Smokes Droplets Flames and Electric Fields BY F. J. WEINBERG Imperial College London S.W.7 Received 23rd Nouember 1972 The paper summarises recent results on the influence of electric fields on carbon silica and lead oxide smokes,as well as on suspensions of fuel droplets in flame systems. The object in each case is to cause the particles to acquire charge for their subsequent manipulation by fields. Examples of using this as a method of controlling the trajectories of particles-either to remove them or to affect the process of their growth or consumption in the reaction zone-are discussed. The latter includes a measure of control over the reaction by varying particle sizes and concentrations and by transposing charged nuclei. Mechanisms of charge acquisition are considered theoretically and it is shown that in the absence of other charging mechanisms (such as thermionic emission ur electrical breakdown of the gas) chemi-ionization in the flame may be used for this purpose.On the supposition that diminishing resources of fossil fuels and increasing concern about pollution will allow consideration of more complex combustion systems in future a theoretical assessment of the maximum effects attainable in practice is carried out for the variety of effects observable in the laboratory. A great variety of smokes-e.g. of soot ash metal oxides from additives-are produced in flames. On the input side suspensions or sprays of fuel droplets are frequently involved. Particulate suspensions associated with flames acquire charge if for no other reason than because flames produce a plentiful supply of ions and in the presence of electric fields these attach to particles.Charged particulates can be manipulated by electric fields not only when they are already fully grown but also during the process of their formation or burning up It is for this reason that the association of electric fields with flames involving smokes or droplets is of practical as well as of fundamental interest. A series of studies 1-6 of these phenomena has been carried out yielding many interesting results showing the large effects which can be exercised by applied fields but perhaps not enough by way of clear distinction between what is of purely academic interest and what methods of electrical control may have practical potential.It is to be expected as one consequence of diminishing resources of fossil fuels and increasing concern about pollution that the use of more elaborate combustion systems- including perhaps the application of electric fields-will come to seem less far-fetched and become more generally accepted. The object of this paper is to bring together the theoretical mechanisms and practical consequences of these effects in order to make suggestions as to the practicability of the various possible schemes. EFFECTS OF MOVING CHARGED PARTICLES BY FIELDS A charged particle will respond to a local field intensity E by acquiring a local velocity v = kE (1) in the direction of E where k is its mobility. The manner in which k depends on particle size and on the charge acquired will be considered in the next section.This 120 F. J. WEINBERG drift velocity of the particle is superimposed upon any flow-induced velocity and may be used to produce a variety of different effects. The first and mat obvious application is to modify the trajectories of fully-formed particles or of non-reacting droplets. They can be induced to deposit in specified places (the electrodes) prevented from depositing on other surfaces caused to deviate from their normal trajectories along flow lines even made to proceed in sine-waves by the application of an alternating field As regards control of deposition the best known example is probably that of " electrostatic " precipitators. In these devices however much energy is expended in maintaining a corona discharge for generating the charges which will attach to particles.In the applications discussed in this paper the charges used are in the main formed spontaneously-for example by chemi- ionization in the reaction zone. In the absence of the field they would merely recombine uselessly. Accordingly the power dissipation is entirely due to the drift of charge and is exceedingly small (see later). An example of using the principle of guiding fully-formed particles is the preven- tion of deposition on a particular surface. In the case illustrated by fig. 1 positively C 5 t imelmin FIG.1 .-Weight of soot deposited on collector plate against time. Curve 1 no field ; curve 2 plate positive with respect to burner.charged soot particles from a flame are prevented from collecting on a cooled plate immediately above it. The upper curve shows the continuously growing mass deposition in the absence of a field the lower that when the collector plate is charged positively with respect to a matrix-electrode in the burner mouth. Under the latter conditions carbon deposits copiously on the matrix and all around the burner mouth although it has to travel downward to reach these sites. It has been shown that all the carbon particles become charged at least when a suitabIe field is applied and can be made to drift to an electrode even against the direction of the gas flow. Incidentally in addition to its site the form of the deposit is altered when deposi- tion is influenced by an electric field.Since field lines converge on the protuberances formed by deposits