Pure & Appi. Chem. VoL 48, pp. 215—228. Pergamon Press, 1976. Printed in Great Britain.

HEAT AND MASS TRANSFER IN THERMAL PLASMAS

I. G. SAYCEDivision of Chemical Standards, National Physical Laboratory, Teddington, Middlesex, TW11 OLW, UK

Abstract—The present status of plasma processes involving heat and mass transfer is surveyed, with particularreference to the proceses of vaporization, condensation and chemical reaction. Some of the more important plasmatechniques are discussed with emphasis placed on means for maximising the overall thermal efficiency of the masstransfer process, and for controlling the properties of the condensed phase produced. Aspects of current theoriesconcerning the above processes are also discussed.

INTRODUCTION

Whenever a condensed phase exists in contact with athermal plasma there occur the simultaneous processes ofheat and mass transfer. Even when no vaporization orchemical reaction of the condensed phase takes place,there remains an important element of mass transfer, inthat the process of convective heat transfer occurs in partby the recombination of dissociated species at theinterface, and transport of species to and from theinterface is thus an essential part of the process. To dojustice to both practical and theoretical aspects of thisbroad subject would be impossible in a single paper, and asomewhat selective approach will therefore be adopted.

The processes which will be discussed are those ofvaporization, and the closely related subject of chemicalreaction when this involves reaction with (or evolution of)gas, and condensation from the vapour phase. All havebeen extensively studied with varying degrees of success,and all have important commercial applications. Since itappears unsatisfactory to attempt to separate the theoryof these processes from their practice, the treatmentadopted will place some emphasis on the practicalimplications of the subject, in an endeavour to point theway toward the most efficient means of perfecting theprocess under consideration. Again, since experimentalpractice almost invariably leads and theoretical under-standing follows, the practical aspects will be consideredfirst.'

VAPORIZATION AND CHEMICAL REACTION

The process of vaporization is perhaps the mostextensively studied of the areas selected, although it is notthe most commercially important at this time. Arisingperhaps from an early notion that the vaporization ofmetallic oxides might lead to new routes to the metalsthemselves, many metal oxides have been heated in, orpassed through, thermal plasmas with a view to affectingvaporization or reduction.1 More recently it has beenappreciated that while total vaporization might be anenergetically inefficient route to most metals, it might wellyield a viable process for preparing certain fine powders,and likewise offer a means of separating sufficientlyvaluable components from otherwise intractable mixtures.2Many of the concepts developed in both practical andtheoretical studies of vaporization have application also inthe field of chemical reaction.

Early attempts atvaporizationgenerally employed eitherthe simple d.c. plasma jet, or induction plasma. The reasonforthischoicelayinthereadyavailabiityofthetwotypesofdevice, rather than in their intrinsic efficiency for the

purpose, which is in neither case high. Indeed of the manyattempts to treat, i.e. vaporize or chemically react,powders in the efflux of a plasma jet or induction plasma,the results have generally been disappointing in terms ofoverall efficiency. It is useful to consider why.

Taking first the plasma jet, it is clearly desirable toinject the material to be treated into the hottest part of theplasma column. Electrode erosion and other designproblems have generally prevented workers from feedingmaterial through the current-carrying region of the arc,and therefore it has been necessary to inject material intothe hot gas stream leaving the torch. This gives rise toseveral sources of inefficiency. Instead of using electricalenergy to heat the powdered feedstock directly, i.e. toeffect the desired process, the energy is first used to heatthe gas, which can be done only at the intrinsic efficiencyof the torch (typically 50-80% in laboratory devices).Also, it is necessary to achieve sufficiently good mixing of,feedstock with this hot gas, and to maintain an adequatelylong residence time, in order to attain the required thermaland chemical equilibrium.

Furthermore the entire process must be effected underconditions where heat losses to the surroundings areminimised. The high velocity, viscosity, and thermalgradients of the conventional plasma jet combine to ensureboth that injection of particles into the hottest region of thegas is difficult, and their retention time is short. Theentrainment of cold gas at the orifice of the torch furtherreduces the overall thermal efficiency.

Should vaporization begin to take place, heat transferthrough the expanding envelope of relatively cool vapourproducts becomes progressively slower as the vaporiza-tion proceeds, particularly after the particles haveachieved a velocity approaching that of the gas. Forexample, the total vaporization of a particle of silica of200 jm diameter at a temperature of 3000°K will lead to avapour cloud of diameter 5 mm (assuming vaporization toform SiO + O2, and uniform temperature across thevapour cloud). Unless a condition of forced convection isachieved, complete vaporization of such particles re-quires heat transfer across a considerable distance fromthe perimeter of the vapour cloud to the centre. Such aprocess will only occur if there is available a substantialsurplus of thermal energy, and a retention time far longerthan the few milliseconds available in a conventional.plasma jet. If it is required to vaporize not one but manysuch particles it is clear that some more efficient devicemust be found.

Similar arguments apply to the vaporization of particlesin the induction plasma. Again the particles do notgenerally pass through the current-carrying region of the

215

216 I. G. SAYCE

plasma, and difficulties are observed in projectingparticles into the plasma fIreball due to the countercurrentflows of hot gas which result from magnetó-hydrodynamiceffects within the plasma.3 Longer retention times arehowever observed when the particles are fed countercur-rent-wise into the upward-flowing plasma, and thisapproach does provide a means of sweeping away thevapour cloud discussed above.4 The technique appearsattractive for permitting the study and theoreticalinterpretation of heat transfer to individualparticles,5 but inview of the basic inefficiency of the induction plasma itappears somewhat unlikely that this device will proveeconomic for particle vaporization on a commercial scale.

A number of schemes have been devised to increase bothheat and mass transfer rates to above those possible in thepreceding simple devices. One of the earliest, developedby Sheer and Korman, is the well-known high intensity arc.6The material to be vaporized is generally compacted withcarbon to form a consumable anode. As the arc current israised, a critical current is reached when the anodic arc rootextends over the face of the electrode, which is caused toevaporate rapidly to form a plume of vapour which streamsaway from the surface. Under these conditions the arc issaid to operate in the high intensity mode, and a highproportion of the input energy dissipated within the arc isreleased in the anode fall zone adjacent to the electrodesurface (Fig. 1). The use of the high intensity arc clearlyobviates the need to employ an intermediate working gas,and the thermal efficiencies can be quite high (9—18 kWh/kgfor vaporization of silica at 7—9 kg/hr at 70—150kW inputpower7).

