o.n. sizonenko, a.i. raichenko, a.s. torpakov* and a.v

O.N. Sizonenko, A.I. Raichenko, A.S. Torpakov* and A.V. Derevianko

Dispersion of Particles in the Emulsion by theElectric Current

Abstract: Possible mechanisms of metal micropowdersgrinding during high-voltage electric discharge proces-sing in hydrocarbon liquid are considered in the presentpaper. Conditions for melting of Fe and Ti powder parti-cles in plasma discharge channel and in microplasmachannels between particles are found out. Regularitiesof nanopores movement and electromagnetic particlecompression are evaluated. It is shown that the currentdensity in the discharge channel is an important para-meter, allowing the assessment of the efficiency of theelectrodischarge dispersion of metal particles.

Keywords: metal powder, high-voltage electric discharge,dispersion, current density, Lorentz force

PACS number. 81.20.Ev, 52.77.-j

DOI 10.1515/htmp-2014-0131Received July 28, 2014; accepted October 12, 2014

Introduction

The high-voltage breakdown of liquid dielectrics isknown to occur by a leader mechanism. During thebreakdown of a suspension of metal powders a paralleldevelopment of several leaders may develop in a hydro-carbonic fluid which can be oriented on the powderparticles being in a suspension state, and upon reachingthese particles they may propagate toward the counterelectrode. The particle on which the leader is closed issubjected to the plasma action, thus displaying the innerstructural and phase changes. If the size of a particle

considerably exceeds the size of the leader head, thenfurther development of this leader stops. Thus, the pre-sence of such inclusions as metal powder particles in asuspension leads to the deviation of the discharge chan-nel route with respect to the linear way due to a forma-tion of a highly divergent electromagnetic fieldconditioned in this case both by the dominant use ofthe electrode system of an “edge-plane” type and thepresence of conductive particles of the powder in thesuspension. As is known, the maximum deviation of thedischarge channel route is observed when the electrophy-sical properties of a dielectric and inclusions are highlydifferent, which is demonstrated by this case [1]. Thisphenomenon is related to the occurrence of localdomains with high heterogeneity in the suspensionvolume, and consequently with the elevated field inten-sity. Here the location of these domains is connected withallocation of the powder particles in the suspensionvolume [2]. Accordingly, even at a prebreakdown stageof a discharge, the powder particles are subjected to highintensities of an electric field, which are concentrated inthe domains with the largest aggregate of particles and tothe plasma of the streamers developing toward theparticles.

When one of the leaders reaches the counter elec-trode, the plasma channel of a high-voltage electric dis-charge is initiated. The radius of the discharge channelmakes to ~3 mm and depends on the energy stored in thecapacitor and released in the channel [3]. Expansion ofthe discharge channel is prevented by the magnetic fieldconstricting the channel and by the working mediumsurrounding the discharge channel. The discharge chan-nel compressed the whole time when the discharge cur-rent is passing through it. The gas–vapor hollow isformed to pulsate after the current stops passing throughthe channel. Channel expansion is accompanied byradiation of pressure waves. Energy density in the dis-charge channel attains large quantities, and the tempera-ture in this local volume may attain ~ 5� 104 K and itdepends on the stored energy. The particles of the pow-der located directly in the plasma discharge channel mayevaporate, and, further on, during fast cooling in thepauses between the discharges, they may transfer to a

*Corresponding author: A.S. Torpakov, Department of PulseTreatment of Disperse Systems, Institute of Pulse Processes andTechnologies of NAS of Ukraine, 43а, Oktyabrskiy Ave., Nikolayev54018, Ukraine, E-mail: [email protected]. Sizonenko, Department of Pulse Treatment of DisperseSystems, Institute of Pulse Processes and Technologies of NAS ofUkraine, 43а, Oktyabrskiy Ave., Nikolayev 54018, Ukraine,E-mail: [email protected]. Raichenko: E-mail: [email protected], A.V. Derevianko:E-mail: [email protected], Frantsevich Institute for Problems ofMaterials Science of NAS of Ukraine, 3, Krzhizhanovsky Str., Kiev03680, Ukraine

High Temp. Mater. Proc. 2015; 34(7): 689–696

solid phase with changing of its dispersity, form andphase composition [4].

