Dynamics of dust particles in a plasma jet
In this paper carry out the computer simulation of the plasma jet with dust particles, which expands in rarefied neutral gas. The problem is considered in the framework of multi-fluid hydrodynamic model, which takes into account the difference in velocity and temperature of the plasma component. Cal...
Збережено в:
| Дата: | 2017 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2017
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/122161 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dynamics of dust particles in a plasma jet / O.Yu. Kravchenko, I.S. Maruschak // Вопросы атомной науки и техники. — 2017. — № 1. — С. 159-162. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-122161 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1221612025-02-09T17:38:52Z Dynamics of dust particles in a plasma jet Динамика пылевых частиц в плазменной струе Динаміка пилових частинок у плазмовому струмені Kravchenko, O.Yu. Maruschak, I.S. Низкотемпературная плазма и плазменные технологии In this paper carry out the computer simulation of the plasma jet with dust particles, which expands in rarefied neutral gas. The problem is considered in the framework of multi-fluid hydrodynamic model, which takes into account the difference in velocity and temperature of the plasma component. Calculations performed using method “big particles” for different ionization degree of plasma, its density and radii of dust particles. The spatial distributions of plasma parameters and dust components obtained at different time points after injection plasma jet. It is shown that at the large ionization degree of plasma (α> 0.001) velocity of the dust particles significantly decreased compared to the case of weakly ionized plasma stream. This result can be explained by deceleration of dust particles by an electric field, the effect of which increases with increasing concentrations of electrons and ions. Проводится компьютерное моделирование расширения плазменной струи с пылевыми частицами в разрежённый нейтральный газ. Задача рассматривается в рамках многожидкостной гидродинамической модели, которая позволяет учитывать различия скоростей и температур компонент плазмы. Расчёты выполнены методом “крупных частиц” для различных значений степени ионизации плазмы, её плотности и радиусов пылевых частиц. Получены пространственные распределения параметров плазмы и пылевой компоненты в различные моменты времени после инжекции плазменной струи. Показано, что при большой степени ионизации плазмы (α > 0,001) скорости пылевых частиц в струе значительно меньше, чем в случае слабоионизированного потока плазмы. Этот результат можно объяснить торможением пылинок электрическим полем, влияние которого увеличивается при увеличении концентраций электронов и ионов. Проводиться комп’ютерне моделювання розширення плазмового струменю з пиловими частинками в розріджений нейтральний газ. Задача розглядається в рамках багаторідинної гідродинамічної моделі, яка дозволяє врахувати відмінності швидкостей і температур компонент плазми. Розрахунки виконані методом “крупних частинок” для різних значень ступеня іонізації плазми, її густини та радіусів пилових частинок. Одержані просторові розподіли параметрів плазми і пилової компоненти в різні моменти часу після інжекції плазмового струменю. Показано, що при великому ступені іонізації плазми (α > 0,001) швидкості пилових частинок в струмені значно менші, ніж у випадку слабкоіонізованого потоку плазми. Цей результат можна пояснити гальмуванням пилинок електричним полем, вплив якого збільшується при збільшенні концентрацій електронів та іонів. 2017 Article Dynamics of dust particles in a plasma jet / O.Yu. Kravchenko, I.S. Maruschak // Вопросы атомной науки и техники. — 2017. — № 1. — С. 159-162. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.27.Lw https://nasplib.isofts.kiev.ua/handle/123456789/122161 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
| spellingShingle |
Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Kravchenko, O.Yu. Maruschak, I.S. Dynamics of dust particles in a plasma jet Вопросы атомной науки и техники |
| description |
In this paper carry out the computer simulation of the plasma jet with dust particles, which expands in rarefied neutral gas. The problem is considered in the framework of multi-fluid hydrodynamic model, which takes into account the difference in velocity and temperature of the plasma component. Calculations performed using method “big particles” for different ionization degree of plasma, its density and radii of dust particles. The spatial distributions of plasma parameters and dust components obtained at different time points after injection plasma jet. It is shown that at the large ionization degree of plasma (α> 0.001) velocity of the dust particles significantly decreased compared to the case of weakly ionized plasma stream. This result can be explained by deceleration of dust particles by an electric field, the effect of which increases with increasing concentrations of electrons and ions. |