However one of the major disadvantages of thistechnique is the need to make strong, thermally shock-resistant, electrodes. Another feature of the method isthat all vapour products must be raised to a temperatureof several thousand degrees in order to maintain theelectrical conductivity of the arc. However silica (forexample) may be vaporized at high rates in the presenceof carbon at temperatures in the region of 2000°C, and to

a

a

S0

0.

heat the gases to higher temperature represents a waste ofthermal energy.

A development of the concept of vaporization from theelectrode surface, which also makes use of the heat inthe arc tail-flame, has been used for the evaporation ofsilica. A d.c. plasma torch has been described whichemploys hollow cylindrical electrodes made of tungsten,8Fig. 2. This was operated while pointing the reactorvertically downward and feeding a stream of silica carriedin a gas vortex onto the inner wall of the lower electrode(usually cathode), or onto the wall of the tungsten tubewhich served to contain the tail-flame. The oxide meltedon the reactor walls and flowed slowly downwards,surrounding the tail-flame. The cathodic arc root thenmoved freely over the surface of the molten silica, whichreceived additional heat from the plasma column stream-ing through the reactor. The silica was thus vaporizedcontinuously and with quite high thermal efficiency(24-53 kWh/kg), and on quenching the vapour from sucha reactor a fine particle silica fume could be recovered.9Relative to the conventional d.c. torch, this approachrepresents a useful means of simultaneously increasingthe retention time and decreasing electrode heat losses. Inthis respect it has certain features in common with someforms of Gerdien torch.'°

Another device which has been used to extendretention time and improve the thermal contact betweenthe gas and the condensed phase is the centrifugal plasmafurnace. This has now been used by several groups formelting and vaporizing refractory materials heated by thesimple plasma torch,"'4 by a transferred arc between twoplasma torches,'5 and even by the induction plasma.'6 Thesimple furnace, heated by a non-transferred plasma jet(Fig. 3) has been used to melt and vaporize such oxides asalumina, magnesia and silica,'3 vaporization of whichoccurs via suboxide, or metallic species, and is thusgreatly enhanced by the addition of gaseous or solidreducing agents. Thus in batch distillations of silica in thepresence of carbon at 30 kW, peak distillation rates ofover 3 kg/hr were observed, implying an energy require-ment even in a small unoptimised furnace of under10 kWh/kg.

Cathode Anode— Distance —

LOW-INTENSITY ARC

100

80a0

Sag

0.

60

40

20

0

vc

1Cathode Anode Percent of arc—Distance — power transferred

to anode materialHIGH-INTENSITY ARC

Fig. 1. Voltage distribution between electrodes in low and highintensity arcs: V. = voltage drop across anode sheath, V =voltage drop across cathode sheath, V = voltage drop across

remainder of plasma column.Fig. 2. Plasma reactor for silica vaporization, MHD Research

Inc.8

There are several sources of inefficiency in using thesimple plasma jet to heat such a furnace. Firstly,.the arc isagain being used to heat the gas stream and a substantialproportion of the energy is lost to the torch cooling water.Secondly, it is necessary to transfer heat efficientlyfrom the gas stream to the furnace contents in a separatestage. It would be preferable to associate these twoprocesses as closely as possible. This has been achievedin a development of the centrifugal furnace in which anarc is struck between a consumable carbon electrode (orother form of cathode) and the melt itself, which acts asanode.'7 The circuit is completed by means of a stationarybrush mechanism at the end of the furnace (Fig. 4). Thearc is struck initially to the carbon exit nozzle and thecathode is withdrawn through the furnace. Once thecontents have melted, the liquid is sufficiently conductingto maintain the anode arc root, and the melt is thus heatedby electron bombardment at this arc root, resistively byJoule heating, andalso by conduction andradiationfromthehot gas Stream. The operation of the furnace is independentof any gas feed, and the concept appears to be one of themost efficient means available for evaporating moltenceramics.

Where the refractory can be made to sublime it may notbe necessary to employ a rotating furnace, and in this casea stationary carbon arc, furnace may well be adequate.'8

Such a furnace has beenused for the vaporization of silicain the presence of carbon, a relatively low temperatureprocess, and a distillation rate of 54kg/hr at 500 kW (i.e. apower consumption of 9.3 kWh/kg) has been reported.

Where it is possible to transfer the arc to the substrateto be vaporized, this represents the most efficient meansof transferring electrically generated heat to that material.In some cases,however, this may be inconvenient, and insuch circumstances transfer of the arc between two ormore plasma torches represents a relatively efficientalternative; indeed 2-torch heating of both horizontal andthe vertical centrifugal furnaces has been reported.'5"9 Inthe latter case there is evidence that some of the currentflow may again be made to occur within the melt. Theadvantages of this approach over the non-transferredplasma jet are clear. The transferred arc is long andoperates at relatively high voltage. Furthermore it may beeffectively surrounded by the material to be treated, and isin proximity to water-cooled 'surfaces only at itsextremities. Finally the thermal input may be made to besubstantially independent of gas flow.

The vertical centrifugal plasmafurnace (Fig. 5) has nowbeen shown to be a thermally efficient tool for thecontinuous melting 'of ceramics.'9 Thus at 60 kW mullite(3A1203.2SiO2) has been melted at some 20 kg/hr, i.e. for aspecific energy requirement of only 3 kWh/kg. It has also

'Heat and mass transfer in thermal plasmas 217

Molten cavity—' wneei LCeramic core

Fig. 3. Centrifugal plasma furnace heated by non-transferred DC plasma jet.

Pulley drive

steel furn,,,,,/"Tphite anodeDection

—raphite brush

—' Axis of rotation To collectionsystem

Iotatinci Dortion

-Water coolingench gas'

—P!v'JiJ purge .. ,Static

,,olten refractorylaterial to be vaporized

Fig. 4. Air-cooled centrifugal furnace heated by transferred DC arc.

