Heating and Coagulation of Nanoparticles in a Plasma Jet
29
3 Numerical Results and Discussion
The plasma jet with nanoparticles is simulated for different plasma pressures and
nanoparticles densities at the inlet. 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.
This section presents the results of the heating of nanoparticles and their coagulation in the plasma jet, as well as their influence on the temperature profile of the
plasma and the velocity of the dust particles.
Figure 1 shows the spatial distributions of the nanoparticle temperature at different
their sizes along the axial coordinate. Figure 1 a corresponds to the plasma pressure
at the inlet P 0 = 4 Torr and (b)—P 0 = 40 Torr. It is seen that the temperature of the
nanoparticles in the plasma stream first grows rapidly, and then its fixed value is set.
Heating of nanoparticles is caused mainly by recombination of ions when they are
collide with nanoparticles. At this, ion ionization energy is transmitted to the heating
of nanoparticles. At low plasma pressure (Fig. 1a), the temperature of nanoparticles
increases with a decrease in their radius. This result can be explained on a simplified
model describing the temperature change of nanoparticles:
Cm d
dT d
dt
=
j
P j .
Here m d , C are mass and heat capacity of dust particle. In the right part of the
equation are energy streams on the surface of the dust particles. Approximate can
be assumed that these streams are proportional to the surface area of the dust, that
is proportional to its radius in the square. At the same time, the mass of the dust is
proportional to its radius in Cuba. It follows that the temperature of nanoparticle is
inversely proportional to its radius. This dependence of the dust temperature on their
radius corresponds to the results obtained for low pressure plasma (P 0 = 4 Torr), but
contradicts the results obtained at the pressure of P 0 = 40 Torr. The reason for this
discrepancy is the cooling of dust particles upon contact with a neutral gas, which
becomes significant at the pressure P 0 = 40 Torr. It should be noted that the cooling
of dust particles with a smaller radius occurs more efficiently than the dust of a larger
radius (provided that they have the same mass). This is due to the fact that in the
first case the total surface of the dust component in contact with the plasma will be
larger. Significant cooling of small dust particles in the case of P 0 = 40 Torr and
leads to a decrease in their temperature compared to the temperature of the larger
dust particles.
The above confirms Fig. 2 where the spatial distributions of the temperature of
the heavy plasma component (ions and atoms) along the axial axis are presented
for the case r d = 50 nm (a) and r d = 200 nm (b). The solid curves correspond to
the plasma pressure at the inlet P 0 = 4 Torr, and the dotted ones corresponds to
29
3 Numerical Results and Discussion
The plasma jet with nanoparticles is simulated for different plasma pressures and
nanoparticles densities at the inlet. 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.
This section presents the results of the heating of nanoparticles and their coagulation in the plasma jet, as well as their influence on the temperature profile of the
plasma and the velocity of the dust particles.
Figure 1 shows the spatial distributions of the nanoparticle temperature at different
their sizes along the axial coordinate. Figure 1 a corresponds to the plasma pressure
at the inlet P 0 = 4 Torr and (b)—P 0 = 40 Torr. It is seen that the temperature of the
nanoparticles in the plasma stream first grows rapidly, and then its fixed value is set.
Heating of nanoparticles is caused mainly by recombination of ions when they are
collide with nanoparticles. At this, ion ionization energy is transmitted to the heating
of nanoparticles. At low plasma pressure (Fig. 1a), the temperature of nanoparticles
increases with a decrease in their radius. This result can be explained on a simplified
model describing the temperature change of nanoparticles:
Cm d
dT d
dt
=
j
P j .
Here m d , C are mass and heat capacity of dust particle. In the right part of the
equation are energy streams on the surface of the dust particles. Approximate can
be assumed that these streams are proportional to the surface area of the dust, that
is proportional to its radius in the square. At the same time, the mass of the dust is
proportional to its radius in Cuba. It follows that the temperature of nanoparticle is
inversely proportional to its radius. This dependence of the dust temperature on their
radius corresponds to the results obtained for low pressure plasma (P 0 = 4 Torr), but
contradicts the results obtained at the pressure of P 0 = 40 Torr. The reason for this
discrepancy is the cooling of dust particles upon contact with a neutral gas, which
becomes significant at the pressure P 0 = 40 Torr. It should be noted that the cooling
of dust particles with a smaller radius occurs more efficiently than the dust of a larger
radius (provided that they have the same mass). This is due to the fact that in the
first case the total surface of the dust component in contact with the plasma will be
larger. Significant cooling of small dust particles in the case of P 0 = 40 Torr and
leads to a decrease in their temperature compared to the temperature of the larger
dust particles.
The above confirms Fig. 2 where the spatial distributions of the temperature of
the heavy plasma component (ions and atoms) along the axial axis are presented
for the case r d = 50 nm (a) and r d = 200 nm (b). The solid curves correspond to
the plasma pressure at the inlet P 0 = 4 Torr, and the dotted ones corresponds to