the growth on electrodes tends to occur in treelike structures and at a much reduced density. This principle can be applied to precipitate any particulate pollutant.6 A some-what modified procedure must be used for substances whose boiling point lies below SMOKES DROPI,ETS FLAMES AND ELECTRIC FIELDS the final flame temperature and which are at the same time not sufficiently active thermionically to emit electrons at temperatures below which they condense from their vapour phase. Lead oxide falls into this category. In that case we should have to depend on charging by flame ions over fairly large distances determined by the condensation process (unless the species happens to have a low ionization potential in the vapour phase).However because of limitations due to space charge (see later) it is unprofitable to maintain fields over large distances and it has been shown that very effective precipitators can be constructed based on small secondary flames used purely as ion sources or even just on special surfaces maintained hot by flame products. An entirely different example is provided by using a field to produce charged fuel droplets and guide them into a flame.5 Fig. 2 shows a burner operated entirely by ion pumps IkHTatomizer t t --FIG.2.-Burner operated entirely by electric fields which inducts air atomizes and charges liquid fuel and guides droplets to mixing vaporization and combustion sections.electric fields in which kerosene is mixed with and burned in air. The burner “breathes in ” its own air using ion pumps based on the Chattock l2 effect. The fuel (to which a small amount of antistatic additive is added to make it more conduct- ing) is dispersed by an electric field which produces a fine spray of charged droplets. The trajectories of these charged droplets are determined by two orthogonal compon- ents of the electric field that between the jet and the matrix which guides them into the flame and that applied by the circumferential ring electrode which serves to vary the cross-sectional area of the spray and to focus it on a part of the matrix. In this manner a highly controllable high-intensity flame has been produced without the use of any fuel pump or air compressor the process being controlled entirely by the potentials applied to the various electrodes.Alternating fields may be used for example to cause droplets to evaporate in shorter distances by lengthening their trajectories in a given distance downstream. Thus trajectories in the form of sine waves with excursion amplitudes of the order of centimetres have been recorded for electrically sprayed liquids subjected to trans- verse a.c. fields. A second group of applications arises when charged particles or droplets are manipulated by fields during the process in which they are formed or burned up. This makes it possible to vary their residence time in the reaction zone and for example exercise control over the size of particles which are formed in flames.Fig. 3 shows an example taken from two different studies.4* The carbon particles derive from a F. J. WEINBERG 3 4 5 0' I I 1 I I 5 applied potential/kV FIG.3.-Particles grown in applied fields ; variation of radius with applied potential. Curves 1 and 2 carbon particles in positive and negative charge flux ; curves 3 4and 5 silica particles in positive flux at electrode separations of 0.35,0.09 and 0.02 m. -I I I I I Ill1 I I I I t Ill. applied potential/kV FIG.4.-Collection rate of carbon from counter-flow diffusion flame as a function of applied potential in flux of positive charge. Curves 1 2 3 and 4respectively on negative electrode exhaust system burner flange and total ; curve 5 current.SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS flat counterflow diffusion flame in which the field is applied between the two burner mouths. The particles of silica smoke were produced in a study of oxide particles generated in premixed flames in this instance by injecting traces of hexamethyl disiloxane. The soot particles could in principle burn up in the flame zone; the silica particles could not. Nevertheless the pattern which here depends upon residence time is very similar. Note that the particles’ volume is reduced by a factor of about 200 in going from zero to 1 kV for e.g. carbon It is also possible to produce the converse effect i.e. to grow giant particles by the application of a suitable field. In the absence of other effects the size to which a particle grows in the reaction zone is due to a residence time determined by the zone’s thickness and the flow velocity through it.By applying a small retarding field so as to hold the particlesstat-ionary ( or as nearly so as possible) aginst the flow in the zone in which they -grow,macroscopic growths ofcarbon have been produced simul- taneously all over the flame frant..