Romanian Reports in Physics, Vol. 57, No. 1, P. 79–84, 2005

CAVITATIONAL MICRO-PARTICLES:PLASMA FORMATION MECHANISMS

IOAN BICA

West University of Timiºoara, Faculty of Physics, Bd. V. Pârvan nr. 4, 1900 Timiºoara, Romania

(Received October 21, 2003)

Abstract. Cavitational micro-particles are a class of micro-particles. To it belong the micro-spheres,the micro-tubes and the octopus-shaped micro-particles. In this paper we present the cavitationalmicro-particles, their production in the plasma and some mechanisms for their formation in the plasma.

Key words: plasma, micro-tubes, micro-spheres, octopus-shaped micro-particles, molar density.

1. INTRODUCTION

We call the particles of dimensions ranging between 1 µm and 100 µmmicro-particles [1]. An interesting class, from the scientific standpoint and fromthat of their applications, is represented by the cavitational micro-particles. Itconsists of micro-spheres [2–4], micro-tubes [5–6] and octopus-shapedmicro-particles. The last ones consist of a central nucleus out of which ligaments(as needle-shaped micro-tubes) branch off in the same plane. The glass micro-spheres[2–3] are used for the production of dielectric materials with low dielectricpermittivity and fluorescent dyes. On the other hand, iron particles are used(experimentally for the moment) in the carriage, dosing and retainment of cytostaticsin tumors, by application of an exterior magnetic field [7].

The ideea of producing absorbant particles with magnetic properties originatedin relation with the detoxification of biological liquids [8], the protection ofimplants [9] the carriage and dosing of anti-cancer medicines in tumors [10]. In allthe cases, the magnetic micro-particles must be non-toxic, high-absorbtion and lowabsorbtion, biodegradable and with a high saturation magnetization [11]. Thecavitational micro-particles finely dispersed in liquid matrices, in the presence of atensioactive, can serve as raw material for obtaining intelligent fluids [12–13] etc.The scientific importance of cavitational micro-particles resides in their formationmechanisms. Conseqently, we will present some formation mechanisms forcavitational micro-particles in their production by plasma procedures.

80 Ioan Bica 2

2. MODEL

At plasma temperatures [14] 0 10,000iT = × K, a solid material changeswholly or partly into vapors. The superficial contact tension of the melt or/and ofthe gas and vapor system is high in comparison with that of the transported gas.Consequently, the shape of the melt is that of a sphere [4–14]. For molar vaporconcentration, of low values in comparison with the molar density of the mixture,the shape of the gas and vapor system may be that of a cylinder [6] for the case of astable movement of the vapors and of the gas and, respectively, of a sphere [5], inother cases. The value of the molar concentration and the condition of the vapormovement can be determined from the energetic condition fixed for plasma incorrelation with the velocity of the material advance in the plasma [3–5, 15]. At thetemperature 0iT of the plasma and for low vapor concentrations in comparison withthe molar density of the mixture, the particles do not feel one another [3]. Also, thevapor and the gas system are isolated from each other by a gas envelope of thesame nature as the one through which they move. Let us consider that this situationcorresponds to the moment 0it (Fig. 1a).

The system-gas interface (the discontinuous circle in Fig. 1a) reaches areaswith temperatures close to the “dew point”. At that moment, namely 1 0 ,i it t> anisobaric transformation takes place, and the vapors in the vicinity of the interfacechange into a liquid membrane of radius 1ir ( 1 0i ir r< ) (Fig. 1b).

Fig. 1 – Stages of cavitational micro-particles formation in plasma. A.Variation of molar concentration C on the Or axis attached to: a) thevapors; b) the vapor cavitational micro-particles; c) the cavitationalmicro-particles. B. Cross sections: 1 – gas vapors; 2 – membrane; 3 –wall of cavitational micro-particles in liquid phase; t0i – the momentof molar concentration vapors C0i and r0i radius formation; t1i – themoment of vapor cavitational micro-particles membrane formation; t2i –the moment of formation of the cavitational micro-particles of wall

thickness 1 2 ;i i ir rδ = − Cci – the critical concentration of germs.

3 Cavitational micro-particles: plasma formation mechanisms 81

In the interior delimited by the liquid membrane, convection currents areformed. They carry vapor elements 0d iV on the interior of the liquid membrane.Between the vapor element 0d iV and the membrane a substance carriage takesplace by non-stationary diffusion. The process continues until there are no morevapors in the interior delimited by the membrane (the moment 2it in Fig. 1c). By thesolidification of the membrane there result glass micro-spheres [4], ironmicro-spheres [3], SiO2 micro-tubes [5] and, respectively, iron micro-tubes (Fig. 2).

