Introduction1)

The production of materials having pre-established

physical properties meets the ever more sophisticated

need of contemporary society. For example, fluids with

controllable rheological properties are achieved from di-

electrical microparticles [1-6] and/or magnetizable mi-

croparticles [7-11]. Fluids having such a property [1-6,

7-10, 12-14] are used in various applications as shown in

references [15-24].

Iron microparticles as a subclass of magnetizable par-

ticles are of great interest. Under full form, we have the

solid phase of magnetorheological suspensions [7-11].

Covered with nanotubes [25], they haves adsorbant

properties.

Under this form, they are used in some cancer therapies

[25,26], in the common knowledge that iron is tolerated

by the living organism, in well-chosen doses [27].

An interesting category of microparticles, for future ap-

plications, are cavitary iron microparticles, namely mi-

crospheres [29-32], microtubes [33] and octopus-shaped

microparticles [34].

Production of cavitary microparticles [35] is determined

by the proper correlation of the technological parameters

(electric current intensity, argon flow and advancemat-

erial velocity) with their plasma formation mechanisms.

In order to provide data concerning the improvement of

the production technology for cavitary iron micropart-

icles in plasma, a model is presented, in what follows,

concerning the formation of these species of micro-

†To whom all correspondence should be addressed.

(e-mail: ibica2@yahoo.com)

particles, in close correlation with technological para-

meters.

Model

Velocity and Temperature Field in the Argon Plasma

Jet

The plasma arc is started in argon medium between the

wolfram electrode and the metal to be processed, con-

nected to the positive clamp of the current source

[35-38]. After penetration of the metal, the plasma moves

as jet [36].

The equation of motion for the plasma jet is of the

Navier-Stokes type. For the stationary case, the plasma

motion equation is [36,39]:

∇∇∆ (1)

in which ρ, , η, and p are the density, the velocity, theviscosity and the gas-kinetic pressure of the plasma.

We assume the plasma jet to have axial symmetry.

Then, the velocity field written in the coordinates r, θ,

and (Figure 1) are:φ

⋅

⋅

and ⋅

⋅

We introduce the notation:

= sinλ θ (2)

and then, the radial velocity vr and the angular velocity

Ioan Bica†

Faculty of Physics, West University of Timisoara, Bd. V. Parvan, No.4, 300223, Timisoara, Romania

Received September 19, 2006; Accepted March 14, 2007

Abstract:The paper presents some mechanisms involved in the formation of iron microparticles (full spheres,

pore microspheres, microtubes and octopus-shaped microparticles), in close correlation with technological pa-

rameters, experimental results and discussion of them.

Keywords: microsphere, microtube, octopus-shaped microparticle, plasma jet, current function

Ioan Bica694

vθ, respectively, become:

vr = -

⋅λ

and vθ= -

λ

⋅

(3)

The current function is represented as the product ofΨ

the radial direction r, the kinematic viscosity v of the

plasma and the function f(r), namely:

=Ψ r⋅v⋅f(r) (4)

We introduce the function from Eq. (4) in the groupΨ

of relations (3) and there results an expression for vr and

for vθ, respectively. vr and vθ will be introduced, in turn,

in Eq. (1). An equation results in vr and one in vθ,

respectively.

Using the equations obtained, pressure p is released and

an equation is obtained in f and , under the form [36]:λ

f2-2(1-λ

2)f'-4λ f = ( )Σ λ⋅ (5)

There, f ' is the derivative of f function of , ( ) is aλ Σ λ

quadratic function of and it contains theλ c integration

coefficients.

For the axial symmetry plasma jet ( ) = 0, and theΣ λ

solution of Eq. (5) is [36], too:

f( ) =λλ

λ

(6)

From Eqs. (4) and (6), it obtains:

= rΨ ν⋅ ⋅λ

λ

(7)

Expression (7) is the current lines equation for the plas-

ma jet with axial symmetry. The plasma motion is con-

sidered [36] as being generated by a forces field , situ-

ated at a point at the infinite and located on the jet axis.

Then, for the case of relatively great plasma flows (c ≤

0.1), Ref. [36] shows that the value of the force can be

obtained from the formula:

≈

ρ⋅ ⋅v

2

From which there results:

≈

⋅(8)

in which is the plasma density at the temperatureρ T

and the pressure p.

The radial shape of the plasma jet velocity is of interest

four our application. Based on this consideration, we in-

troduce from Eq. (7) inΨ vr in the group of relations (3)

and we obtain:

vr =

λλλ

(9)

For = 0( =1), from expression (9) the velocity alongθ λ

the symmetry axis (Oz) of the plasma jet is obtained. The

expression of c from Eq. (8) is introduced in the ex-

pression so obtained and

vr =

(10)

is obtained.

The transferred plasma arc column is traversed by an

electric current of intensity I. The magnetic field gen-

erated by I produces the confination of the transferred

plasma arc. Under the Pinch effect, along the cross-sec-

tion of the plasma column of radius R, at points located

on it, at distances r from the axis of the column, the pres-

sure is [35,36]:

p =

(R2- r

2)

where µ0 is the magnetic permeability of the vacuum.

The pressure p, for r [0,∈ R] generates the force:

⋅⋅

(11)

The pressure due to the superficial plasma tension has

been neglected here.

From relations (10) and (11) the axial velocity of the

plasma jet is obtained, written by renouncing the index r,

namely:

⋅⋅⋅

(12)

in which r is the distance measured along the jet axis (θ

= 0) from the plasma generation point.

The plasma jet is generated at the transfer point of the

plasma arc (the origin O of the coordinates system Oxyz

in Figure 1). For the distance nozzle-rod of 5 10⋅-3m,

and nozzle diameter of 3 10⋅-3m, using the method de-

scribed in Ref. [40], the diameter of the anode spot is es-

timated to be 0.5 10⋅-3m.