218 I. G. SAYCE

yielded promising results for the continuous fuming of tinas oxide from low grade slags.2 Tin fuming is convention-ally practised in the presence of sulphur, when the speciesSnS is volatilized. The method results in the evolution oflarge quantities of sulphur dioxide, but the resultingpollution can be avoided using the plasma furnace, byvolatilisation of the lower oxide SnO. Thus, operating atabout 40 kW, 80% of the tin content has been removedfrom a 3.4% tin slag fed at 9kg/kr, i.e. a slag treatmentrate of 4.5 kWh/kg. Lower specific energy requirementswould of course be obtained if a sulphide fuming processwere attempted. In related work involving arc transfer totin silicate melts held in a conventional carbon arc furnace,oxide fuming has again been demonstrated. The use ofsuch a transferred arc leads to efficient heat transfer and isalso reported to give rise to an element of electrolysis inthe fuming process.20'2'

The above devices offer various means of vaporizingmaterials from the surface of the plasma-heated bulkmelt. There are, however, situations where it is required toheat a particulate feedstock, where it may be required toeffect vaporization from, or chemical reaction of, a streamof discrete particles. The difficulties of achieving this aimwiththe simpleplasmaheaterhave alreadybeenmentioned.It will be recalled that we require to bring the particles intoclose and prolonged thermal contact with the hot gas, ifpossible to introduce the particles into the current-carrying(energy dissipating) region of the plasma, and to arrange ifpossible to have the power input independent of gas flow, sothat we are notheatinganunnecessarilylarge volume of gas.

Early work on vaporization, using such an approach,was described by Whyman.22 A vertical d.c. arc was main-tained between water-cooled electrodes, and this arc wassurrounded by a water-cooled cylindrical rotor, Fig. 6.The effect of this rotor was to establish a radialacceleration on the gas, superimposed upon the verticalgravitational field. Under these circumstances the convec-tive cooling, which serves to constrict the normal verticalarc, is avoided, and the arc column expands outward tothe walls of the rotor. Whyman et a!. found that it waspossible to feed particles into the arc column, byentrainment into the cathode jet flows which exist aroundany cathodic arc root, and to obtain vaporization of theparticles so entrained.23

Anode assembly(copper)

Fig. 6. Expanded arc

This effect had earlier been observed by Maecker,24who noted that where any current-carrying plasma columnis constricted, there exists a radial component of currentflow. The resulting magneto-hydrodymanic (MHD) forcesgive rise to a pressure drop in the region of the constriction.Thus there is a low pressure zone in the vicinity of thecathodic arc root. This gives rise to an Inflow of gas,resulting in the well-known cathode jet in the conventional carbon arc. Maecker also observed that this naturalconvective flow permitted the entrainment into the arccolumn of carbon particles released in the vicinity of thearc root.

While efficient particle injectiOn into a simple plasmacolumn is difficult, the exploitation of these MHD forcescan ensure efficient particle entrainment into the current-carrying region of the arc. Thus the Maecker effect hasbeen employed in a device described by Sheer eta!.25'26 Bymaintaining an arc between a shielded tungsten cathodeplaced on the axis of the device, and three porous carbontranspiration-cooled anodes set around the axis above thecathode, an extended arc column is stabilised in space(Fig. 7). A powder-laden gas may be efficiently introducedinto this arc column in the low pressure region whichexists around the cathode tip. By feeding gas at highvelocity into this zone the natural convection may be.enhanced, and the introduced gas may be drawn into thecolumn with up to 100% efficiency.25 If this gas feed Isladen with particles, these particles are likewise drawninto the column.26 The effect appears to be self-enhancing,i.e. up to a certain point, increase in gas flow or powder•feed rate results in heat removal in the cathode regiOnandgreater constriction of the arc. This in turn results in moreefficient entrainment of the powder-laden gas stream..

This device, using the fluid convectiOn cathode

Cathode assmbly

Water—cooledrotor tube

Cooling water

-o $

Coolingfwater

LiquidjFused

product

layer

Fig. 5. Centrifugal furnace for continuous feed, heated bytransferred arc between plasma jets.

Hfurnace for vaporization of powders,

(Whyman22).

Sheath gas

Tungsten cathode—'

Fig. 7. Fluid-convection cathode, transpiration cooled anodedevice for particulate treatment.25

(FCC), has been used as a heater for reactive gases.25Thus while the cathode itself must be shrouded in a gasinert to hot tungsten, the major gas flow, injected via anannular orifice around the cathode, may consist ofvirtually any gas (see Fig. 7). Again this outer gas flowmay carry a powder stream, which may be heat treated oreven substantially vaporized.26 Constrictionof the arc inthecathode region leads to very high local gas temperatures,and temperatures of over 20,000°K have been observed.Such high temperatures lead to correspondingly high ratesof heat transfer by conduction and radiation. The approachwould appear to be very promising for heat treatment,chemical reaction, or partial vaporization of the feedstock.However for total vaporization it would appear to suffersome disadvantages relative to otherapproaches mentionedabove.

it is interesting to note that the similarities between theFCC heater with 3 transpiration anodes and the Ionarcheater which uses a comparable shielded cathode and 3consumable carbon anodes27 (Fig. 8). Powders aredirected into the cathode jet region of the Ionarc heater bya series of ports set around the cathode orifice, and theMaecker effect will again be important in ensuringsuccessful entrainmeut of particles into the current-carrying region of the arc.

At the National Physical Laboratory a related devicehas been studied,28 Again, powders are injected intothe Maecker pumping zone around a shielded cathode, butwith our experience with transferred arcs betweenplasma jets we have chosen to employ 3 plasma jets asanodes. This assembly gives reliable operation witheffectively non-consumable electrodes and permits theuse of oxidising atmospheres when required. Theequipment appears very promising for such applicationsas particulate spheroidization and reaction, and whenoperating at 120 kW it is possible to treat refractorypowders at over 1 kg/mm to effect greater than 95%spheroidization.

Remarkably high loadings (e.g. 1 kg of 100-200 unparticles fed to 801/mm at STP of gas) may be achievedin this type of device. Higher loadings might be achieved

in a fluidized bed, but at high temperatures the conven-tional fluidized bed may present problems of containmentand agglomeration of molten particles. The use of aplasma-heated spouted bed as described by flonet et al.29permits a solution to some of these. Where such a spoutedbed permits a comparable entrainment of particles, i.e.equally good contact between the particles and thecurrent-carrying region of the arc, and where collectionand containment problems are overcome, then the twoapproaches would appear capable of achieving compara-ble results.