* The control of residence time in reaction zones merges into direct interaction with the reaction process by modifying the concentration of one of the participating species. Depending on the type of reaction the relevant concentration may be in the form of total surface area of the cloud of particles (if reaction proceeds on the surface) or of the number density of particles in the smoke (where coalescence is the important process).Again an example from studies on flame carbon is taken. Fig. 4 shows rates of mass deposition OII various parts of a counterflow diffusion flame system when the ion flux through the pyrolysis zone is positive (so that attachment charging reinforces thermionic emission and all particles are charged positively-as evidenced by the confinement of the deposit to the negative electrodes). The total mass de- posited decreases by about 98 % by the time the applied potential reaches 1 kV. Thus the decrease in particle size is not due to any large increase in the number of particles formed as the surface on which growth normally occurs is being rapidly removed. (Note the contrast with pollutants such as metal oxides which cannot burn up in the flame so that decreased particle size brought about by decreased residence time must be accompanied by an increased number of particles.) A fourth distinct means of interaction by fields is the removal of charged nuclei.Growth on charged nuclei can occur by chemical reaction or by purely physical condensation-as happens for example in the Wilson cloud chamber.’-’ This occurs because in an atmosphere of saturated,vapour droplets below a certain size cannot exist in equilibrium when the surface energy made available by their contraction is sufficient to supply all the latent heat of vaporization. The effectiveness of a nucleus in overcoming this threshold is greatly enhanced when it is charged for then the surface charge on the incipient droplets opposes the surface tension and diminishes the surface energy.Charged nuclei being very small tend to have a much larger mobility than the fully-formed particles. Whereas a small field may be used to transport them to a zone in which they are required (e.g. a pyrolysis zone) a large field will very greatly diminish their number. It has been shown that in the presence of large fields the mass rate of deposition of soot from flames is almost entirely made up of particles which do not have a charged precursor (even though they all acquire charge later in their existence and even though they might all have originated on charged nuclei in the absence of a field). For smalter fields local intensity can be used to control the local concentration of charged nuclei Whenever ions and charged particles of mobility k drift in a field a body force F per unit volume acts on the gas i.e.F = jlk (2) F. J. WEINBERG where j is the local current density. This induces a gas flow (the " Chattock wind effect "l 2 the precise nature and magnitude of which 3* depends on the geometry of the field and the surrounding surfaces. Although this is incidental to the subject of controlling particulate suspensions by fields it is inevitably present and usually quite large because of the low k values. It also has severaf uses in its own right. These range from modifying heat transfer from flame gases to mixing flame stabilisation and other situations where control over the fluid mechanics without the use of solid walls is beneficial 14* l5 to combustion.Two such processes are particularly relevant here. One is the impingement due to fluid mechanical forces which contributes to causing particulates to deposit on electrodes in any kind of electrical precipitator. The other is the application of ionic winds to gas pumping as in the air induction states uf fig. 2. The velocity obtainable per ion pump stage is of the order of several I00 cm/s,13p l4 so that for fuels burning in air one or two stages are generally adequate. SIZE CHARGE AND MOBILITY The manner in which the field modifies the trajectory of ii charged particle is defined in terms of the particle mobility k by eqn (1). The mobility in turn depends on the particle radius r and its charge Ne (e being the electronic charge positive or negative).These quantities vary with time according to the history of the particle's growth or burning up the rate of charge acquisition being itself a function of r. These histories become modified by the application of a field from the moment the first charge has been acquired. The mobility is calculable at any instant depending on the regime which is determined largely by the particle radius r. Starting from the very smallest at molecular diameters the theory of small ions (see e.g. ref. (16)) applies. Here the mobilitv is 0.235[(M + Mi)/Mi]o*Spi k=-9 w-1)OMl0% (3) where p is density M is the molecular weight and D is the dielectric constant; the suffixes i and 0 denote ion and carrier gas respectively.For larger ions the effects of divergence of the field induced around them by their own charge becomes negligible and the classical Langevin equation k = 0.815 (e;li/Mc)[(Mi+ M)/MJ0s5 (4) becomes relevant. When particles become large in comparison with the mean free path I. and no longer " sense the gas as individual collisions ",the viscosity q and density p become the relevant gas properties. In the Stokes regime the mobility then is k = eN/6nqr (5) and in the Newton regime at a field strength E k = (eN/0.22rrpE)o.5/r. (6) Which of these is applicable depends on the Reynolds number attained. Using eqn (5) for Re< 3 and (6) for Re> 700 keeps error to below 20 %. The equation k = 0.12(Ne)'e7 ' /r(Ep)0*299r10.43 (7) has been proposed for the intermediate region.I8 The case of particles continuously acquiring charge along their trajectories has also been considered.For bombardment charging (see later) the equations become k = Er/2nb/ (8) SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS in the Stokes regime and k = 2.08/p0*5 (9) in that covered by Newton's