should also be stressed that the model describes only
the time-averaged radical production although the voltage
is pulsed with kHz frequency.
Example results from the model for a helium flow rate
of 5.5 slm and a distance of the dish from the nozzle of
1.5 cm are shown in figures 4 and 5. The former shows
the number density of the atomic oxygen radical while the
latter shows the number density of the hydroxyl radical. It
is apparent that the oxygen radical is present within 1 cm
of the nozzle, which corresponds to the re-association
time of 2.6 ms. Therefore, the model is in good qualitative
agreement with previously published afterglow models
which have shown that the number density of atomic
oxygen drops by an order of magnitude in approx. 3 ms
[3].
[3] T. Murakami, K. Niemi, T. Gans, D. O’Connell, and
W. G. Graham, Plasma Sources Sci. Technol. 23, 025005
(2014).
[4] X. Han, W. A. Cantrell, E. E. Escobar, and S.
Ptasinska, Eur. Phys. J. D 68, 46 (2014).
[5] C. R. Wilke, J. Chem. Phys. 18, 517 (1950).
[6] E. L. Cussler, Diffusion: Mass Transfer in Fluid
Systems, 3rd ed. (Cambridge University Press,
Cambridge, 2009), p. 580.
[7] T. Murakami, K. Niemi, T. Gans, D. O’Connell, and
W. G. Graham, Plasma Sources Sci. Technol. 22, 015003
(2013).
[8] M. Capitelli, C. M. Ferreira, B. F. Gordiets, and A. I.
Osipov, Plasma Kinetics in Atmospheric Gases (Springer,
Berlin, 2000), p. 300.
[9] K. Niemi, J. Waskoenig, N. Sadeghi, T. Gans, and D.
O’Connell, 055005, (2011).
[10]
X. Y. Liu, X. K. Pei, X. P. Lu, and D. W. Liu,
Plasma Sources Sci. Technol. 23, 035007 (2014).
[11] G. V. Naidis, J. Appl. Phys. 112, 103304 (2012).
[12] J. Jansky, Q. T. Algwari, D. O’Connell, and A.
Bourdon, IEEE Trans. Plasma Sci. 40, 2912 (2012).
4. Acknowledgements
Adam Obrusník is a Brno Ph.D. Talent Scholarship
holder – funded by the Brno City Municipality. This work
was supported by the project CEITEC - Central European
Institute of Technology (CZ.1.05/1.1.00/02.0068) from
European Regional Development Fund. K.P.A and S.P.
would like to thank the U.S. Department of Energy Office
of Science, Office of Basic Energy Sciences under Award
Number DE-FC02-04ER15533
Fig. 4. The number density of atomic oxygen in the
afterglow for a helium flow rate of 5.5 slm and the
nozzle-dish distance of 1.5 cm.
Fig. 4. The number density of the hydroxyl radical in the
afterglow for a helium flow rate of 5.5 slm and the
nozzle-dish distance of 1.5 cm.
3. References
[1] M. Laroussi, Plasma Process. Polym. 11, 1138 (2014).
[2] D. B. Graves, Plasma Process. Polym. 11, 1120
(2014).
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