Results

Since the suspension affected by the high-voltage electricdischarge is a mix of powder particles suspended in adielectric and the layer of the particles on the bottom ofthe chamber, it is rational to consider the process withthe unequal distribution of the disperse phase. When thepulse current passes in such a medium, the skin effectwill occur. It is known that when the concentration of theconductive component (in this case the powder particles)changes, the current will change in a non-monotonousway. At the low value of concentration the electric con-ductivity will be small, and at some value called theconductivity threshold it will start sharply increasing byseveral orders [5]. The considered suspension belongs tothe class of electro-rheological suspensions, because itconsists of conductive particles in dielectric liquid. Suchsuspensions in the absence of an electric field have anear-Newtonian behavior, but when the electric field isapplied, the suspensions behave as Bingham plasticswith a yield stress that varies as a power of the electricfield. Such behavior can be attributed to the formation ofstructures via particles polarization induced by the elec-tric field, and they brake when the shear rate is increased[6]. Polarization can lead to rearrangement of particles influid [7]. Thus, to divide the suspension conventionallyinto two domains, where the domain 1 will have the lowconcentration of particles, and the domain 2 will havehigh concentration (see Figure 1), then we may assume

that the domain 1 is contaminated with a liquid dielectricwith low electric conductivity, while the domain 2 will bea conductor with higher electric conductivity. Then in thedomain 1 the breakdown of a liquid dielectric will occur,and the domain 2 will serve as a counter electrode.Consequently, in the domain 2 the skin effect willdevelop, and the discharge current will reach the counterelectrode basically via the skin layer and the vicinities,and the greatest influence of the current will be producedon the joints and the particles lying in these domains,respectively. On the other hand, we may expect that thedomain 2 will also be devoid of uniform distribution ofconductivity, and consequently, the most obvious dis-charge pattern in domain 2 will be formation of smalldischarge channels in the domain near the skin layer.

Proceeding to consideration of the microlevel pro-cesses, we may assume that both for the particles lyingdirectly in the high-voltage electric discharge channel inthe domain 1 and for the particles lying in small channelsin the domain 2, the suspension of molten metal particles(drops) arises in the channels. Thus, both in the cases ofTi and Fe powder treatment these particles will haveparamagnetic properties.

During the electrodischarge action the particles of thetreated powders are affected by the Lorentz volumetricforce, which has an electromagnetic background [8]. Ininitial metal particles there are various defects, the con-centration and distribution of which depend, in particu-lar, on the method of these particles’ production. It isentirely possible that in the treated powder particles, inparticular Fe and Ti, the nonconductive nanosized poresand inclusions are present which in these conditions willbe subjected to the action of the expulsive force condi-tioned by the Lorentz force action on the surroundingmaterial. Let us consider this process for the case ofmolten particles.

The condition for the transition of the particles to theliquid state is:– attaining the melting temperature which makes for

the considered powders 1,539°С for Fe and 1,668°Сfor Ti;

– obtaining the heat quantity necessary for melting.Then

Qp ¼ m c � ΔT þ λð Þ;where Qp is the quantity of the heat necessary for meltingthe particle; c is the specific heat capacity of the materialof the particle; m is the weight of the particle; ΔT is thedifference between the melting temperature and the initialtemperature of the particle; λ is the specific melting heat ofthe material of the particle. Heat capacities of Fe and Ti are

Figure 1: Scheme of the first discharge in the series in accordancewith the short cylinder model.Note: 1, kerosene; 2, side surface of the plasma discharge channel;3, powder layer with kerosene; 4, electrode edge; 5, plasma chan-nel; 6, conductive channel in the powder with kerosene; 7, conduc-tive bottom of the chamber.

690 O.N. Sizonenko et al.: Dispersion of Particles by the Electric Current

equal to cFe¼ 444 J/(kg · K) and cTi¼ 540 J/(kg · K), respec-tively, the specific melting heat makes λFe¼ 277� 103 J/kgand λTi¼ 18.8� 103 J/kg, respectively.

Since the particles heating is conditioned by theelectric current, let us evaluate the conditions of meltingby the Joule–Lenz’s law:

w ¼ �J � �E ¼ J2

σ

where w is the heat release power per volume unit, J isthe current density, σ is the specific conductivity of themedium, E is the field intensity.

At standard conditions the specific conductivity of Feand Ti makes σFe¼ 10� 106 S/m and σTi¼2.38� 106 S/m(for pure Ti without mixes), respectively. The quantity ofthe heat supplied to the particle during the electric cur-rent action will make:

Q ¼ J2 � t � Vσ

;

where t is the electric current passing time; V is theparticle volume.

Thus, the condition of melting of the particles will be:

J2 � t � σ � ρ c � ΔT þ λð Þ ð1Þwhere ρ is the density of the material of the particles (forFe ρFe¼ 7,874 kg/m3, for Ti ρTi¼ 4,540 kg/m3).