It is because of the very multiplicity of devices whichhave been used to effect the simultaneous processes ofheat and mass transfer that this paper has commencedwith a description of the devices rather than with a reviewof the theoretical treatment of the processes occurring. If adevice were to be selected for achieving the most efficientheat and mass transfer, then it might well be one of thetransferred arc devices with FCC for a purely particulateapproach, or a transferred arc centrifugal furnace if thematerial is to be treated as a liquid film. No theoreticaltreatment of either process has yet been published.Indeed there have been relatively few theoretical studiesof simultaneous heat and mass transfer in plasmasystems, and fewer still in which the theoreticalpredictions have been coupled with any attempt atexperimental verification.

THEORETICAL ASPECTS OF VAPORIZATION

Rains and Kadlec reported the results of experiments inwhich alumina powders of various particle sizes were fedinto an argon induction plasma at powers between 5 and7kW.3° Vaporization of the particles (primarily as Al,A120 and AlO species) was observed, and after rapidquenching (by injection of hydrogen, carbon monoxide ormethane into the plasma tail flame), it was possible tocollect a pyrophoric powder containing a substantialpercentage of free aluminium metal. The conversion washighest when quenching with methane, the presence of

Heat and mass transfer in thermal plasmas 219

Tungsten cathode

Sheath gas

IPowder feed

mabfecarbon anodes

Fig. 8. Ion-arc heater for particulate treatment.27

(3)

(4)

(5)

220 . I. G. SAYCE

carbon minimizing the partial pressure of oxygen, and radiative heat loss term. The two radiative terms werethus suppressing the backreaction to oxide. Any decom- therefore ignored.position of methane on the hot alumina particles might In calculating the heat transfer coefficient h, it wasalso be expected to increase the conversion to metal by assumed that the relationsimple carbothermic reduction.

The degree of conversion was foundexperimentally to • Nu = 2.0 + O.6(Re)"2(Pr)"3 (2)increase with decrease in powder feed rate or particlesize, and with increase in plasma input power. By could be applied where the Nusselt number is given byassuming that the percentage conversion corresponded to Nu = h.DIx(x = thermal conductivity of argon), thepercentage vaporization, a qualitative agreement was Reynolds number by Re = DVpg/t (V the velocity ofachieved with estimates of the degree of vaporization gas relative to the particle; t = the gas viscosity; g theobtained using a simple computer modelfor the process. In gas density) and the Prandtl number by Pr = Cji/this model it was assumed that surface heat transfer was (C — the specific heat of particle). The overall heatthe rate-determining step, but no allowance was made for transfer coefficient is then given bythe heat absorbed by the diffusing vapours. By simultane-ous solution of the heat, mass and momentum balance h = (/D)[2.O + O.6(Re)"2(Pr)"3].equations, estimates of the degree of vaporization showedsimilar trends to the experimentally determined percen- The thermal conductivity x was assumed to be the sum oftage conversions, but were in error by —100%., The three contributionsdisparities may be due, as suggested by Waldie,3' to theneglect of the heat absorbed by the diffusing vapours or

.

X Xatoms + Xambii,olar + Xelectrons

possibly to the neglect of non-continuum effects. How-ever since some degree of back reaction appearsinevitable it may be unreasonable to expect that thedegree of vaporization should correspond any more

.for which values were taken from the literature. It wasnecessy to use an average value for the boundary layercalculated using the relation

closely to the degree of conversion than is observed inpractice.

The processes involved in the vaporization of oxides in

- i-; J x dTI(Tg — T)T

an induction plasma have been considered in somewhat and the other quantities in the relations for Re and Prgreater detail by Borgianni et al.,32 who treated alumina were calculated at the mean temperature of the boundaryand certain other oxides in argon plasmas at 3.5—5.5 kW. layer.The partially dissociated oxide particles were collected on The overall heat transfer coefficient h calculated in thisa water-cooled cold finger and analysed. It was assumed way makes no allowance for the enthalpy taken up by thethat the quench rate was very much higher than the rate of mass counterfiow of the evolved vapour Above theback reaction and that the analysed product was decomposition tnperature a modified value was there-representative of the composition of the plasma. The fore used by taking account of the overall enthalpy changedegree of decomposition of alumina was found to be from T to Tg, and the enthalpy of decomposition at Td.33unaffected by variation in mass flow from 8 X iO to1 8 x 102 g/sec but the other trends were similar to thoseobserved by Rains and Kadlec. The percentage of free

Allowance was also made for the fact that the vaporizingspecies represent an additional heat smk within theboundary layer.34

aluminium was found to depend onthe inputpower, particle The equation of motion was calculated assuming thesize and distance of the quench from the injection point. A applicability throughout of Stokes law, but allowing formaximum of 12% free metaiwas achieved (60 m particles a change in diameter m time (this rncreasmg withS 5 kW input power)by collecting material at the end of the temperature until the decomposition tempera'ture Td andluminous region of the plasma thereafterdimmishing) Forthe velocityand viscosity of the

In their theoretical treatment Borgianni et at. assumed plasma, the values were assumed to be those applying at thethat at any point in time and for a particles of diameter D mean temperature at the boundary layerat temperature T in a gas of temperature Tg the The heat taken up by particles was thus calculated as afollowing heat balance applied function of time and compared with results derived from

iiD2h(Tg T) + h (Tg) q(dT/dt)chemical analysis of the quenched products The resultsof such a comparison are shown for two particlediameters in Fig 9 in which (in the absence of any direct

+ AHr4(dnfdt) + irD2uT (1) measurements of plasma temperature) the dotted linesrepresent the calculation for isothermal plasma tempera

where h is the heat transfer coefficient by the processes of tures and the continuous line shows the results calculatedconduction and h (Tg) represents the contribution of assuming the particles were travelling down the axisradiation to the heat flux to the particle Of the terms on through a temperature regime similar to that observed in athe right hand side of the equation q(dT/dt) represents comparable argon plasma by Vurzel et It appears thatthe enthalpy gain of the particle (qp being the heat the smaller (60 m) particles pass through a lowercapacity of the particle) HTd is the enthalpy of temperature regime than the larger particles (135 j.m) anddecomposition and dn/dt the rate of decomposition of the the authors suggested that this resulted from a greaterparticles in mol/sec. The final term in which €, is the radial spread of the smaller particles in passing throughemissivity of the particle and o the Stefan—Boltzmann the plasma This was attnbuted to the effects ofconstant, represents the radiative heat loss of the particle.Borgianni et at assumed that under the conditions

thermophoresis which exist in regions of high temperaturegradient3637 but may also result from the magneto

applying the radiative gain in heat of the particle from the hydrodynamic recirculating gas flows which exist ingas was small and could be equated approximately to the induction plasmas

