Evaluation of precursor evaporation in Si nano-particle synthesis by
radio-frequency induction thermal plasmas
V. Colombo1,2, E. Ghedini1,2, M. Gherardi1, P. Sanibondi1
Alma Mater Studiorum – Università of Bologna
1
Department of industrial engineering (DIN)
2
Industrial Research Center for Advanced Mechanics and Materials (C.I.R.I.-M.A.M.)
Via Saragozza 8-10, 40123 Bologna, Italy
Abstract: The evaporation of micro-sized silicon solid precursor in a laboratory scale
radio-frequency induction thermal plasma system for nano-particles synthesis has been
investigated numerically using a customized version of the commercial CFD code ANSYS
FLUENT©. Two turbulence models and two evaporation models have been compared and it
is shown that under high loading conditions for precursor injection the results can be strongly
affected by the choice of the model.
Keywords: Thermal plasmas, Nanoparticle synthesis, Modelling
1. Introduction
In the last decades, the synthesis of nanopowders [1]
has become of prime importance among the industrial
applications of inductively coupled thermal plasmas,
which include thermal spray, powder densification and
spheroidization, and waste treatment [2]. Usually in these
applications, the material treatment is accomplished
introducing a precursor, which can be either gas, liquid or
solid, by means of an injection probe in the middle of the
plasma discharge, resulting in an in-flight treatment. In
nanopowder synthesis, the precursor is evaporated and,
after the vapour is transported to colder regions of a
reaction chamber where the gas temperature is usually
below 2000 K, nucleation of nanoparticles occurs; as a
consequence, complete evaporation is necessary for
process optimization. When the precursor has an initial
solid or liquid state, the injected particles are heated and
accelerated by the plasma and they start to vaporize when
the surface temperature is higher than the melting point.
Precursor evaporation plays a fundamental role in RF
induction thermal plasma synthesis of nanoparticles,
especially at industrial scale where complete evaporation
is necessary to maximize process yield and cost
effectiveness. Since particle evaporation deeply relies on
the flow state inside the plasma torch, still not completely
clear, we investigated the particle heating using two
different turbulence models that predict different flow
behaviours: a turbulence model that results in high
turbulent flow – the standard k-ε (KE) - and a turbulence
model that results in an almost laminar flow inside the
torch – the Reynolds Stress Model (RSM).
Also, two different models for the computation of
vapour production from heated particles have been used,
describing two different mechanisms for vapour mass
transfer from the particle surface to the plasma free
stream: evaporation at boiling point and vaporization
driven by vapour concentration gradients. Evaporation is
a heat-driven mechanism in which it is assumed that, once
the particle has reached its boiling point, all the heat
delivered to the particle leads to vapour production,
whereas the mechanism driven by vapour concentration
gradient between the particle surface and the plasma free
stream accounts also for vaporization below the boiling
point. Even though evaporation models have been deeply
studied in the past [3], investigations were carried out
only for thermal spray applications, where it was shown
that the differences predicted by the models could be
reasonably neglected; on the contrary, due to the plasma
temperature being closer to the boiling point of the treated
material, especially under high loading conditions, it can
be shown that the two evaporation models used in this
work predict quite different results when applied to
inductively coupled thermal plasma system for
nanoparticle production [4].
2. Modelling approach
A 2-D model for the plasma torch and reaction chamber
has been implemented in the ANSYS FLUENT©
environment in an axisymmetric geometry. The model
includes the following hypothesis:
Plasma is in local thermodynamic equilibrium
(LTE);
Combined diffusion approach of Murphy is used to
model the diffusion in a mixture of two non-reactive
gases;
Turbulent effects are taken in account through either
standard k-ε model or Reynolds Stress Model;
Plasma is optically thin and radiative losses are
taken in account considering only the presence of
argon in the mixture; resonance lines are neglected
in the computation of radiative losses;
Composition is computed taking in account six
species: Ar, Ar+, H2, H, H+ and electrons;
Viscous dissipation term in the energy equation is
neglected;
Displacement currents are neglected.
Mass, momentum and energy equations are solved as in
[4, 5] in coupling with electromagnetic field equations
written in the vector potential form.
Turbulent effects in the downstream region of the
discharge have been included in the flow calculations
using two different models: the standard k-ε model (KE)
and the Reynolds Stress Model (RSM).
The precursor particles are assumed to be spherical and
with a negligible thermal inertia. The particles trajectory
is obtained by solving the equation of motion including
turbulent dispersion on the particles. The heating history
of the precursor particle in the solid-phase is obtained by
solving the energy balance equation. When the particle is
fully in the liquid-phase, two models have been used to
predict precursor evaporation: the vaporization model
(Vap.) and the boiling model. The vaporization model
assumes that mass transfer between the particle and the
plasma starts as soon as the concentration of vapour at
particle surface is higher than the partial pressure of
vapour in the free stream plasma. The boiling model
(Boil.) assumes that mass transfer starts when the particle
material reaches its boiling point.
The 2-D domain analysed in this work included a
PL-35 Tekna plasma source and an axisymmetric reaction
chamber, schematically shown in Fig. 1.
Fig. 1 Detail of the computational domain (dimensions in
mm).
The origin of x-axis is located at the top of the reaction
chamber. Working gases are supplied through three
different inlet regions located in the head of the torch:
carrier gas from the probe tip (6 slpm pure Argon),
primary gas from the gap between the probe and the
quartz tube (12 slpm pure Argon) and sheath gas from the
inlet between the quartz and ceramic tubes (60 slpm Ar +
6 slpm H2). A no-slip boundary condition is applied on all
the internal walls, while a 300 K temperature has been
fixed at the external walls of the torch and the internal
walls of the chamber. The operating pressure has been
fixed at 40 kPa. The electromagnetic field equations are
solved in an enlarged domain extending 40 mm outside of
the torch in the y-direction, using the extended field
approach [5]. The coupled power has been set to 10 kW,
which corresponds to typical lab-scale generator plate
power of 18 kW. The precursors are characterized by a
particle size distribution with mean diameter equal to 10
m.