| format |
Article |
| author |
Kravchenko, O.Yu. Maruschak, I.S. |
| author_facet |
Kravchenko, O.Yu. Maruschak, I.S. |
| author_sort |
Kravchenko, O.Yu. |
| title |
Dynamics of dust particles in a plasma jet |
| title_short |
Dynamics of dust particles in a plasma jet |
| title_full |
Dynamics of dust particles in a plasma jet |
| title_fullStr |
Dynamics of dust particles in a plasma jet |
| title_full_unstemmed |
Dynamics of dust particles in a plasma jet |
| title_sort |
dynamics of dust particles in a plasma jet |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/122161 |
| citation_txt |
Dynamics of dust particles in a plasma jet / O.Yu. Kravchenko, I.S. Maruschak // Вопросы атомной науки и техники. — 2017. — № 1. — С. 159-162. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT kravchenkooyu dynamicsofdustparticlesinaplasmajet AT maruschakis dynamicsofdustparticlesinaplasmajet AT kravchenkooyu dinamikapylevyhčasticvplazmennojstrue AT maruschakis dinamikapylevyhčasticvplazmennojstrue AT kravchenkooyu dinamíkapilovihčastinokuplazmovomustrumení AT maruschakis dinamíkapilovihčastinokuplazmovomustrumení |
| first_indexed |
2025-11-28T19:52:44Z |
| last_indexed |
2025-11-28T19:52:44Z |
| _version_ |
1850065102851538944 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2017. №1(107)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2017, № 1. Series: Plasma Physics (23), p. 159-162. 159
DYNAMICS OF DUST PARTICLES IN A PLASMA JET
O.Yu. Kravchenko, I.S. Maruschak
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
E-mail: kay@univ.kiev.ua
In this paper carry out the computer simulation of the plasma jet with dust particles, which expands in rarefied
neutral gas. The problem is considered in the framework of multi-fluid hydrodynamic model, which takes into
account the difference in velocity and temperature of the plasma component. Calculations performed using method
“big particles” for different ionization degree of plasma, its density and radii of dust particles. The spatial
distributions of plasma parameters and dust components obtained at different time points after injection plasma jet.
It is shown that at the large ionization degree of plasma (α> 0.001) velocity of the dust particles significantly
decreased compared to the case of weakly ionized plasma stream. This result can be explained by deceleration of
dust particles by an electric field, the effect of which increases with increasing concentrations of electrons and ions.
PACS: 52.27.Lw
INTRODUCTION
The application of nanoparticles is rapidly growing
in nanoscale science and engineering. During the last
years many techniques for nanoparticles synthesis have
been developed, particularly several research groups
worldwide apply plasma processes for the synthesis of
particulate matter [1]. One of the most promising
methods of coating is spraying using plasma jets [2, 3].
Coating quality depends on the physical parameters
such as the velocity of sputtered particles, their charge
and temperature. In this regard, the study of the
dynamics of dust particles in the plasma jets that can be
used for transportation of dust particles to the substrate
is of considerable interest. Unlike gas jets with
dispersed phase, where the drag force determines the
movement of dust particles, dust particles are charged in
plasma and the electric force acts on them too. The
purpose of this work is to study the spatial distribution
of dust particles in the plasma jet and influence of the
electric field on their dynamics.
In this paper carry out the computer simulation of
the plasma jet with dust particles, which expands in
rarefied neutral gas.
1. MODEL AND SIMULATION METHOD
In this paper, we simulate the outflow of the plasma
jet with dust particles through a round hole of radius R0
in the rarefied neutral gas. It is assumed that the plasma
velocity V0 and its density 0 are constant at the inlet
during the plasma jet expansion. The plasma considered
in this article consists of four species, namely electrons,
neutral argon atoms, singly ionized argon ions and
nanoparticles. They will be denoted by the subscript
e, a, i and d, respectively. We use hydrodynamic model
to describe the expansion of the plasma jet with dust
particles. In the model ions, electrons and neutral atoms
have the same drift velocity ,w u v due to effective
momentum exchange, and dust particles have drift
velocity ,d d dw u v . Here u, ud are radial velocity
components and , d are axial velocity components.