Heat and mass transfer in thermal plasmas 221

Fig. 9. Heat absorbed by A1203 particles (diameter 60 ,wm and135 .tm), as a function of distance from the injection point.Continuous lines, curves calculated assuming the temperatureprofile along plasma axis given by Vurzel et a!.;35 dotted lines,

isothermal curves; circles, experimentally determined.

Inview of the complexities and approximations involved,the extent of agreementbetweenexperimentalandpracticaldata is of considerable interest. The authors note that betteragreement should be possible by making better allowancefor the gas temperature regime through which the particlespass, by improvements in calculating the laws of motion ofthe particle, andbymakingbetterallowancefortheeffectofvapour species on the thermal conductivity of the boundarylayer.

Full allowance for this last effect would be verydifficult, but Capitelli et al. extended the above work by acomparable study in which alumina particles wereinjected into an argon induction plasma containing 5 or8% of nitrogen.38 Their theoretical analysis, whichassumed that the electron and gas temperatures of theboundary layer were equal, showed that in the presence ofdissociated and ionising nitrogen species the heat transferrates were markedly increased, the probable non-equilibrium nature of the plasma boundary layer beingexpected to increase the heat transfer rate still further.However attempts at experimental verification of theseconclusions indicated a reduced level of decomposition,presumably as a consequence of the shorter length andthe lower mean temperature of the argon-nitrogenplasmas.

Johnston39 has also developed the calculation methodof Borgianni et aL to take account of the radiative heatloss of particles, together with the radiative heat gain fromneighbouring particles in the plasma flow. It was foundthat doubling the density of 250 m particles (from1 x 10—2 x iO m3) in an electrically augmented flame

(assumed to be at a constant temperature of 4000°K) led toa 10% reduction in decomposition time. At these gastemperatures the contribution of radiation from the gaswas again assumed to be minimal.

In a very extensive theoretical study Bonet et a!. hawconsidered the processes involved in the evaporation of aspherical particle in somewhat greater detail.° It wasassumed that no reaction took place between the particleand the plasma gas, that the particle was large incomparison with the mean free path of the plasmaspecies, and that the plasma was in local thermodynamicequilibrium. It was also assumed that the vapour speciesformed only a minor proportion of the total plasma. Thislatter assumption represents a rather serious limitation ofthe method, in that any efficient vaporization techniquewill be required in practice to yield a high partial pressureof the volatile species. However under the assumedconditions, Bonet et a!. were able to derive equations forheat and mass transfer which applied under varyingphysical properties of the plasma, The relative importanceof the various effects considered is set out in Table 1. Thetreatment for the separate cases of optically thick andoptically thin thermal plasmas, and the solution of thevarious equations involved by the method of perturbation,are given in the above paper.

The treatments mentioned above have assumed that theplasma was in a state of local thermodynamic equilibriumwith all plasma species at the same effective temperature,and also that vapour species form a relatively smallproportion of the plasma gas. The situation is, however,very differentin all the devices listed above whichoffer highthermal efficiencies. In each of these, the processes ofelectrical heating of the gas and of transferring that heat tothe particle are not separated, but are combined in oneprocess.

This means that the plasma may be far from localthermodynamic equilibrium, and this very fact willpromote a greatly enhariced rate of heat transfer. Thus inthe Ionarc27 and fluid convection cathode de-vices,22'23'25'26'28 the particles are heated in the current-carrying region of the arc in which, in the presence of alarge proportion of cooler particles, the electron tempera-ture will be substantially higher than the mean gastemperature, and the heat and mass transfer rates will besignificantly improved. Again, at the high local tempera-tures observed in the fluid convection cathode device,25the contribution of radiation from the gas will beconsiderable. In those devices where the material to betreated forms part of the electrode system, e.g. the highintensity arc,6 or the transferred arc centrifugal furnace,17there also exists the added effect of the high density of

Distance (cm)

Table 1. Relative importance of various effects onvaporizationof aa thermal plasma, Bonet et aL4°

sphericalparticle in

Very finePhenomenon particles Fine particles Large particles

Radiation from particle Major MajorThermal conductivity of gas effects effectsSoret effecttThermal diffusionFick diffusionRadiation from plasma Negligible MinorDuf our effect effectsForced convection

Alleffectshave

comparableimportance

•

tFlow of matter caused by a temperature gradient.IPlow of heat resulting from a concentration gradient.

222 I. G. SAYCE

energy release which exists in the anode fall zone, coupledwithresistiveheatingofthesubstrate,andafulltreatmentofthese subjects remains to be undertaken.

CONDENSATION

The subject of heat and mass transfer during vaporiza-tion in a thermal plasma has been considered separatelyfrom the second broad area to be discussed in this paper,that of condensation from a plasma-heated system. An allembracing theory would include both areas in the generalcase, but because the temperature regimes and ex-perimental difficulties encountered in practice are verydifferent, they are best considered as separate subjects.Again, the practical aspects will be discussed first.