Considering that in the process of the high-voltageelectric discharge the current density changes over time,the left part of relation (1) should be written in an integralform:

ðtpt0

J2dt � σ � ρ c � ΔT þ λð Þ ð2Þ

where t0 is the process initiation time and tр is the pro-cess termination time.

Relation (5) may be written as:

J2mtp � σ � ρ c � ΔT þ λð Þ;where Jm is the mean current density in the dischargechannel; tр is the discharge time.

Tentative assessment shows that for the supposedtype of the research the most characteristic dischargetime will be no more than 10 µs. This condition allowsfor assessing the mean current density in the dischargechannel necessary for the transition of Fe and Ti particlesto a liquid state. The initial temperature of the powderparticles is expected to meet the standard conditions(T0¼ 25°C), and ΔTFe¼ 1,514°С and ΔTTi¼ 1,643°С,respectively. In this case:

Jm �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiσ � ρ c � ΔT þ λð Þ

tp

s

Rated values of the minimum mean current densitynecessary for melting of Fe and Ti with the action timeof 10 µs made JmFe¼ 8,645� 1010 A/m2, JmTi¼ 3,129� 1010

А/m2, respectively. Such values of mean current densitycan be properly achieved both in the discharge channeland in microplasma channels between the particles.Therefore, the suggestion on the transition of particlesto a liquid phase during the electrodischarge action maybe deemed as correct.

It is interesting, how pores could behave in variousconditions? For example, the formation of microporosity isknown to occur in scales of metal during reaction withsulfur [9]. Due to the passing of the electric current throughthe medium around the pore (with the radius ri ~nm)locating at a distance r from the vertical axis passingthrough the center of the spherical particle with the radiusr0 (~ µm) and owing to the pinch effect the electromagneticexpulsive quasi-Archimedean force is active [10]:

Fem ffi μ0I2r3i

πr40

λe � λi2λe þ λi

r ð3Þ

where μ0 is the magnetic constant (1.25663706� 10−6

N/A2), I is the current strength in the discharge channel,A, λe is the conductivity of the medium (liquid material)around the pore, λi is the conductivity of the materialinside the pore (gas, plasma). For the case of treatment ofthe Fe powder the specific conductivity in the liquidphasе (at temperature 1,550°С) makes 724.6 S/m.

The motion of the pores is prevented by the viscousfriction force. As a whole, the system of the forces actingon the nanopore is presented in Figure 2. Assuming thatλi<0 (in case of nanopores filled with air), force (3)should expulse the nanopores toward the particle sur-face. In other words, the pore at which t¼0 was locatedat a distance r¼ rs from the origin of the radial coordinateof the cylindrical system will locate over the time t at thedistance:

r ¼ rsexpμ0J

2r2i12η

t� �

ð4Þ

where η is the viscosity. In case of Fe powder treatment(at temperature 1,550°С) η¼ 7� 10−3 N s/m2, for theliquid Ti (at temperature 1,730°C) η¼ 3,66� 10−3 N s/m2.

For assessing the possibility of the action by theforces arising during the high-voltage electric dischargeand affecting the structure of the particle, let us makeevaluations for the single nanopore with the radius 100nm located in the Fe particle with the radius 10 µm at the

O.N. Sizonenko et al.: Dispersion of Particles by the Electric Current 691

distance rs¼0.1 µm from the particle center. Let us takeJ¼ 8,645� 1010 А/m2, since in accordance with previouscalculations, during the electrodischarge treatment theattained values of the mean current density in the dis-charge belong to this order, and this current densityvalue, as shown above, is the condition for the meltingof Fe particles.

Figure 3 shows the timedependence of the distance betweenthe center of the given pore and the particle center.

Still, the characteristic time of the electrodischargeaction is the time of some 1–10 µs. Figure 4 shows thetime dependence of the distance between the center ofthe given pore and the particle center with the time rangeto 10 µs. This dependence is close to the linear one, sinceit is essentially the fragment of the dependence displayedin Figure 3 in a very narrow range where the exponentdegrades into the straight line.

As is shown in Figure 4, the impact of the current withdensity J¼ 8,645� 1010 А/m2 during 10 µs does not lead toany significant motion of the given nanopore. The longertime of the current action is associated either with suchchange of the circuit parameters which will deteriorate theefficiency of the action due to the decreased currentgrowth rate or density, or with the considerable increaseof the stored energy. Therefore, the motion of nanoporesunder the action of the expulsing electromagnetic forcewill affect the dispersion of particles when the currentdensity is J� 8,645� 1010 А/m2.