The ions temperature equals to neutral atoms
temperature T, but electrons temperature Te
can differ
from them.
The continuity equation for heavy plasma
component (ions and neutral atoms) is equal to
0.
n
div nw
t
(1)
Here n is sum of ion density ni and neutral atom
density na.
The continuity equation for ions is equal to
2 / ,i
i r e i i d
n
div n w n n I n e
t
(2)
where ne is electron density. The right hand side
describes the ion destruction due to three particle
recombination and recombination at the interaction with
dust particles.
The rate coefficient for three particle recombination
is given [4]
9/220 6 11.1 10 .r eT m s
(3)
The ion current on dust particle Ii is described by
OLM theory [5] and is equal to
2
2
0
1
4 / 2
d
i d e
d
eq
I r n e w
r m w kT
. (4)
Here rd is dust particle radius, T is ion temperature, qd
is dust particle charge, e is proton charge, m is the ion
and neutral atom mass.
The continuity equation for dust particles is equal to
0,d
d d
n
div n w
t
(5)
where nd is dust particles density, ,d d dw u v is drift
velocity of dust particles.
The dust particle charge is calculated from the
equation
,d
d d e i
q
w q I I
t
(6)
where electron current on dust particle is equal to
1/2
2
0
8
exp .
4
e d
e d e
e d e
kT eq
I r n
m r kT
(7)
160 ISSN 1562-6016. ВАНТ. 2017. №1(107)
The momentum equations for heavy plasma particles
(ions and atoms) are given by
1
,d r
i r
i i i
nu n fP e
div nuw n E
t m r m m
(8)
1
,d z
i z
i i i
nv n fP e
div nvw n E
t m z m m
(9)
where P=nkT is the plasma pressure, Er and Ez are
radial and axial electric field components, mi is ion mass
(in our case the neutral atom mass is equal to the ion
mass), f is force of the aerodynamic interaction
between plasma and dust particle (fr and fz its
components along axis r and z). It consists of a friction
force between dust particles and neutral particles dnf , as
well as between the ions and the dust particles dif .
According [5] neutral drag force can be approximate
as
28
2 ,
3
dn d a Tn df r n mV w w (10)
where
1/2
2 8 /TnV w kT m is total atom speed (a
combination of directed and thermal speeds). The ion
drag force can be expressed as
col coul
di i Tn i Tnf n mV w n mV w , (11)
where ( )col coul is the momentum collision cross
section corresponding to the collection of ions by direct
ion impacts (electrostatic Coulomb collisions).
The momentum equations for dust particles are
given by
,
d d d d r
d d d
d d
d
d r
d
n u n fP
div n u w
t m r m
q
n E
m
(12)
,
d d d d z
d d d
d d
d
d z
d
n v n fP
div n v w
t m z m
q
n E
m
(13)
where αd is volume fraction of dust particles.
Equations for internal energies ions and atoms ε,
electrons εe and dust particles εd are given by
,
enei ddiv w Pdiv w Q Q n Q
t
(14)
,
e
e e e
ei en d ed
div w P div w divq
t
Q Q n Q
(15)
d d
d d d d d ed iddiv w n Q n Q Q
t
. (16)
Here the heat flux is given by ( )e e eq T T ,
where
e(T ) is the coefficient of electron thermal
conductivity, Q, Qed, Qid are the energy exchanges
between a dust particle and neutral atoms, electrons and
ions [5], Qei is the energy exchange between electrons
and ions, Qen is the energy exchange between electrons
and neutrals.
The equation of conservation of momentum for
electrons if we neglect their inertia, as well as the force
of friction of the electrons with atoms, ions and dust
particles has the form
e een E P . (17)
This relation expresses the electric field E .
The system of equations (1-17) is solved
numerically by the method of large particles [6].
2. RESULTS AND DISCUSSION
The calculations were performed for various
densities of plasma ρ0 and dust component ρd0 at the
inlet, various values of ionization degree of plasma α
and radius of dust particles rd. Simulations continued
until a steady-state flow of plasma. As results, spatial
distributions of the plasma parameters and disperse
phase parameters (densities, drift velocities,
temperatures and the plasma pressure) were obtained in
various times after the start of injection of the plasma jet
into the space filled with gas.