We consider the radial distance to be half on the anode

spot radius, that is r = 125 10⋅-6m. Then, for = 2.9 ×η

10-4kg/s m, = 0.02 kg/mρ⋅

3at the argon plasma tem-

Formation of Iron Microparticles in the Argon Plasma Jet 695

Figure 1. Installation for production of microparticles in plas-

ma (general view): A-plasma generator (1-wolfram electrode,

2-nozzle), B-current source (with falling characteristic), C-ma-

terial advance system, 3-contact nozzle, 4-carbon-steel rod;

5-transferred plasma arc; 6-plasma jet; I-current intensity;

Oxyz-coordinate system; θ, r, φ-spherical polar coordinates;

vr, vθ-plasma jet velocity components, v-plasma axial jet veloc-

ity, vt-rod advance velocity.

Figure 2. The axial velocity of the plasma jet function of the in-

tensity I of the current through the transferred plasma arc. =

theoretical values; °°°° = experimental values.

perature of 10,000 K [36] and r = 125 µm, there results

from (12) the axial velocity of the plasma jet function of

I (Figure 2).

The experimental values of the axial velocity of the

plasma jet were determined by using a pressure probe

(strongly cooled) connected to a differential water man-

ometer [32]. At equilibrium between the dynamic pres-

sure of the plasma and the water column pressure, there

takes place the relation:

Figure 3. The plasma jet velocity vj in points x/R on the cross-

section of the plasma jet at values I of the electric current in-

tensity through the transferred plasma arc as parameter.

vexp =

(13)

in which ρW and h are the density and the unevenness of

the water column, and g is the gravitational acceleration.

For = 0.02 kg/mρ3[36], ρW = 1,000 kg/m

3and g =

9.81 m/s2, expression (13) assumes the form:

vexp = 31.31⋅h0.5

(14)

The values of the axial velocity determined experiment-

ally and calculated by formula (14) are shown in Figure

2. The differences between the experimental and the the-

oretical values are due to the modification of the plasma

transport properties by temperature [36] on one hand,

and the weight positioning of the probe on the plasma jet

axis, on the other hand.

We assume that the plasma jet, in the immediate prox-

imity of the generation point, still preserves the cylinder

form.

Then, the distribution of the plasma jet velocity on the

cross-section of the column of radius R (along the axis

Ox) is:

vj = v

(15)

and is of the shape in Figure 3.

We introduce F from expression (11) in relation (9) and

we obtain:

≈

⋅(16)

Ioan Bica696

Figure 4. The value c function of the intensity I of the current

through the transferred plasma arc in argon medium.

For v = 1.45 × 10-3m

2/s at argon plasma temperatures

of 10,000 K, in formula (10) c is calculated function of

I. The values obtained are shown in Figure 4.

It can be noticed in Figure 5 that the current lines in the

argon plasma jet are identical for [0.0 0.90].λ∈

Modifications of the spectrum of the current lines occur

for 0.95 1.0.≤λ≤

According to Ref. [36], the plasma jet isotherms are cal-

culated by means of the formula:

≅⋅⋅

⋅⋅

(17)

in which Q is the source power transferred to the plasma,

CP = 4,000 J/kgK is the argon plasma specific heat at

temperatures of 10,000 K [36].

Prandtl’s number is calculated by the formula:

ℵ

⋅ (18)

(a) (b)

(c) (d)

Figure 5. Distribution of the current lines in the argon plasma jet for a) I = 100 Adc (c = 0.009); b) I = 275 Adc (c = 0.004); c) I = 175

Adc (c = 0.008); d) I = 375 Adc (c = 0.002) and values of const.Ψ

Formation of Iron Microparticles in the Argon Plasma Jet 697

Table 1. Q for Different Values of I

I (A) 100 175 275 375

Q (W) 400 612.5 972.5 1,025

Figure 6. Values of the temperature T at points x/R on the

cross-section of the argon plasma jet for values I of the electric

current intensity through the transferred plasma arc in argon

medium.

where = 2.9 10η ⋅-4kg/s m, and = 0.625 J/s m⋅ ℵ ⋅ ⋅

K are the viscosity, the specific heat at constant pressure

and the thermal conductivity of the argon plasma at tem-

peratures of 10,000 K [36].

The power injected by the current source in the trans-

ferred plasma arc is Q. For a conversion factor of about

10%, the power Q function of intensity I of the current

through the transferred plasma arc has the values in

Table 1.

Along the plasma jet axis ( = 1), the plasma jet temλ -

perature will be called axial temperature and will be de-

noted by T0. For Pr = 1.856 and known values of ρ, Cp,

and v, at distances r = 0.005 m, from formula (17) we ob-

tain:

T0 = 32.2⋅Q (19)

We consider that the distribution T of the temperature

on the cross-section of the plasma jet is:

(20)

where Tm = 300 K is the initial temperature of the argon.

We introduce the expression of T0 from Eq. (19) in ex-

pression (20) and, for values of Q in Table 1 correspond-

ing to I, we obtain the distribution T of the temperature

on the cross-section of the plasma jet, under the form of

the graphs in Figure 6.

Figure 7. Values of the dd diameter of the metal drops in points

x/R on the cross-section of the plasma jet, for values I of the in-

tensity of the electric current through the transferred plasma arc

as parameter;⋅⋅⋅⋅experimental data (obtained by optical mi-

croscopy).

The values of T thus obtained are normal for the argon

plasma [36-38].