The current density necessary to shift the given pore witha 100 nm radius for the 0.05 µm distance within 10 µswas calculated by formula:

J ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiln

rrs

� �� 12η

μ0r2i t

� �sð5Þ

z

0

JH

Fem

r

i

FL

J

Figure 2: System of the forces acting on the bubbles in the particle(liquid or solid).Note: i – the bubble (pore); r – the distance from the origin of theradial coordinate of the cylindrical system (axial coordinate z¼0–inthe center of the particle) to the bubble; J – current density; Н –magnetic field intensity (induced by the current); FL – Lorentz forceμ0 · [ J�H ] acting on the medium around the bubble; Fem – quasi-Archimedean force expulsing the bubble toward the surface of theparticle.

Figure 3: Time dependence of the distance between the centerof the given pore and the particle center for J¼8,645� 1010 А/m2.

Figure 4: Time dependence of the distance between the center of thegiven pore and the particle center with the time range to 10 µs.


For this case, the required value of the current density isJ< 5.2� 1011 А/m2.

In addition to the current density, the efficiency ofthe Lorentz force also largely depends on the sizes of thegiven pore. Figure 5 shows the dependence of the dis-tance between the particle center and the center of thegiven pore and the size of the pore (or other inclusion)under the density J< 5.2°� 1011 А/m2 during 10 µs (otherparameters correspond to the previously considereddata).

As follows from Figure 4, for the particles with noncon-ductive inclusion with the radius over 200 nm the effec-tive action of the expulsing force produced on the pores(inclusions) will be more noticeable.

Electrodischarge treatment is a cyclic process; thepulse number varies from 1,000 to 4,000. When sameparticle goes to the plasma channels, the shift of thepores will accumulate. Under the action of forces Femthe pores will concentrate near the surface, and partiallythey will leave the particle. We may expect that with theincrease of the pulse number the increase of porosity inthe sites adjacent to the surface should weaken the par-ticle, since, for example, the Young modulus E of thesolid porous medium is decreased (E ffi E0ð1� #Þ2,where E0 is the modulus of the pore-free material, ϑ isthe porosity). In the same manner, with the growth of theporosity of metal (solid and liquid), its strengthdecreases. Therefore, during the action of the high-vol-tage electric discharge, the “fatigue” effect will beobserved in the particles of the powder conditioned bythe local concentration of nanopores under the particlesurface (Figure 6).

The first stage of porosity variation is accumulation ofirreversible changes leading to origination of a crack onthe surface of a solid particle. Origination of both electro-magnetic and mechanical effects (collisions and interac-tion with compression–rarefaction waves) that have astochastic character will lead to the further stage of acavern or surface crack propagation for some particles,and, finally, the destruction.

Aside from the action on the pores, the Lorentz forceinfluences immediately on the material of a particle, i.e.the molten particle in the plasma “cord” will go throughthe all-round volumetric compression. Therefore, theaction of the force FL on the liquid metal in a moltenparticle will promote acceleration of its crystallizationand the increasing density of the solidified particle inaddition to deformation and destruction of these parti-cles. The quantity of the volumetric Lorentz force actingon a particle may be evaluated by a formula:

FL ¼ μ0J2r

2ir ð6Þ

A specific feature of the process of the electrodischargetreatment is associated with small values of the processtime (10−6–10−5 s), and since the process occurs in a fluidthat is slightly heated during the discharge, then rightafter termination of the discharge current passingthrough the molten particles they are cooled and almostimmediately crystallized. Accordingly, in the event whentheir volume and density change in a liquid phase, thechances for preserving these changes in a crystallizedmetal particle will be great.

The all-round volumetric compression of fluids isknown to have a volumetric compression coefficient βр.To take the pressure increment as ΔР¼ p – р0, and the

Figure 5: Dependence of the distance between the particle centerand the center of the given pore and the size of the pore.

(a) (b) (c) (d)

Figure 6: Origination of the elevated porosity near the particle sur-face leading further to the “fatigue destruction.” (а) Homogeneousporosity; (b) elevated local near-surface porosity without the changeof the particle shape; (c) elevated local near-surface porosity withthe chance of the particle shape; (d) resulting “fatigue destruction”.


volume change as ΔV¼V – V0, then V¼V0 · (1 – βр · ΔР),ρ¼ ρ0/(1 – βр · ΔР), where V and V0 are volumes, and ρand ρ0 are densities at pressures p and р0, respectively.

In particular, for the liquid iron at the melting tempe-rature the volumetric elasticity modulus makes KFe¼ 109.7GPa. Here, the volumetric compression coefficient of liquidiron will be equal to βрFe¼ 9.116� 10−12 Pa−1.

The electromagnetic field pressure providing the all-round compression of the considered particles may beevaluated as Pem ¼ B2

�2μ0.