An example of the spatial distribution of the plasma
density is presented in Fig. 1 at t=10 ms after the jet
injection. It is seen, that the shock wave is formed
during the plasma jet expansion into a neutral gas.
Fig. 1. Spatial distribution of plasma density at t=10 ms
after the plasma jet injection
The spatial distributions of the dust particles velocity
along the symmetry axis of the jet are shown in Fig. 2
for rd=100 nm, 0=0.006 kg/m
3
, V0=40 m/s. The solid
curve corresponds to the plasma ionization degree
α=0.001, the dash curve correspond to α=0.05 and the
dot curve corresponds to α=0.1. We can see that dust
particles are accelerated in the stream in the region
z 3R0 to a velocity
m
dzv , which remains almost
constant with further increase of coordinate z. The
reason for this effect is the rapid reduction of the
frictional force fF between dust particles and the
plasma with increasing z due to the reduction of plasma
density at the jet expansion (Fig. 3). Our model also
takes into account the effect of the electric force on dust
particles. Its action is directed against the movement of
dust particles, as they have a negative charge.
ISSN 1562-6016. ВАНТ. 2017. №1(107) 161
0 2 4 6 8
0
2
4
6
v
d
/v
0
z/R
0
=0.0001
=0.05
=0.1
Fig. 2. Spatial distributions of dust particles velocity
along z-axis for various plasma ionization degrees at
t=5×10
-3
s
Note, that the increase of ionization degree reduces
the velocity of the dust particles, because the effect of
the electrical force on their dynamics increases.
0 2
0
2
4
frictional force
z/R
0
F
f
0,0
0,4
0,8
plasma density
0
Fig. 3. Spatial distributions of the plasma density and
the frictional force along z-axis
Fig. 4 shows distributions of dust component density
in the expanding plasma jet along the axis of symmetry
z at different radii of dust particles. It is seen that the
density of dust particles with greater radius decreases
with increasing of coordinate slower. The maximum
velocity, to which the dust particles are accelerated, also
depends on their radius and the plasma density in the
flow. Appropriate dependences are shown in Fig. 5.
Curve 1 represents the dependence of
m
dv on rd in semi-
logarithmic scale at V0=40 m/s, 0=0.00122 kg/m
3
,
=0.001. It is seen that with the increase of the dust
particles radius their velocity decreases. Curve 2
represents the dependence of
m
dzv on the plasma density
at the inlet in semi-logarithmic scale. The plasma flow
velocity is much greater than velocities of dust particles
and is about the same in all variants calculations. For
example, the axial component of the plasma flow
velocity is 140 (m/s) at z=5R0. It indicates the need
to use a two-speed hydrodynamic model describing the
plasma jet with dust particles. An increasing of plasma
density leads to an increase of the frictional force
between the plasma and dust particles and to the
increase of the dust particles velocity.
0 2 4 6 8
0,00
0,04
0,08
d
/
0
z / R
0
r
d
=40 nm
r
d
=100 nm
r
d
=1 mkm
Fig. 4. Spatial distributions of the dust component
density along z-axis for various radii of dust particles at
t=5×10
-3
s
0,01 0,1 1
0
2
4
6
0
2
4
6
1
v
m
d
/v
0
r
d
, m
1,0x10
-3
1,0x10
-3
5,0x10
-3
1,0x10
-2
1,0x10
-2
2
kg
Fig. 5. Maximum velocity of dust particles in the plasma
jet as a function of their radius (curve 1) and the plasma
density at the inlet (curve 2)
Radial distributions of the axial flux of dust
component are presented in Fig. 6 for the different radii
of dust particles at the distance z = 0.06 m from the
inlet. Our results demonstrate significant heterogeneity
dust flow radially. First, the dust particles are distributed
only within a certain channel, the radius of which is
smaller for larger dust particles. The axial flow of the
dust component has a maximum near the axis of
symmetry of the plasma jet, and tends to zero with
increasing radius.