Pulverization of the Metallic Solid

The nozzle diameter of the generator in Figure 1 is

0.003 m. For a filling coefficient of the nozzle of 0.75, it

results that the diameter of the transferred plasma arc col-

umn is 0.00225 m. Then, for powers in the plasma arc

ranging between 4,000 K and 10,250 K (corresponding

to I(A) [100 375]) there result power densities in plas∈ -

ma ranging between 945 and 2,422 MW/m2.

For such values of power densities, the rod portion in-

troduced in plasma at the velocity vt melts. If the kinetic

energy of the plasma jet is greater than or at least equal

to the superficial energy of the melt, the metallic solid

changes into drops. Mathematically, the condition stated

is under the form:

0.5ρ⋅ ≥

(21)

in which = 1.2 N/m is the superficial tension of theσ

iron melt and d is the drop diameter.

The maximum drop diameter is obtained from condition

(21) and has the form:

⋅

(22)

From expressions (15) and (22) the dimensional dis-

tribution of drops on the cross-section of the plasma jet is

obtained and it has the graphic form in Figure 7.

It can be noticed from Figure 7 that the drops are poly-

disperse. Their diameter decreases considerably with the

Ioan Bica698

(a) (b) (c)

Figure 8. Drop generation velocity nd at points x/R on the cross-section of the plasma jet for values of the intensity I of the electric

current through the transferred plasma arc and material advance velocities as parameter: a) vt = 0.001 m/s; b) vt = 0.00150 m/s; c) vt =

0.00125 m/s.

Figure 9. function of x/R, for intensitiesβ I of the current

through the transferred plasma arc as parameter.

increase of I. On the contrary, the drop diameter in-

creases for x R.→

We consider that the quantity of substance is preserved

during the transformation of the metallic solid into drops,

namely 2d2dρpnd = 3d

2dtρmνt, from which we obtain:

(23)

in which nd is the number of drops generated per unit of

time, ρm and ρp are the metal and the drop densities and

vt is the rod advance velocity in plasma.

For dt = 0.003 m, ρm = 7,800 kg/m3, ρp= 6,700 kg/m

3

and values of dp in Figure 7, introduced in expression

(23), we obtain, as in Figure 8, values of nd in points x/R

on the cross-section of the plasma jet. It can be noticed

from Figure 8 that nd increases considerably with the in-

crease of I and vt. On the contrary, nd decreases towards

the marginal areas of the plasma jet.

Formation of Sphere-Shaped Microparticles

Micrometric-size particles, full inside, and sphere-shap-

ed, will be called sphere-shaped microparticles. They are

obtained following drop solidification on leaving the

plasma jet in the collecting chamber. For drops to be

spherical, the necessary and sufficient condition is that

[35]:

⋅ (24)

in which the notations used are the known ones.

The values of the adimensional parameter at pointsβ

x/R on the cross-section of the plasma jet are the ones in

Figure 9. They are obtained by corroborating equality

(24) with vj = vj(x/R)I in Figure 3.

It can be noted from Figure 3 that for I = 100 Adc,

sphere-shaped drops are produced for . But, for 0 ≤ x/R

1. But, for≤

1) I = 175 Adc, for 0.5β ≤ x/R 1;≤

2) I = 275 Adc, for 0.85β ≤ x/R 1;≤

3) I = 375 Adc, for 0.92β ≤ x/R 1.≤

Formation of Microspheres

The axial zone of the plasma jet (0.0 ≤ x/R 0.2) has≤

temperatures of over 10,000 K, function of the intensity I

of the current through the transferred plasma arc (Figure

3). Here, the drops of sizes dp 10 µm instantaneously≤

change into vapors. For velocities nd of drop generation,

properly chosen, the molar concentration C0 of the va-

pors is much smaller as compared with the molar con-

centration of the gas and vapors mixture. It results that

the vapors do not sense one another and can be assimi-

lated to an ideal gas.

We consider that the transformation of the drops into

Formation of Iron Microparticles in the Argon Plasma Jet 699

Figure 10. Variation of d0 function of x/R for intensities I of

the current through the transferred plasma arc as parameter.

vapors is achieved at constant pressure. Then, by the iso-

baric transformation law, the equivalent diameter of the

vapor sphere is:

d0 = d⋅

(25)

in which T is the vapors temperature considered to be

equal to that of the plasma and Tmelt = 1,800 K [41] is the

temperature of the liquid metal.

For values of T in Figure 6 and of dd in Figure 7, re-

spectively, introduced in expression (25), d0 = d0(x/R)Iare obtained, as in Figure 10.

Driven by the plasma jet, the spheres reach regions with

temperatures close or equal to the ones of the “dew

point”. For iron vapors, at pressures close to those of the

collecting medium ( 0.15 MPa), the “dew point” tem∼ -

perature is T1 2,000 K [33]. On reaching the “dew≈

point”, the sphere-gas interface changes into a liquid

membrane.

The transformation is isobaric. Then, from the isobaric

transformation law, the membrane diameter is obtained,

namely:

de = d0 ⋅

(26)

We introduce in relation (26) the values of T in Figure 3

and those of d0 in Figure 10, respectively, and we obtain

de = de(x/R)I, under the form of the graphs in Figure 11.

The gas and vapors mixture in the interior delimited by

the membrane will be divided into elements of volume

dV. Due to the temperature gradient, the volume ele-

ments dV reach the interior part of the membrane. Here,

in a short time, and in turn, each element dV transfers va-

pors by diffusion.

Figure 11. Values of de at points x/R on the cross-section of the

plasma jet for intensities I of the current through the transferred

plasma arc as parameter;⋅⋅⋅⋅experimental data (obtained by

optical microscopy).

The diffused vapors condense. The diffusion times be-

ing short, the transport of substance by diffusion takes

place in non-stationary regime [30-35].