For each model, four simulations have been carried out
with different precursor feed rate (1, 2, 3.5 and 5 g/min).
3. Results
The models tested in this work resulted in very different
evaporation rate and efficiency. On one side, the
turbulence models adopted predict a different flow regime
inside the torch, which is fully turbulent for the KE model
and almost laminar for the RSM, influencing the
thermo-fluid-dynamic behaviour of the plasma
surrounding the evaporating particle and thus influencing
the evaporation process; on the other side, the models for
precursor evaporation determine directly the rate of mass
reduction of the precursor particles and also have an
indirect influence on the plasma, determining the heat
required by the particle to completely evaporate and,
consequently, the loading effect on the plasma. In Fig. 2,
results for plasma temperature and precursor evaporation
contours are reported: RSM model results in a higher
cooling of the axial channel where precursor is flowing,
with respect to KE model; with the vaporization model,
the evaporation is predicted to start in a more upstream
position with respect to the boiling model.
Results for total precursor evaporation obtained with
different models have been collected in Fig. 3, while in
Fig. 4 results for particle thermal history and evolution of
particle diameter have been reported only for the particles
with initial diameter equal to 17 m.
The RSM-boiling model predicts the lowest
evaporation efficiency and for feed rate higher than 1.5
g/min, the onset of a cold channel along particle
trajectories blocks further evaporation as the feed rate is
increased, limiting the evaporation rate to 1 g/min. In this
case, particles flowing inside the cold channel cannot be
heated up to the boiling point and the diameter is
unchanged along the whole trajectory (see for example
particle with initial diameter of 17 m in Fig. 4), whereas
particles with initial diameter of few microns are
dispersed in the hot plasma region and they are
evaporated.
Turning to the KE turbulence model, the evaporation
efficiency is increased since the higher turbulence
predicted in the torch region allows a higher heat transfer
from the hot plasma core to the region cooled by particle
injection, resulting in a lower loading effect; however, the
evaporation efficiency is around 80%, because particle
with higher initial diameter cannot be completely
evaporated before leaving the high temperature region of
the plasma. Particle temperature in this case can reach the
silicon boiling point at 3538 K and at that point the
diameter starts to be reduced, even if the evaporation is
not complete.
models predict a lower loading effect and a more efficient
mass transfer for fixed heat flux from the plasma: also
particle with relatively high initial diameter are
completely evaporated. In this case, the particles reach the
plateau temperature around 3100 K, as kinetically
determined by the equilibrium between heating from the
plasma and cooling due to evaporation:
where
is the saturation pressure, T is the plasma
temperature, , dp, ρp are the temperature, diameter and
density of the particle, respectively;
is the universal
gas constant,
is the molecular weight of the
precursor; Nu and Sh are the Nusselt and Sherwood
numbers, respectively;
and
are the thermal
conductivity of the plasma and the diffusion coefficient of
vapours around the particle.
Fig. 2 Temperature and evaporation contours in the torch
region for the case with precursor feed rate of 1 g/min.
On the contrary, when the vaporization model is
adopted, the evaporation efficiency is close to 100% for
both KE and RSM turbulence models; in this case, the
Fig. 3 Evaporation rate (top) and efficiency (bottom) as a
function of precursor feed rate for different models
adopted.
measurements [5]. Further experimental work compared
with modelling results of the same experimental setup is
required to fully answer the question.
Fig. 4 Particle temperature (top) and diameter (bottom)
obtained with different models adopted in this paper.
Simulations performed for particles with initial diameter
of 17 m, case with precursor feed rate of 3.5 g/min.
Since very different results can be obtained, the
question of which model is in better agreement with
reality arises. However, no validation of evaporation
models has been fully reported yet because of difficulties
in experimentally measuring the evaporation rate; even if
some related experimental works have been presented on
measurement of precursor vapour concentration [7] and of
the size distribution of treated and untreated precursors
[8], a direct comparison between modelling and
experiments remains an unsolved issue. A conclusion on
the accuracy of these models maybe will be possible in
the future by comparing results from modelling and
experimental measurements for test cases with simplified
and well controlled operating conditions (mainly torch
coupled power, precursor feed rate, and gas composition).
Regarding the choice of the turbulence model, some
validation has been reported for the region downstream
the plasma torch and to some extent also inside the torch,
demonstrating that KE model is fitting enthalpy probe
4. Conclusions
The precursor evaporation process in an inductively
coupled thermal plasma system for nanoparticle
production has been modelled adopting different models
for turbulence and particle evaporation. Very different
results have been obtained using different models. Among
turbulence models, standard k-ε predicts a turbulent flow
inside the torch that reduces the plasma cooling effects of
a high precursor loading conditions; with the Reynolds
Stress Model, on the contrary, an almost laminar flow has
been obtained, where loading effects are higher and result
in a lower evaporation efficiency. As for the models for
particle evaporation, the boiling model resulted in lower
evaporation efficiency and a higher loading effect with
respect to the vaporization model. Even though
evaporation models have been deeply studied in the past,
investigations were carried out only for thermal spray
applications, where the differences between results
predicted by the models were limited and could be
reasonably neglected. On the other hand, due to the
plasma temperature being closer to the boiling point of
the treated material, especially under high loading
conditions, the two evaporation models predict quite
different results when applied to inductively coupled
thermal plasma system for nanoparticle production; up to
date, there is no experimental evidence to define which
model better describes the real process, strengthening the
need for further experimental and modelling work to
settle the issue.
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