Fig. 2 – Iron micro-tube producedin the transferred plasma arc (7000W) in argon flow (0.75 ⋅10–3 m3/s) at atmospheric pressure.

The metal drop moves more and more slowly in the plasma of the transferredelectric arc because of the plasma velocity and of the vapors. At a given moment,the drop becomes immobile. Then, around the drop, the hydrodynamic spectrum ofthe movement of the vapor and gas mixture is composed of a movement around acircular obstacle, combined with the movement produced by a definitely locatedwhirl [16].

For the potentially plain movement of the gas and vapor fluid, stagnation pointsare formed on the circle resulting from the intersection of the drop and of the planeof movement (Fig. 3), when the condition takes place [17]:

sin4 4v R R∞

Γ αθ = =π π

(1)

where: Γ is the circulation of velocity, v∞ is the fluid medium velocity at longdistances from the drop, R is the drop radius and / v∞α = Γ is a notation.

Because of the distribution of velocities on the circular section of the plasmajet or/and of the intermitent introduction of the metal into the plasma, on thebackground of the low molar concentration of the vapors in comparison with themolar density of the mixture, it results that the magnitude α is not constant and ittakes only some values, namely:

82 Ioan Bica 4

Fig. 3 – Fluid spheres: 1 – micro-sphere or/and drop, 2 –vapors and gas cylinder, a, b, c, …, g – stagnation points ofthe vapors and gas fluid medium, R – radius, Oxy – Car- tesian system of coordinates, (r,θ) – polar coordinates.

4 Rnα = π (2)

where 1 11, ,0, ,12 2

n = − − is called discretization factor.

From siny R= θ and the condition (1) there results:

or 4 4

y y nRv∞

Γ α= = =π π

(3)

It can be noticed from the last relation of the group (3) that for that for1 11, ,0, and 1,2 2

n = − − there result eight stagnation points on the circle of radius R

(Fig. 3).They are the beginning or/and end of the current lines in the cylinders 2

(Fig. 3), formed of vapors and gas. Out of these cylinders ligaments are formed bythe mechanisms described above. By the solidification of the system formed of thedrop and the ligaments, octopus-shaped micro-particles are formed (Fig. 4). Theligaments are open at the top when for C0I (mol/m3) ∈ [0.0012, 0.071], the

under-cooling ∆Ti, of the gas-cylinder interface in Fig. 3 has values rangingbetween [17] 1000 K and 1900 K.

Fig. 4 [17] – Iron octopus-shaped micro-particles produced in the transferredelectric plasma arc (voltage on the arc:80 Vdc, current intensity through thearc: 300 Adc, in argon medium (flow:1 × 10–3 m3/s) carbon steel plate (500 ×× 200 × 20 mm) cut at the velocity: 7.22 × 10–3 m/s.

5 Cavitational micro-particles: plasma formation mechanisms 83

The air in the environment is trained by the plasma jet. The nitrogen [18] inthe air is well solubilized in the melted iron. From the equations for solidification-melting and, respectively, from the equation of the thermic balance on theliquid-solid surface, the solidification velocity of the micro-sphere wall is determined.

The nitrogen solubilized in melt, forms, by nucleation, bubbles in the meltedmetal wall of the micro-sphere. The rising velocities of the bubbles (max. 2.5 ×× 10–8 m/s) are low in comparison with the solidification velocity of the melt(min. 0.92 m/s). It results that in the micro-sphere wall pores appear, as seen in Fig. 5.

Fig. 5 – Iron micro-spheres with pores.

3. CONCLUSIONS

The cavitational micro-particles (micro-spheres, micro-tubes and octopus-shaped micro-particles) are produced in the argon plasma at an environmentalpressure.

The micro-spheres, the micro-tubes and the ligaments of the octopus-shapedmicro-particles are formed of vapors with low values of the molar concentration incomparison with the molar density of the gas and vapor mixture, the first one onthe unstable and the last two on the stable movement of the vapors.

The ligaments of the octopus-shaped micro-particles are open at the top forwell-chosen values of the sub-cooling of the vapor and gas cylinders.

The nitrogen in the air favors the formation of pores in the wall of themicro-spheres.