After exhaustion of vapors inside the sphere, the mem-

brane thickens and a microsphere is obtained. The micro-

sphere thus obtained has its outer diameter de and its in-

ner diameter di. The microsphere wall is formed of melt

and is of thickness:

(27)

We consider that the formation of microspheres in the

plasma jet is achieved without substance loss, that is:

(28)

in which Cc is the molar concentration of the germs in

liquid phase

⋅⋅Δ

Δ (29)

where ΔE = 40 MJ/Kmol K [41] is the diffusion activat-

ing energy, equal to the energy of vapor condensation, R

is the universal constant of ideal gases and ΔT = T-T1 is

the undercooling of the gas and vapors system.

From the conservation equation (28) and expression

(29) we obtain:

di = de

⋅

(30)

and

Ioan Bica700

(a) (b)

(c) (d)

Figure 12. Values of the undercooling ΔT at points x/R on the cross-section of the plasma jet, for which iron microspheres are

formed, for as parameter and: a) I = 100 Aα dc; b) I = 175 Adc; c) I = 275 Adc; d) I = 375 Adc.

= 0.5 (δ ⋅ de-di) =

0.5⋅de⋅

⋅

(31)

We make the notation:

=α

⋅Δ

Δ (32)

and then, the last equality in the group (31) becomes:

= 0.5δ ⋅de (1-⋅ ) (33)

For ≠, from expression (33) there results the con-

dition:

< 1α (34)

Expression (34) will be called the condition of micro-

sphere formation.

From expression (32),ΔT is obtained, namely:

Δ

⋅

Δ(35)

We introduce values of T from Figure 3 in expression

(35) and we obtain ΔT = ΔT (x/R)α,I, under the form of

the graphs in Figure 12, for which iron microspheres are

formed in the argon plasma jet.

We introduce the values of de from Figure 11 in ex-

pression (33) and we obtain = (δ δ x/R) ,α I, under the

form of the graphs in Figure 13.

It is noticed from Figure 12 that decreases considδ -

erably with the increase of andα I. On the contrary, for

fixed and I, the thickness of the microsphere wall inα -

creases monotonously with the increase of x/R, up to x/R

0.85, after which the growth of becomes abrupt.≈

Formation of Iron Microparticles in the Argon Plasma Jet 701

(a) (b)

(c) (d)

Figure 13. The thickness of the wall of the microspheres generated at points x/R on the cross-section of the plasma jet for andδ α I

as parameters. Note: de is the outer diameter of the microspheres.⋅⋅⋅⋅experimental data (obtained by optical microscopy).

Pore Microsphere Formation

The hollow microparticles with discontinuities in the

wall bear the name of pore microspheres. They are

formed, as we will see in what follows, by abrupt decel-

eration of microspheres on leaving the plasma jet.

The microspheres in the plasma jet have their walls

made of melted metal. In the cavity of the microsphere,

with inner diameter di, there is argon.

The temperature of the argon on leaving the jet, will be

assumed to be equal to that of the liquid metal.

The velocity of the microspheres will be taken as equal

to that of the plasma jet. On leaving the jet, the velocity

of the microspheres decreases abruptly and becomes

equal to ≪ .

Because of deceleration, the gas mass in the micro-

sphere cavity is acted upon by the density of volume

force:

≈

⋅

for di ≈ de

and vj >> vm (36)

in which ρAr = 1,078 kg/m3at TAr = Tmelt = 1,800 K and

pressure of 0.15 MPa [39].

The force has the direction of the velocity of the plas-

ma jet and the sense opposed to and it acts upon the

hemisphere of the sphere, as shown in Figure 14. From

the microsphere wall, on the action of , there comes theaction of the volume density of superficial force:

′

(37)

in which h is the height of the spherical cap.

Ioan Bica702

Figure 14. Microsphere (model): 1-liquid microsphere wall;

2-gas (Ar); re-the outer radius; ri-the inner radius; rp-the radius

of the sphere cap (of the microspheres); h-the height of the

spherical cap; -the inertial force; -the microsphere velocity

(equal to that of the plasma jet) [32].

When

⋅

>>

(38)

in the microsphere wall, a pore of diameter dP = 2rP is

formed.

Using the notations in Figure 14, the formula for the

calculation of the height of the spherical cap is:

or

⋅

(39)

We introduce the last expression from the group (39) in

condition (38) of pore formation and we obtain:

ε

⋅⋅

, with << 1ε (40)

in which is an adimensional value, numerically equalε

to the ratio between the superficial energy of the melt

and the kinetic energy of the plasma jet.

The notation:

(41)

was introduced in expression (40).

From expression (40), following simple calculations,

there obtains:

ε⋅

⋅⋅

(42)

We introduce relation (42) in expression (41) and obtain:

ε⋅

⋅⋅

(43)

The graphical representation of the dp function of x/R for

and I as parameters is the one in Figure 15. To achε -

ieve this representation, formula (43) was used, in which

vj from Figure 3 and de from Figure 11 were introduced.

From Figure 15 it can be noted that the formation of

pores in the microsphere walls is achieved in the axial

zone and in the zones adjacent to it of the plasma jet. The

diameter of the pores is considerably influenced by the

intensity I of the current through the transferred plasma

arc and by the adimensional parameterε.

Formation of Microtubes

Microtubes are cylinder-shaped microparticles. For mi-

crotube formation, the advance velocity of the electrode

rod must be fixed so that along the lines in the plasma jet

melt-filled cylinders form. Let be the advance velocity

of the electrode rod. Then, at equilibrium, the con-

servation equation is of the form:

⋅⋅⋅

⋅⋅ (44)

in which nc is the number of cylinders with melt gen-

erated in the time unit, dc and lc are the diameter and the

length of the cylinder.

