Materials Science and Engineering B77 (2000) 293 – 296
Letter
Obtaining of micro-spheres in plasma: theoretical model
Ioan Bica
Faculty of Physics, West Uniersity of Timisoara, Bd. V. Paran no. 4, 1900 Timisoara, Romania
Received 1 December 1999; received in revised form 31 May 2000; accepted 12 June 2000
Abstract
The paper presents the mechanism of formation of iron and glass micro-spheres in plasma. We developed a set of equations
for computing the inner and outer micro-sphere radii, and for describing their dependence on technological process parameters.
© 2000 Elsevier Science S.A. All rights reserved.
Keywords: Micro-spheres; Plasma; Glass
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1. Introduction
To know the dependency of dimensional characteris-
tics of micrographies on technological parameters of
particle obtaining, is a problem of high practical impor-
tance. In paper [1] a model of micro-sphere formation,
by using the sol–gel method, is proposed.
In this paper, the diameter and the thickness of the
wall of micro-sphere, as a function on the gas–vapor
system and sub-cooling and on the iron or glass vapor
quantity respectively, will be determined, when plasma
method is used.
The technological process description of micro-sphere
obtaining in plasma, is presented in [2].
2. Theoretical model
The production of micro-spheres with pre-established
physical characteristics is the result of experimental
research. The elaboration of a theoretical physical
model, which takes into account all parameters that
contribute to the production of the micro-spheres, is very
difficult. Although, in the following, our goal is to
describe the mechanisms that intervene in the process of
producing micro-spheres in the plasma jet, but without
exhausting the subject.
At temperatures T 3000 K [3], the materials of
interest (in the present case, the steel rods and the glass
powder, respectively) are in vapor state.
Let’s assume that at temperature T the vapors partial
pressure is p
v
, and the total pressure of the vapor–
plasma gas mixture is p. Then,
X =
p
v
p
(1)
is the molar ratio of the vapors.
The molar density C
m
of the vapor – plasma gas
mixture can be computed (for low vapor concentrations)
from the law of perfect gases,
C
m
=
p
RT
(2)
where R is the universal constant of the perfect gases,
and p is the total pressure of the mixture. Let’s consider
that the vapors mixed with the plasma gas occupy the
volume of a sphere with the radius r
0
,
r
0
=
3
4
m
1
C
0
1
3
(3)
where m is the mass of vapors, is the molar (atomic)
mass of the vapors, and
C
0
=
p
v
RT
(4)
is the molar concentration of the vapors.
In places having temperatures T
1
T, the vapors in
the peripheral areas of the sphere condense. In this way,
a sphere with the radius r
1
forms (r
1
r
0
), having
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