Condensation from the plasma-heated vapour has twoimportant practical applications: the deposition of con-densate on a substrate (a process which may involveheterogeneous nucleation on the substrate), and theproduction of fine particles (homogeneous nucleation, ornucleation by ions present in the plasma). Growth byheterogeneous nucleation on a substrate is a particularlyimportant area of technology in low pressure plasmas, butthese are beyond the scope of the present paper. Suchgrowth in thermal (atmospheric pressure) plasmas hasreceived relatively little attention, but one of the first andmajor practical applications in the field is the growth ofsilica boules from the oxidation of silicon tetrachioride inan oxygen induction plasma.4' This relatively expensiveroute to silica is used only when the highest purity productis required. It was used first for the production ofhydroxyl-free silica for spectroscopic purposes, whereconventional boule growth in the oxy-hydrogen flame wasunsatisfactory, but more recently, the method has alsobeen employed for the production of pure and dopedsilicas for use in the manufacture of optical fibres.4"42

Silicon tetrachloride vapour is passed centrally throughthe oxygen plasma, and the stream of vapour products isdirected on to the hot surface of the boule. It is probablethat growth occurs as a mixture of both heterogeneousnucleation on the boule surface and homogeneousnucleation of fine silica particles, which then impact on thesurface. Conditions are quite critical if the collectionefficiency is to be high, and if the silica is to be depositedbubble-free in the correct viscous state. If the tempera-ture is too low, growth occurs as a porous deposit (whichcan be sintered into a dense form in a separate process43),and if the temperature is too high, the silica may be toomobile andthe boule will notbe self-supporting. Inaddition,deposition efficiency will be reduced. Adjustment ofaerodynamic flow patterns, temperature gradients, vapourpressure, and in particular the degree of supersaturation atthe boule surface, are clearly critical, and the achievementof an efficient process appears to have evolved byconsiderable patient development rather than by resort totheoretical analysis.

A subject attracting widespread attention by workers inthe field of thermal plasmas is the process of homogene-ous condensation to produce fine particles in suspensionin the hot gas stream. The method has been used toprepare ultrafine particles of oxides, and other refractorymaterials, and its use to prepare titania pigments, andthixotropic silica powders, represents two of the mostpromising applications of thermal plasmas to date.

A note of caution may be relevant at this point. Thecondensation processes to be discussed below occur inplasma-heated systems, however they do not in generaltake place at plasma temperatures. Their relevance to

workers studying thermal plasmas is that plasmas areused to generate the required hot gas streams, or toprovide the stream of vaporized material. However, itmay prove desirable to effect the condensation reactionat much lower temperatures if the product is to beachieved in the required form, or if the specific energyrequirement is to be minimized. In certain cases, forexample the production of oxide powders, the process ofinterest has much in common with that occurring during atypical flame synthesis reaction.

The commercially important condensation of silica asan ultrafine powder has been extensively studied.Ultrafine silicas prepared by chemical routes are used on ascale of some tens of thousands of tonnes per annum forthe control of viscosity of resins, varnishes, paints etc., asreinforcing fillers and in many other applications. Thesematerials are generally made either by the vapour phasehydrolysis of silicon tetrachloride in an oxy-hydrogenflame, or by the supercritical hydrolysis of ethyl silicateester. However, a number of groups have attempted toproduce active siicas by direct vaporization of naturalsilica followed by condensation under suitableconditions.'4'26'"7 The vaporization aspects have beendiscussed above, but the condensation process will nowbe considered in greater detail.

The required condensation conditions are of coursecritically dependent on the nature of the desired product.While the precise structure of the sub-surface material ina thixotropically active silica gel may be uncertain, it 'iswidely accepted that these materials may be considered asan agglomeration of chains of ultrafine particles ofamorphous silica, each of which has a surface coverage ofsilanol (Si—OH) groups, there being three distinguishabletypes.45'48 These are, firstly, isolated silanol groups whichare sufficiently spaced to be unable to interact with eachother, secondly, similar groups with neighbouring silanolgroups which are close enough to permit hydrogen bondingbetween the two, and thirdly, hydroxyl groups arising fromwater adsorbed at the silica surface.

The unusual properties of this highly hydroxylatedsurface are essential in the use of Aerosil siicas forviscosity control in liquids. Thus, when suspended in apolar liquid (e.g. water), the viscosity of the liquid isrelatively little changed, and the surface hydroxyl groupsare saturated by water molecules. However if a similarproportion of silica is added to a non-polar solvent, a gelstructure is set up and the viscosity rises very markedly.This property is the basis for the application of thesesilicas in problems of flow control, and is interpreted asresulting from cross-linking of adjacent chains byhydrogen bonding to form a loose network throughout theliquid. The structure breaks down on agitation butre-forms once motion of the liquid ceases.

It is clear that for a thixotropically active silica product,a high degree of hydroxylation is required. Thus in anyvapour phase route to such products one must ensure thatthere is an adequate partial pressure of water, or ofhydroxylated polymeric silicon-containing precursors inthe condensation zone. However this is not the onlycondition which must be satisfied.

On heating an Aerosil, progressive loss of water takesplace. Initially, adsorbed water is evolved, and subse-quently, by condensation of neighbouring silanol groups,siloxane linkages (Si—O—O--Si) are formed. Up to 200°Cthe water loss is reversible, but thereafter an irreversiblechange takes place and above 1100°C no surfacesilanol groups remain. The material is no longer

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Heat and mass transfer in thermal plasmas 225

modynamic calculations provide a useful predictivefacility. It was estimated that, under typical experimentalconditions, the temperature of the stream of reducedvapour within the furnace was approximately 2400°K andthat the species contained in the vapour were in thefollowing ratios: Al20 : C : N2 (plasma gas) =1 : 2 : 20.

Using JANAF thermochemical data,55 the equilibriumconcentrations of the various species were calculated,and these concentrations were then used in a furthercalculation in which the hypothetical adiabatic flametemperatures were computed assuming combustioi inpredetermined quantities (gross excess) of various poten-tial oxidizing agents. The three selected were (per mole ofalumina vaporized): 02, 50mol injected at 300°K; H20(steam), 40 mol injected at 400°K; and C02, 40 molinjected at 300°K. The computed flame temperatures werethen: 02. 1788°K, H20 1664°K, and CO2 1409°K. The lattertwo oxidants gave lower temperatures than the oxygenflame temperature because the carbon monoxide present inthe product gases is not reoxidized, and the heat of thecombustion reaction is thus substantially less than that ofthe aluminium species in oxygen.

In this way it was established that, even at the highdilutions employed in practice, a considerable degree ofcontrol of flame temperature could be achieved by choiceof oxidant. When the three oxidants were used experimen-tally, corresponding trends were observed in the crystal-line structures and the surface areas of the three powders.Thus X-ray powder photography revealed that allcontained y-A1203, but the oxygen quenched material alsocontained c5 -A1203 a higher temperature modification.Furthermore there appeared to be an increasing propor-tion of amorphous alumina in the series 02< H20<C02,corresponding to the decreasing flame temperature in thecondensation zone. The surface areas of typical samplesexhibited a corresponding trend, the powders quenched inoxygen, water and carbon dioxide yielding typical values of72, 123 and 137 m2 g1 respectively.