The diameter dc is longest when the kinetic energy of

the plasma jet is equal to the superficial energy of the

melt. It results that for the case of microtubes a relation is

obtained which is analogous to expression (22) and iden-

tical values dc = dd at points x/R on the cross section of

the plasma jet.

We introduce dc = dd, from Figure 7, in the conservation

equation (44) and imposing that lc = 100⋅dd, it is ob-

tained from the same equation that nc = nc(x/R)I,, under

the form of the graphs in Figure 16. The diameter of the

electrode rod is d = 0.003 m.

It is noticed from Figure 16 that nc increases with the

increase of and is considerably influenced by the in-

crease in the intensity I of the electric current through the

transferred plasma arc. On the cross-section of the plas-

ma jet, nc has a maximum value for 0 ≤ x/R 0.12,≤

which depends on I and , after it decreases monoto-

nously to a minimum value which depends on the above-

Formation of Iron Microparticles in the Argon Plasma Jet 703

(a) (b)

(c) (d)

Figure 15. Zones on the cross-section of the plasma jet and diameters of the pores, for diameters de of the microspheres and I, re-

spectively, as parameters; °°°°°° = experimental data (obtaibed by optical microscopy).

(a) (b) (c)

Figure 16. The number nc of melt fibres generated in the time unit of points x/R on the cross-section of the plasma jet for intensities I

of the current through the transferred plasma arc and rod advance velocities in plasma: (a) = 0.0010 m/s; (b)

= 0.0015 m/s; (c)

= 0.0020 m/s.

parameters.

In the region 0≤ x/R 0.80, the plasma has high tem≤ -

perature values (Figure 6). Along the current lines, the

melt lines change into vapors. We consider the process to

be of the isobaric type. Then, each melt fibre changes in-

to a cylinder with vapors of diameter:

Ioan Bica704

Figure 17. The diameter dce of the cylinder with iron vapors at

points x/R on the cross-section of the plasma jet and intensities

I of the electric current through the transferred plasma arc in ar-

gon medium.

(45)

It was considered here that the length lc0 of the cylinder

with vapors is equal to the length Lc of the cylinder

formed of melt (fibre). The vapor cylinders lie along

each current line in Figure 5. Their interfaces reach

points of the jet at which the temperature is equal or

close to that of the “dew point” (T1 = 2, 000 K) for the

iron vapors. The interface changes abruptly into a cylin-

der-shaped membrane. In the isobaric process hypoth-

esis, the membrane diameter is:

⋅

which, with relation (45), becomes

⋅

(46)

For dc = dd in Figure 7, introduced in expression (46), we

obtain

under the form of the graphs in Figure

17.

It can be noticed from Figure 17 that the outer diameter

of the cylinder with iron vapors decreases considerably

with the increase in I for zones of interest in the plasma

jet, as it results from Figure 16, that is, for 0 ≤ x/R ≤

0.40.

In the interior delimited by the membrane, a convective

movement of vapors occurs, due to the difference be-

tween the temperature of the membrane and that of the

vapors inside the cylinder. As in the case of the micro-

spheres, between the volume elements dV of vapors and

the membrane there takes place a transport of substance

in non-stationary regime.

At the end of the process, there are no longer vapors in-

side the cylinders of diameter . Microtubes are formed

with the inner diameter and the outer diameter

. The

thickness of the wall of the microtube is:

⋅ (47)

The quantity of substance in microtube formation is

preserved, which, mathematically, takes the form:

⋅ = ⋅

) (48)

in which the notations used are the common ones.

In the conservation equation (48) it was considered that

the length of the cylinder with vapors does not change on

microtube formation. From relations (29), (46), and (47),

following simple computations, we obtain:

⋅Δ

Δ and

(49)

For microtube formation it is necessary that

< 1, so,

from the first expression of group (49) there results:

⋅Δ

Δ ,

which suggests the introduction of the notation :

⋅Δ

Δ (50)

and then:

(51)

is the condition for iron microtube formation in the plas-

ma jet. It is identical to condition (34) of iron micro-

sphere formation in the argon plasma. So, the under-

cooling ΔT on iron microtube formation is identical to

the undercooling ΔT (Figure 12) necessary for iron mi-

crosphere formation in argon plasma jet.

From the group of relations (49) and in Figure 17 and

for αc in expression (50) as parameter, following simple

calculations, δc = δc(x/R)I,α is obtained - under the form

shown in Figure 18.

It can be noticed from Figure 18 that the thickness of

the microtube wall depends considerably on the intensity

I of the electric current through the transferred plasma

Formation of Iron Microparticles in the Argon Plasma Jet 705

(a) (b)

(c) (d)

Figure 18. Values of δc at points x/R on the cross-section of the plasma jet, with and I as parameters;α is the outer diameter of

the iron microtube.⋅⋅⋅⋅experimental data (obtain- ed by optical microscopy).

Figure 19. Movement of vapors around the drop: 1-drop; 2-gas

and vapors cylinder; a,b,...g-stagnation points; R-radius; Oxy-

system of cartesian coordinates; (r,θ) - polar coordinates [34].

arc and on the undercooling ΔT through the parameter

(Figure 12), respectively. At the x/R increases,α δc

grows, and for x/R 1, the microtubes change into→

fibres.

Formation of Octopus-ShapedMicroparticles

The particles with microsphere central nucleus from

which ligaments under the form of microtubes (or fibres)

branch off will be called octopus-shaped microparticles.

Their formation, as will come out of what follows, is the

result of the movement of the vapors around a micro-

sphere or around a sphere-shaped drop.

Let us assume a drop (or microsphere) surrounded by

vapors in movememt. For the study of the movement of

the drop and of the vapors, we place at the center of the

drop the system of coordinates in Figure 19.