REFERENCES AND NOTES

1. R. D. Codle, Particle Size. Theory and Industrial Applications. Reinhold Publishing Corporation,New York, 1965.

2. G. J. Liu, J. David, Sr. Wilcox, J. Mater. Res. 10 84 (1995).3. I. Bica, Mater. Sci. Eng B77 210 (2000). For low C0i by comparison with the density C of the

vapor-gas mixture, the particles do not feel one another. It then results from the law of perfect

gases that 1/ 3

00

R3 ,4

i ii

i

m Tr

p⎛ ⎞= ⎜ ⎟π µ⎝ ⎠

where mi is the vapor mass, µ is the molar mass, R is the

84 Ioan Bica 6

universal constant of the ideal gases; T0i is the plasma temperature and pi is the vapor pressure.At the temperature T1, of the “dew point”, the interface I in Fig. 1, undergoes isobaric

transformation. There results (Fig. 1b) 1/ 31 0 1 0( / ) .i i ir r T T= ⋅ The transfer of substance between

0d iV (of vapors) and the membrane is described by the equation 2

22 0; 0 ,iX XD t tt r

∂ ∂− = ≤ ≤∂ ∂where X is the molar fraction of the vapors, D is the diffusion coefficient and t2i is theformation time of the wall of thickness 1 2i i ir rδ = − (Fig. 1c).

4. Glass micro-spheres of diameters between 2 µm and 24 µm, and wall thickness between 0.4 µmand 1.6 µm are produced by the rotating electric arc method (voltage on the arc: 50 Vdc,current intensity: 100 Adc, arc rotation frequency: 850 s–1) in argon (7.5 l/min) and at a powderflow (equivalent diameter: 30 µm) of 2 g/min.

5. SiO2 micro-tubes between 10 µm and 11.2 µm are produced in the plasma jet (voltage on the arc:80 Vdc, current intensity: 240 Adc, argon flow: 0.5 × 10–3 m3/s) from chemotte rods (equivalentdiameter: 30 × 10–3 m).

6. I. Bica, Plasma Chem. Plasma Process, 23 175 (2003).7. U. O. Häfeli, G. J. Paner, J. Magn. Magn. Mater., 194 76 (1993).8. M.V. Kutushov, A. A. Kuznetsov, V. I. Filipov, O. A. Kuznetsov; in: U. Häfeli, W. Schült, J.

Teller, M. Zborowski (Eds), Scientific and Chemical Applications of Magnetic Carriers,Plenum Press, New York, 1996, p. 391.

9. M. A. Vladimirsky, V. I. Filipov, A. A. Kuznetsov, in: U. Häfeli, W. Schült, J. Teller,M. Zborowski (Eds), Scientific and Chemical Applications of Magnetic Carriers, PlenumPress, New York, 1996, p. 353.

10. A. A. Kuznetsov, A. R. Harutynnyuan, E. K. Dobrinsky, in: U. Häfeli, W. Schült, J. Teller,M. Zborowski (Eds), Scientific and Chemical Applications of Magnetic Carriers, PlenumPress, New York, 1996, p. 379.

11. A. A. Kuznetsov, V. I. Filipov, O. A. Kuznetsov, V. G. Gerlivanov, E. K. Dobrinsky,S. I. Malashia, J. Magn. Magn. Mater. 194, 22, (1999).

12. A. J. Margida, K. O. Weiss, J. D. Carlson, Int. J. Mod. Phys, B10 3335 (1996).13. I. Bica, Mat. Sci. Eng. B98 89 (2003).14. I. Bica, Mat. Sci. Eng. B86 269 (2001).15. I. Bica, Rev. Metal. Madrid 35 287 (2000).16. I. Bica, Formation of iron micro-tubes in plasma, J. Magn. Magn. Mater-(in press).17. The quantity of vapors necessary for the formation of iron micro-tubes is conserved. It then

results from Figs. 1a and 1c that 221 i ix a− = and ( )2

0 exp ,i i i il x a−β = where 2 02 0

1 1, ,i i

i ii i

r rx x

r r= =

0 , /ii i i

i

Ll E R T

L= β = ∆ ∆ are notations, ai is a parameter, L0i is the vapor and gas cylinder

length, Li is the micro-tube length, ∆E = 40⋅106 J/kmol⋅K is the diffusion activation energy,and 0 1i iT T T∆ = − is the sub-cooling. T1 = 2000 K is the dew point temperature for the iron

vapors. For 01, 1, [1.1, 5.5]i i ia x l< > ∈ and ( ) [1000,1900],iT K∆ ∈ open top ligaments(needle-shaped micro-tubes) result.

18. I. Bica, Rev. de Sold. Madrid 26 96 (1996).