While for the considered system B ¼ μ02H and

H ¼ Jr=2, the resulting pressure of the electromagneticfield may be written as:

Pem ¼ μ0J2r2

8ð7Þ

Figure 7 shows the dependence of the pressure of theelectromagnetic field acting on the molten particle duringthe current action with density J≈5.2.1011 A/m2 and itsradius (in a size range to 100 µm). The analysis of thisfigure shows that when all the particles with the size over50 µm are supplied to the plasma channel, they gothrough the electromagnetic pressure of over 100 MPa.

Relation (5) shows that the electromagnetic pressure alsostrongly depends on the current density in the dischargechannel, which is shown in Figure 8.

Thus, while considering, e.g. the particle of the mol-ten iron, it is possible to determine the change of itsdensity and volume under the electromagnetic pressurein the process of the electrodischarge treatment. Thevolume of the spherical particle is V0¼ (4/3)πr3. Thenthe volume of the particle with the radius 50 µm(V0¼ 5.236� 10−13 m3) under the action of the current

with the density J≈5.2� 1011 A/m2 should reduce toV¼ 5.231� 10−13 m3, and the density of the same particlewill increase from 7,874 to 7,882 kg/m3. Such a change ofthe volume testifies to the reduction of the radius of thegiven particle to r¼ 49.98 µm. Therefore, the electromag-netic pressure is likely to contribute insignificantly to thedispersion of particles, yet it may produce an effect onthe change of their microstructure. It should be notedthat in accordance with Figures 5 and 6 the role of theelectromagnetic pressure in the dispersion process con-siderably increases in proportion to the increase of thesizes of the treated particles and the density of the cur-rent passing through them. This conclusion is confirmedby the dependence of the change of the radius of theparticle under the action of the current with densityJ< 5.2� 1011 A/m2 and the initial radius of the particlegiven in Figure 9

Figure 7: Dependence of the electromagnetic pressure acting on theparticle and the particle size.

Figure 9: Dependence of the Fe particle radius change on its initialradius.

Figure 8: Dependence of the electromagnetic pressure acting on the5 µm particle and the current density.


The analysis of Figure 9 confirms that the mostessential effect is produced on the particles with thesize over 20 µm. Figure 10 shows the dependence of thechanging 25 µm radius of the Fe particle and the currentdensity. The dependences given in Figures 9 and 10 con-firm that the quantity of the current density produces asignificant effect on the dispersion and density of thepowder particles with the size over 25 µm after treatment.Nonetheless, the action of the electromagnetic pressureon the particles with the size less than 20 µm at anycurrent densities is negligible.

Discussion

The experience of the research of the electric explosion ofconductors shows that when the current density reachescertain values of an order of 1010 A/mm2, the pattern ofthe discharge current action on the conductor changes inquality, and the decisive role in destruction is thenplayed by the processes of the high-temperature explo-sion which are likely conditioned by the growing instabil-ity of magnetic hydrodynamics [11].

In addition, the action produced on the particles bythe high-concentration energy flows initiates the ablationeffect when the electric current evacuates smaller parti-cles from the surface of the larger one [12]. Thus, thedestruction occurs after the portion of energy is suppliedto the atoms, and this portion exceeds the bondingenergy in the crystal grid. While oscillating in the fieldof the electromagnetic wave and interacting with eachother, their temperature sharply increases, and they startleaving the surface of the solid body in way of neutralparticles, and also as positive or negative ions. Such

phenomena should lead to a considerable change ofboth micro- and mezostructures of the treated material,in particular, the parameters of its crystal grid, which isconfirmed by the data specified in Reference [13] testify-ing to the change of the parameters of a crystal grid a forthe Fe powder and a and с for the Ti powder during anelectrodischarge action, which is an indirect proof of theorigination of the ablation effect during the electro-discharge treatment.

Conclusions

1. It is shown that the current density in the dischargechannel is an important parameter allowing theassessment of the efficiency of the electrodischargedispersion of metal particles. The influence of thecurrent density on the dispersion of the treated pow-ders is associated with a row of physical mechanismsproviding the fining of the particles due to theirheating, melting, electromagnetic pressure and thechange of their inner structure due to local concen-tration of nonconductive inclusions, mainly the smal-lest pores.

2. The system of the analysis is developed to enabledetermining the conditions of melting of the particlesduring the high-voltage electrodischarge treatment ofthe suspension (emulsion) with the studied particles.

3. Dispersion of the particles with the size below 1 µm islikely to occur by an ablation mechanism.

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Figure 10: Dependence of the change of the Fe particle with the25 µm radius and the current density.


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o.n. sizonenko, a.i. raichenko, a.s. torpakov* and a.v

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