Because of the viscosity of the gas and vapors mixture,

the drop (or, as the case may be, the microsphere) meets

Ioan Bica706

with resistance in its advance. At a given moment and for

a short time, the drop becomes immobile (the relative ve-

locity of the drop is null). At that moment, the hydro-

dynamic spectrum of the fluid medium around the drop

consists of a movement around a circular obstacle, com-

bined with the movement produced by a punctual whirl

[34].

The punctual whirl occurs around a circle resulting

from the intersection of the drop (or microsphere) with

the motion plane of the gas and vapors medium. Then,

the characteristic motion function is [40]:

∞

⋅⋅

+

⋅

∞

⋅

⋅

φ⋅ (52)

from which there result:

- the potential of the velocities :

φ ∞

⋅

⋅ (53)

- the current function:

∞

⋅

⋅ (54)

in which v∞ is the velocity of the gas and vapors mixture,

is the velocity circulation [40] andΓ .

The differential equation of the current lines is d (Ψ r,θ)

= 0 and then, from Eq. (54) we obtain the current lines

equation, namely:

∞

⋅

⋅ (55)

wherefrom, for r = R there rezults

⋅ ,

which means that the circle resulting from the inter-

section of the sphere with the gas-vapors mixture motion

plane is a current line.

From expression (52) it can be noticed that the velocity

of the complex motion of the gas vapors mixture around

the drop [40] is:

∞

⋅⋅

⋅ +

⋅∞⋅

⋅

⋅

Wherefrom is obtained from the gas-vapors mixture ve-

locity along:

- the Ox axis:

∞

⋅⋅

⋅ (56)

- the Oy axis:

∞⋅

⋅

⋅ (57)

From expressions (56) and (57), for r = R, we obtain:

∞⋅

⋅ , and

∞⋅⋅

⋅

from which the resulting velocity module is obtained:

⋅∞ ⋅

(58)

It can be noticed from expression (58) that stagnation

points of the gas and vapors mixture, on the circle of r =

R radius, are obtained for:

⋅∞

⋅

(59)

in which ∞

is a notation.

Because of the distribution of velocities vj in the plasma

jet and because of the low molar concentration of vapors

by comparison with the molar concentration of the va-

pors and gas mixture, the value is not a constant valγ -

ue, taking on discrete values [34]:

⋅⋅ (60)

în which

-will be called discretization

factor.

From and condition (63), there results:

⋅∞

, or ⋅ (61)

that is a straight line parallel to the Ox axis.

From the last relation of the group (61), for

, eight stagnation points are obtained on the R radi-

us circle (Figure 19). With relation to these points, the

current lines along which stand the vapors and gas cylin-

ders, occupy the following positions (Figure 19):

Formation of Iron Microparticles in the Argon Plasma Jet 707

-are tangential to the circle at points a and d;

-they prick the R radius circle (the drop) at points e and

g and,

-have their origin on the R radius circle at points b and c.

Between the vapor and gas cylinders there is only gas.

By the mechanisms described under “Formation of iron

microtubes”, ligaments are formed of the gas and vapors

cylinders. The direction of the ligaments is that of the

current lines in the plasma jet (Figure 5). The circular

form of the ligaments is due to the lowering of the molar

concentration of vapors along the current line [34].

Experimental Results and Discussion

The overall scheme of the installation for microparticle

generation, by pulverization of the metallic solid in the

argon plasma jet is described in Figure 1.

The installation comprises [35] the plasma generator A,

the current source B, the system of material advance C

and a command and functional blocks interblockage sys-

tem (not located in Figure 1). The plasma generator is of

laminary stabilization and it is water-cooled. The current

source, with falling characteristic, has the idle operation

voltage of 260 Vdc ±5 %.

It yields a current by electrical discharge in argon me-

dium, continually adjustable between 70 Adc and 350 Adc.

The material advance system allows the uniform in-

troduction of the metallic solid in plasma, at advance ve-

locities continually adjustable between 0.002 m/s ±1 %

and 0.015 m/s ±1 %. The plasma generator is fed with

technical argon from the compressed gas cylinder, by

means of a pressure reductor with flowmeter.

The argon flow can be adjusted continually between

0.0001 m3/s ±5 % and 0.001 m

3/s ±2 %, at a constant

pressure of 1.5 × 105N/m

2.

The metallic solid, from which microparticles are ob-

tained, is a carbon steel rod with the diameter d = 0.003

m ±10 %. The chemical composition (in massic %) of

the steel is the following:

C:0,19; Mn:10,85; P:0,045; S:0,045; Si:0,40 and

Fe:88,47.

The plasma generator has its nozzle with a diameter of

0.003 m ±5 %. The distance between the nozzle and the

rod is set at 0.005m ±10 %. The intensity of the electric

current by discharge is set at I = 175 Adc ±10 %. The ve-

locity of the rod and the flow D of argon are techno-

logical parameters which change during the experiment.

1) At v = 1.25 × 10-3m/s and D = 0.35 × 10

-3m

3/s, parts

of the rod melt. The melt, in steady flow, is carried by

the plasma jet and projected onto the wall of the collect-

ing chamber. By solidification, a compact mass is ob-

tained.

By lowering the advance velocity of the electrode rod to

v = 1.10 × 10-3m/s, the melt is partially in steady flow.

The solidified melt is under the form of microparticles

mixed up with various solidified forms (Figure 20(a)).

Indeed, at v = 0.00125 m/s, the drops generation veloc-

ity is of 6 × 1011drops/s in the discharge axis (Figure 8).

By lowering velocity to 0.0010 m/s, the drops generation

velocity diminishes 5 times (Figure 8).

The advance velocity of the rod is kept at the same

value. But the argon flow increases from 0.35 × 10-3m

3/s

to 1 × 10-3m

3/s. Now, microparticles are obtained in the

collecting chamber, in proportion of 95 %. Their shape

and dimensions are those in Figure 20(b).