The water-quenched powder was extensively studied inan endeavour to establish whether it was possible toprepare the alumina analogue of thixotropic silica.Materials were definitely prepared with properties closelycomparable to those of commercially made fumedaluminas (prepared by flame hydrolysis of aluminiumhalides in an oxy-hydrogen flame56); however it appearedthat the contained water was readily lost on heating andthe morphology observed in high activity silicas wasnever demonstrated for an alumina product. If any similarmaterials are to be prepared by a plasma route, it wouldappear that the reoxidation will have to be effected ateven lower temperatures than those employed above.

Ultrafine silicas,57 and aluminas58 have also beenprepared by oxidation of the metal halides in the oxygeninduction plasma. This device has also been used in thepreparation of'mixtures of oxides, and of mixed oxides byco-condensation. Barry et a!. found that when chromiaand titania were co-condensed from an oxygen plasma fedwith the mixed metal halides there was extensiveformation of the mixed oxide solid solution,59 but withchromia and alumina there was relatively little tendencyto form such a solid solUtion.58 Presumably the differencein relative vapour pressures of the two oxides meant thatcondensation of chromia commenced only near thefreezing point of the alumina droplets, which condensedfirst.6° Subsequently, by injecting reactants into theplasma tailfiame, McPherson was able to raise thechromia vapour pressure substantially and to attain mixed

oxides with up to 18 wt % of chromia in solution in thealumina phase.6°

Mixed oxides have also been successfully preparedusing the centrifugal furnace. Thus when alumina andmagnesia are simultaneously evaporated from their 1: 1mixture, in the presence of carbon as reducing agent, thevapour may be reoxidised at the furnace exit to yield anultrafine spinel (MgA12O4).61 Due to the differing vol-atilities of the two metal oxides it is difficult to control therelative proportions of the two components in batchvaporization experiments, but with continuous operationthe relative proportions will (after the attainment ofequilibrium) be identical to that found in the feed.

There have been numerous reports of the production ofother ultrafine powders from plasma systems includingcarbides,62 nitrides62'M and metals.62'67' However inthe studies reported there has been little attempt tocontrol the quench conditions or the particle size of theproduct and these studies will not be considered furtherhere.

Having discussed some of the factors which have beenemployed in practice to control the properties of finepowders condensed from the plasma heated system, someof the more theoretical treatments will now be considered.Again it may be noted that the vapour in the condensationzone will generally be well below "plasma" temperatures,and the treatments applied by workers in the fields ofrocket combustion products and flame synthesis are thushighly relevant. Most early studies in the field assumedthat nucleation and particle growth were the mainmechanisms which controlled the ultimate particle size. Atypical approach was that of Hermsen and Dunlap, intheir treatment of the growth of alumina particles in analuminium vapour flame.69

The nucleation of particles in metal vapour flames isgenerally accepted as a homogeneous process. In classicalnucleation theory, it is assumed that in a supersaturatedvapour, particles smaller than the critical nucleus areformed by collision of molecules of vapour with statisticalprobability, but being smaller than the criticalpucleus, most re-evaporate. Only those which attain thesize of the critical nucleus continue to grow. The radius ofthe critical nucleus r is expressed by the Gibbs—Kelvinequation as

- 2uNV6r RT1nS (9)

where o is the surface tension of the liquid, N theAvogadro number, Vb the volume per molecule of thesubstance condensing, R is the gas constant, T theabsolute temperature, and S the supersaturation. Apply-ing this type of approach to the condensation of liquidalumina there are considerable uncertainties regarding themeaning of supersaturation (in a system in which thecomposition of the vapour differs chemically from that ofthe liquid), and, if the critical nucleus is very small,uncertainty regarding the value of the surface tension inrelation to that of the bulk liquid.

However, noting these difficulties, Hermsen and Dunlapemployed classical nucleation theory to calculate anucleation rate, and thereafter assumed that particlesgrew by diffusion of condensing species to the surface,where they condense giving out a latent heat ofcondensation.69 Ignoring non-continuum effects, the rateof growth is then limited by the processes of transfer ofheat from the condensing particle, and by the rate of

226 I. G. SAYCE

diffusion of vapour species to the particle. Hermsen andDunlap found that the latter limitation was negligibleunder the conditions assumed. They thus found a strongdependence of ultimate particle size upon the initialtemperature of the system, with smaller particlesresulting from lower initial temperatures. This effect isborne out by the experimental evidence. However theyalso found that as the partial pressure of reactantsincreased, so too did the nucleation rate, and inconsequence the ultimate particle size decreased. Sucheffect is not always demonstrated in practice.

Among the factors noted by the above authors, but notincluded in the model, was the possibility of growth ofparticles by collision and coalescence. In a recent paper49Ulrich showed that this process played a major part indetermining the ultimate size of particles in silicasynthesis flames, which involve the combustion of apremixed stream of silicon tetrachloride, hydrogen andair. Ulrich noted that the microscopic zones from whichindividual particles grow are very much smaller than themacroscopic turbulent eddies existing in the flame. Thispoint is borne out by consideration of certain factorsrelevant to the production of a typical pyrogenic silica,see Table 3. It thus appears that growth may beconsidered to take place in a quasiquiescent fluid by thethree microscopic processes viz., chemical reaction,nucleation, and Brownian motion.