0 1 2 3 4
0,00
0,02
0,04
d
*v
d
r, cm
r
d
=50 nm
r
d
=100 nm
r
d
=200 nm
Fig. 6. Radial distributions of the axial flow of the dust
component at 0.06z m and various dust particles
radii
162 ISSN 1562-6016. ВАНТ. 2017. №1(107)
CONCLUSIONS
The plasma jet with dust particles has been
investigated using a multi-hydrodynamic model, which
takes into account the effect of the electric field on the
dust particles dynamic. We studied spatial distributions
of dust particles and their velocities in the plasma jet at
different plasma ionization degrees, plasma densities at
the inlet and radii of dust particles. It is shown that at
the large ionization degree of plasma (α> 0.001)
velocity of the dust particles significantly decreased
compared to the case of weakly ionized plasma stream
due to their deceleration by electric field.
REFERENCES
1. L. Boufendi, M.Ch. Jouanny, E. Kovacevic,
J. Berndt, M. Mikikian. Dusty plasma for
nanotechnology // Journal of Physics D: Applied
Physics. 2011, v. 44, № 17, p. 174035.
2. R. Perekrestov, P. Kudrna, M. Tichý. The deposition
of titanium dioxide nanoparticles by means of a hollow
cathode plasma jet in dc regime // Plasma Sources
Science and Technology. 2015, v. 4, № 3, p. 035025.
3. G. Nava, F. Fumagalli, F. Di Fonzo. Nanoparticles jet
deposition of silicon, silicon-carbon and titania hierarchical
nano-structures for energy applications // 22
nd
International
Symposium on Plasma Chemistry, July 5-10, 2015,
Antwerp, Belgium, p. II-5-25.
4. J.Goldfinch, D.C. Pack. The expansion of a plasma
from a spherical source into a vacuum Part 1. Fully-
ionized flow // Journal of Plasma Physics. 1971, v. 6,
№ 1, p. 137-152.
5. P.K. Shukla, A.A. Mamun. Introduction to Dusty
Plasma Physics. Bristol: “Institute of Physics
Publishing”, 2002.
6. O.M. Belozerkovskiy, Yu.M. Davydov. Metod
krupnyh chastiz v gasovoj dinamike. M.: "Nauka", 1982,
p. 392 (in Russian).
Article received 28.11.2016
ДИНАМИКА ПЫЛЕВЫХ ЧАСТИЦ В ПЛАЗМЕННОЙ СТРУЕ
А.Ю. Кравченко, И.С. Марущак
Проводится компьютерное моделирование расширения плазменной струи с пылевыми частицами в
разрежённый нейтральный газ. Задача рассматривается в рамках многожидкостной гидродинамической
модели, которая позволяет учитывать различия скоростей и температур компонент плазмы. Расчёты
выполнены методом “крупных частиц” для различных значений степени ионизации плазмы, её плотности и
радиусов пылевых частиц. Получены пространственные распределения параметров плазмы и пылевой
компоненты в различные моменты времени после инжекции плазменной струи. Показано, что при большой
степени ионизации плазмы (α > 0,001) скорости пылевых частиц в струе значительно меньше, чем в случае
слабоионизированного потока плазмы. Этот результат можно объяснить торможением пылинок
электрическим полем, влияние которого увеличивается при увеличении концентраций электронов и ионов.
ДИНАМІКА ПИЛОВИХ ЧАСТИНОК У ПЛАЗМОВОМУ СТРУМЕНІ
О.Ю. Кравченко, І.С. Марущак
Проводиться комп’ютерне моделювання розширення плазмового струменю з пиловими частинками в
розріджений нейтральний газ. Задача розглядається в рамках багаторідинної гідродинамічної моделі, яка
дозволяє врахувати відмінності швидкостей і температур компонент плазми. Розрахунки виконані методом
“крупних частинок” для різних значень ступеня іонізації плазми, її густини та радіусів пилових частинок.
Одержані просторові розподіли параметрів плазми і пилової компоненти в різні моменти часу після інжекції
плазмового струменю. Показано, що при великому ступені іонізації плазми (α > 0,001) швидкості пилових
частинок в струмені значно менші, ніж у випадку слабкоіонізованого потоку плазми. Цей результат можна
пояснити гальмуванням пилинок електричним полем, вплив якого збільшується при збільшенні
концентрацій електронів та іонів.
http://iopscience.iop.org/journal/0963-0252
http://iopscience.iop.org/journal/0963-0252
|