By increase of the argon flow up to 0.001 m3/s, the in-

tensity of the current through the transferred plasma arc

decreases due to plasma resistance increase [35,36]. The

tension on the plasma arc increases. Following injection

of increased power in the arc, the velocity vj of the jet in-

creases, reaching values for I = 275 Adc. The plasma ve-

locity, in the axial zone (0 ≤ x/R 0.3) has values of≤

800 m/s (Figure 3). The diameter of the drops decreases

100 times (Figure 7). On the contrary, the drops gen∼ -

eration velocity increases up to 1,000 times (Figure 8).

The shape of the drops is spherical for jet regimes 0.85

≤ x/R 1.≤

We consider that the size of the drops does not change

by solidification. Then, a good correlation is observed

between the polydispersion of the drops in Figure 7, for I

= 275 Adc, and the one shown in Figure 20(b).

It can be seen on the optical microscope that some of

the microparticles have pores (Figure 20(c)). Analysing

them, we see that they are hollow inside (Figure 20(d)).

Of 450 microspheres, 35 % have pores. The medium-

sized microsphere has a diameter of 10 µm and the wall

thickness of 0.75 µm.

Indeed, for de (µm) corresponding to I = 275 Adc and

0.2 0.8, in regimes 0.0≤ε≤ ≤ x/R 0.6 (Figure 15)≤

of the plasma jet, the microspheres are decapped or they

show pores with diameters dp, fractions of the outer di-

ameter de, according to the value of the ratio between the

superficial energy of the melt and the kinetic energy of

the plasma jet.

At v = 1.25 × 10-3m/s and D = 0.65 × 10

-3m

3/s, are ob-

tained microparticles, microspheres and about 15 % mi-

croparticles with a central nucleus (microsphere) from

which ligaments branch off in the same plane. It can be

noticed from Figure 21 that the ligaments (under the

form of tentacles) are hollow inside.

The particles with such shape will be called octopus-

shaped microparticles. Their mean dimensions are:

-for the nucleus (diameter: 12 µm; wall thickness: 0.5

µm);

-for ligaments (length: 88 µm; equivalent diameter: 2

Ioan Bica708

(a) (b)

(c1) (c2)

(d1) (d2) (d3)

Figure 20. Shapes and sizes of iron microparticles: (a) microparticles, microspheres and melted iron mass; (b) microparticles and mi-

crospheres; (c1 and c2) pore microspheres; (d1, d2, and d3) decapped microspheres.

µm; wall thickness: 0.35 µm)

According to the model (Figure 5), the current lines (Ψ

= const.) are parallel. In fact, the current lines intersect

one another. It results that in some jet regions, the vapors

mix up with drops or microspheres in the wall in melt

phase.

By movements of the vapors described by the character-

istic function f*(r,θ) - relation (52)- and by fulfilling

condition (60), around the drop (or microsphere) the

eight stagnation points are formed. Here grow, along

each current line, ligaments of the shape shown in Figure

21.

At v = 1.15 × 10-3m/s and D = 0.75 × 10

-3m

3/s, it can

be noticed in the plasma that the melt moves along con-

tinuous parallel trajectories.

Formation of Iron Microparticles in the Argon Plasma Jet 709

Figure 21. Octopus-shaped iron microspheres.

Following solidification of the melt, fibres are obtained,

as shown in Figure 22. Seen on the optical microscope,

they appear like tubes, having shapes and sizes shown in

Figures 22(b) and (d).

The mean microtube has:

-length: 100 µm; -diameter: 27.64 µm and wall thick-

ness: 0.25 µm

The microparticles have their surface covered with

Fe3O4, as can be seen on the roentgenogram in Figure 23.

For I = 275 Adc, corresponding to the argon flow used,

the diameter

of the generated microtubes and the

thickness δc of the wall in Figures 17 and 18 sufficiently

verify those of the experimentally obtained microtubes.

(a)

(b)

(c)

(d)

Figure 22. Fibres (a) and iron microtubes (b, c, ..., d).

Conclusion

1) The sphere-shaped microparticles, microspheres, pore

Ioan Bica710

Figure 23. Röentgenogram

microspheres, microtubes and octopus-shaped micro-

particles are formed in the argon plasma jet by pulveriza-

tion of the metallic solid;

2) The size and shape of the microparticles depend on

the field of velocities, the field of temperatures and the

spectrum of the movement of the vapors, drops and plas-

ma;

3) According to the model worked out, by correlation of

the technological parameters (electric current intensity

through plasma arc and material advance velocity) at

points on the cross-section of the plasma jet, micro-

particles are generated of optimally specified shapes and

sizes.

Acknowledgment

We are indebted to CNCSIS/Bucharest for partial finan-

cial support.

References

1. M. S. Cho and H. J. Choi, Mater. Sci. Forum, 449,

1201 (2004).

2. S. T. Lim, M. S. Cho, H. J. Choi, and M. S. Jhon, J.

Ind. Eng. Chem., 9, 336 (2003).

3. S. T. Lim, M. S. Cho, I. B. Jang, H. J. Choi, and M.

S. Jhon, IEEE Trans. Magn., 40, 3033 (2004).

4. (a) M. S. Cho, S. T. Lim, I. B. Jang, H. J. Choi, and

M. S. Jhon, IEEE Trans. Magn., 40, 3036 (2004); (b)

S. T. Lim, H. J. Choi, and M. S. Jhon, IEEE Trans.

Magn., 41, 3745 (2005).

5. (a) M. S. Cho, H. J. Choi, I. J. Chin, and W. S. Ahn,

Micropor. Mesopor. Mater., 32, 233 (1999); (b) O.