Once chemical reaction has taken place to producehypothetical Si02 molecular vapour species, homogen-eous nucleation will lead to condensation of the product.However, from calculations of critical nucleus size (usingproperties valid for bulk silica), Ulrich found that thecritical nucleus might contain as few as one or two silicamolecules, and that any larger particles would be stableunder the conditions existing in the flame. Ulrichtherefore concluded that the final particle size distributionin this system is not determined by chemical reaction(which is rapid), nor by nucleation, but rather byBrownian coagulation of the multiplicity of particlescontaining (initially) very few molecules of silica.Particles collide, and with a certain (unknown) stickingcoefficient mutually adhere. Above the melting point of theoxide such particles coalesce. When the droplet has cooledto below the melting point coalescence no longer takesplace, but rather interparticulate sintering occurs toproduce the well-known chain-like aggregates. As Suther-land has shown,7° the morphology of the chains producedsuggests that they are built up via accretion of small clustersof particles, rather than by addition of discrete particles.Further growth of aggregates ceases when the temperaturedrops below the sintering temperature of the material, and

inter-particulate collisions become elastic.The surface area of the product is determined by the

size of the ultimate particle, which is in turn determinedby the number of collisions which take place betweenmolecular clusters up to the point at which the particlesolidifies. Coagulation phenomena in systems where theKnudsen number (the ratio of molecular mean free path toparticle diameter) is greater than 10, may be calculateddirectly from kinetic theory, and thus Ulrich calculated,forexample, product surface area as a function of residencetime for two different initial particle size distributions (Fig.12). Clearly the effect of initial distribution is soondominated by Brownian growth, and the surface area of theeventual silica is thus unaffected by the early history of thereaction.

The rate of particle growth by chemical reaction wasfound to be strongly dependent on the initial concentra-tion, but insensitive to flame temperature. However theultimate size of the particle is dependent upon flametemperature, because growth by collision and coalescenceof particles soon becomes predominant, and continuesuntil the system has cooled to below the melting point ofthe oxide. It follows that the ultimate particle size, andsurface area of the product, depends on the retention timeat temperatures above the "minimum coalescence temp-erature", and in a conventional flame this retention timeincreases with increasing initial flame temperature.

Ulrich found that available experimental data on bothoxide and carbon-forming (i.e. soot-forming) flames wereconsistent with the collision-coalescence model, butgenerally a quantitative comparison was difficult becauseof uncertainties in the residence times for particle growthin these flames. In carbon-forming flames growth of liquid

0

1x109 1x108 1x107 1x106 1x10' 1x104

Residence time (s)

Fig. 12. Specific surface area of silica product vs residence timecomputed by Ulrich.49 Conditions; temperature 2000°K, pressure1 atm, silica mole fraction 0.135, sticking coefficient unity.Solution A assumes initial population of silica particles all 4 A

diameter, solution B, equal numbers of 4 A and 8.6 A particles.

oIution100 -

Table 3. Characteristic dimensions of the particle environment in silica synthesis flames(Ulrich49)

Standardsilica

High surfacearea silica

Surface areaEquivalent particle diameter

200 m2g'136 A

400 m2 g'68 A

Diameter of spherical fluid volume elementrequired to produce an average particle 5440 A 2720 A

Ratio of fluid element diameter toparticle diameter 40 40

Number of Si02 molecules per particle 2.9 x 10 3.64 x 10Mean free path of typical gas molecules

at 1 atm pressure, 2000°K 4800 A 4800 AMinimum Knudsen number 35 70

Heat and mass transfer in thermal plasmas 227

high molecular weight hydrocarbon droplets again occursby Brownian collisions, until, with loss of hydrogen, thesedroplets solidify and no longer coalesce.71

A rather similar model to that discussed above has beenused by Cozzi and Cadorin to predict the particle sizedistribution of titania particles obtained by oxidation oftitanium tetrachloride in a lean carbon-monoxide—airflame.72 The major difference lies in the requirement withthis system particles be produced of larger ultimate particlesize (in the region of 0.2 gm), and in the assumption in themodel that particle growth via surface reaction andcondensation was significant over the major part of theresidence time. In Ulrich's work these processes wereassumed to be complete within a very small proportion ofthe total growth time. Cozzi and Cadorin's model leads toplots of the form shown in Fig. 13, in which the effect ofthe varying constants in the system may be observed. Inthe example shown nucleation is complete after some5x i03 sec, and thereafter the particles grow by surfacereaction and coagulation, the latter being more significantin the later stages of the process.

Recently Lillicrap and Lawton46 have developed themodel of Ulrich for the condensation of submicron silicafumes, which were obtained by air-quenching a stream ofvapourwhichhadinitsturnbeenformedbyheatingsiicaina neutral atmosphere in a plasma furnace. Experimentallythe surface area of the product was found to beapproximately proportional to the volume of quench air.Agreement between the experimental results and theorywas however not good, apossible reason for the divergenceof results being the difficulty of maintaining accurate andreproducible values of such variables as the rate of

1010

pcrii3)

'io i0 10—2 10-1t(s)

Nucleation

Surface reaction

CoagulationFig. 13. Condensation of titania as computed by Cozzi andCadorin,72_showing particle concentration (), mean particlediameter (d), and degree of conversion (ii) as functions of time.Nucleation rate 7 x lO cm3 sec, surface reaction constant1 x iO' cm3 sec, coagulation constant 7 x iO cm3 sec', initial

molecular concentration of TiCL, 1.1 x io' cm3.

production and enthalpyof silica vapour emergingfrom theplasma furnace.46

At this stage it may be relevant to sound a note ofcaution regarding all these theoretical treatments of oxideparticle growth, particularly where they are applied tosystems where the purpose of the experiment is theproduction of thixotropically active silicas. The theoreti-cal treatments necessarily assume an oversimplified viewof the reaction/condensation process and, as indicatedabove, there is strong evidence to suggest that thecondensation of a thixotropically active product is inreality a very complex process. In practice the vapour willcontain SiO together with Si202, Si303 and polymericspecies. Reaction with water vapour will lead to speciessuch as

and

40H—Si"

OH

H=0 (Ref. 45)

H"and no doubt complex polymeric species containing silane

. and silanol groups. Further heating of these polymerichydroxylated species will cause evolution of water andhydrogen, and the thixotropic product will then be formedas discrete particles which thereafter aggregate, coalesceand later sinter into the well known grape-like clusters.No theoretical model yet postulated takes account of anysuch complex, multistage process.

In concluding this brief and selective survey, it appearsthat in each of the fields discussed above viz., vaporization,reaction and condensation, there are manypromising areas for experimental study, including anumber of fields of considerable commercial interest.However, for the present, our theoretical understandingand predictive capabilities leave considerable scope forimprovement, particularly where they concern systems ofreal practical interest. It seems probable that the processof bringing together the practical and theoretical aspectsof the subject will provide a challenge to both experimen-talist and theoretician alike for some years to come.

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