Quadrat and J. Stejskal, J. Ind. Eng. Chem., 12, 352

(2006); (c) J. H. Sung, M. S. Cho, H. J. Choi, and M.

S. Jhon, J. Ind. Eng. Chem., 10, 1217 (2004).

6. (a) H. J. Choi, M. S. Cho, and K. To, Physica A,

254, 272 (1998); (b) F. F. Fang and H. J. Choi, J.

Ind. Eng. Chem., 12, 843 (2006); (c) X. P. Zhao and

J. B. Yin, J. Ind. Eng. Chem., 12, 184 (2006).

7. V. Bashtovoi, D. Kabachnikov, A. Reks, L. Suloeva,

G. Bossis, and O. Volkova, Magnitnaia Ghidrodin-

amika, 36, 233 (2000).

8. S. T. Lim, M. S. Cho, I. B. Jang, and H. J. Choi, J.

Magn. Magn. Mater., 282, 170 (2004).

9. I. B. Jang, H. B. Kim, J. Y. Lee, J. L. You, and H. J.

Choi, J. Appl. Phys., 97, 10Q912 (2005).

10. (a) M. S. Cho, Y. H. Cho, H. J. Choi, and M. S.

Jhon, Langmuir, 19, 5875 (2003); (b) J. W. Kim, S.

G. Kim, H. J. Choi, and M. S. Jhon, Macromol.

Rapid Commun., 20, 450 (1999); (c) J. H. Sung, D.

P. Park, B. J. Park, and H. J. Choi, J. Ind. Eng.

Chem., 12, 301 (2006).

11. I. Bica, J. Magn. Magn. Mater., 299, 412 (2006).

12. (a) J. M. Ginder, L. C. Davis, and L. D. Elie, Int. J.

Mod. Phys. B, 10, 3293 (1996); (b) A. Maity and M.

Biswas, J. Ind. Eng. Chem., 12, 311 (2006).

13. T. M. Simon, F. Reitich, M. R. Jolly, K. Ito, and H.

T. Banks, Math. Computer Modelling, 33, 273

(2001).

14. R. Haghgovie and P. S. Doyle, Phys. Rev. E, 70,

061408 (2004).

15. I. Bica, J. Magn. Magn. Mater., 241, 273 (2001).

16. (a) W. H. Liao and D. H. Wang, J. Intell. Mater.

Syst. Struct., 14, 111 (2005); (b) J. W. Kim, H. J.

Choi, H. G. Lee, and S. B. Choi, J. Ind. Eng. Chem.,

7, 218 (2001).

17. F. D. Goncalves, M. Ahmodian, and J. D. Carlson,

Smart Mater. Struct., 15, 75 (2006).

18. I. Bica, J. Magn. Magn. Mater., 270, 321 (2004).

19. M. Li, T. C. Lim, V. H. Guan, and W. S. Shepard Jr.,

Smart Mater. Struct., 15, 141 (2006).

20. K. Worden, W. A. Bullough, and J. Haywood, Smart

Technologies, pp. 193-218, World Scientific, Singa-

pore (2003).

21. I. Bica, Physica B, 371, 145 (2006).

22. (a) I. Bica, J. Ind. Eng. Chem., 12, 620 (2006); (b) I.

Formation of Iron Microparticles in the Argon Plasma Jet 711

Bica, J. Ind. Eng. Chem., 12, 501 (2006).

23. I. Bica, J. Ind. Eng. Chem., 12, 806 (2006).

24. I. Bica, Smart Mater. Struct., 15, N147 (2006).

25. A. A. Kuznetsov, V. J. Filippov, O. A. Kuznetsov,

V. G. Garlivanov, E. K. Dobrinski, and S. J.

Malashin, J. Magn. Magn. Mater., 194, 22 (1999).

26. A. A. Kuznetsov, A. R. Harutyunyan, E. K.

Dobrinski, V. J. Filippov, A. F. Vanin, and O. A.

Kuznetsov, In “Scientific and Clinical Application of

Magnetic Carriers”, pp. 379-389, Ed. By Häfeli et.

al., Plenum Press, New York (1997).

27. U. O. Häfeli and G. J. Pawer, J. Magn. Magn.

Mater., 194, 76 (1999).

28. I. Bica, Romanian Reports in Physics, 57, 79

(2005).

29. I. Bica,Mater. Sci. Eng. B, 77, 293 (2000).

30. I. Bica,Mater. Sci. Eng. B, 88, 107 (2002).

31. I. Bica, J. Magn. Magn. Mater., 257, 119 (2003).

32. I. Bica,Mater. Sci. Eng. A, 303, 191 (2005).

33. I. Bica, J. Magn. Magn. Mater., 270, 7 (2004).

34. I. Bica, J. Magn. Magn. Mater., 279, 289 (2004).

35. I. Bica, The Physics and the Technology of Materials

in Plasma, pp. 298-347, Mirton Press, Timisoara

(2006).

36. J. F. Lancaster, The Physics of Welding, pp.71-81,

Pergamon Press, Oxford (1984).

37. M. Vardelle, C. Trassy, A. Vardelle, and P.

Fauchais, Plasma Chem. Plasma Process, 11, 185

(1991).

38. S. Paik, X. Chen, P. Kong, and E. Pfender, Plasma

Chem. Plasma Process, 11, 229 (1991).

39. I. Bica, Elements of Fluids Mechanics, Mirton Press,

pp. 211-224, Timisoara (2004).

40. I. Bica and C. Marin, Analele Universitatii din Timi-

soara, 31, Seria Fizica (1994).

41. Fl. Oprea, D. Taloi, I. Constantin, Al. Ivanescu, and

R. Roman, Metallurgic Processes Theory, p. 122,

Didactical and Pedagogical Press, Bucharest (1984).