law. These values are too large by about 20 % because the particles never quite attain their equilibrium charge under bombardment.18 The numerical values are in fact very high exceeding I /20th of the mobility of a molecular ion in some cases. As regards the mechanisms by which particles or droplets acquire charge there is much variety ranging from the spontaneous processes of thermionic emission to those which are entirely contrived by the application of a field.When the object is to produce a charged dispersion of liquid or solid fuel,5 dispersion in a field (but in the absence of breakdown) is ideally efficient in terms of minimizing the wastage of charge deliberately provided. In this the particulate phase may be treated as the fragments of an initially continuous charged capacitor,' resulting in high levels of specific charge and of mobility. Fig. 5 shows results for droplets of kerosene with some I 1 1 1 1 I I f I 50 I00 drop diameterlpm FIG. 5.-Electrically sprayed droplets ; charge against diameter. Circles horizontal ; triangles, vertical sprays. Curve from theory see eqn (10). anti-static additive dispersed by an electric field the solid line being calculated on the theory of a disintegrating charged condenser which yields Ne = 9,/%nr2E.(10) In this way many millions of electronic charges can be impressed upon a small droplet; the experimental points obtained for a range of horizontal and vertical sprays conform well to the theory. For solid fuel dusts the dispersing field is applied to a fluidized bed of the p~wder.~ These methods give rise to suspensions which are highly controllable by fields right up to the point of burning. In flame zones other methods of charging become useful particularly thermionic emission and the attachment of chemi-ions produced in the reaction zone. Ther-midnic emission is specific to materials of low work function and depends on local temperature as well as on the nature of the material.Since it always leaves the particles with a positive charge it is important to apply fields in such a way as to F. J. WEINBERG subject the smoke to a flux of positive ions so as to reinforce rather than to oppose thermionic charging. In the absence of an applied field the thermionic emission current density is j = BT2exp (-e4/kT) (11) where B like 4,the work function is characteristic of the material ; e is the electronic charge k the Boltzmann constant and T the temperature which determines the number of electrons with sufficient energy to escape. When the emitter is a positively charged particle of small radius r two additional terms arise in the work function 2o ; (Ne/r)due to the surface charge (Ne) and (e/2r)due to the dipole induced by the departing electron The current then becomes j = BT2exp {( -e/kT)[4+ (N+ +)(e/r)]).If an electric field E is applied so as to assist the removal of electrons the effective work function of the material is decreased (the Schottky effect) and the emission current density then becomes j = BT2exp [-(e/kT){$-(eE)*)]. This theory has been further elaborated for very small particles for clouds of reacting particles and for the simultaneous presence of ions in fieldsi4 The use of fields to induce chemi-ions from the reaction zone to attach to any particles generated in flames is based on two mechanisms " diffusion " charging and " bombardment " charging. The former refers to the attachment of charge as the result of ion particle collisions due to random thermal motion of the ions and occurs irrespective of the local field intensity except insofar as this determines local ion concentration.The rate of charge acquisition by this mechanism is given by d(Ne)/dt = zr2cni exp [-e2(N-+)/rkT] (14) where c and ni are the root mean square velocity and the concentration of the ions respectively. Bombardment charging is due to ions drifting along lines of field intensity which terminate on the particle due to the dipole induced on it by the applied field. The ions drift at a very much higher velocity than the particles do so much so that the velocity of the latter can generally be ignored by comparison. The rate of charging then is d(Ne)/dt = 3zr2ji[ 1-(Ne/3Er2)]2.(15) For a non-conducting particle the right-hand side is multiplied by D/(D+2) which is of the order 1. In this case there is an equilibrium charge Ne = 3Er2 (16) which is due to the formation of an electrostatic stagnation point upstream when the effect of the dipole is neutralized. However it turns out that when large fields are applied to flames the equilib- rium conditions-indeed all the retardation effects due to appreciable particle charge in bombardment diffusion and thermionic charging-are often irrelevant. This is because the field tends to remove the particle from the charging zone in a time too short for its charge to become appreciable. There are obvious exceptions to this- for example see above for the case of using a small field to hold particles stationary against the gas flow in order to produce large agglomerates-but when it applies a unified and greatly simplified theory may be used for calculating the charge acquired by particles.6 Thus in principle particle charge inability and hence trajectories in fields are SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS calculable.However the physics of the subject is rather in advance of the chemical kinetics (not perhaps an unusual state of affairs at least in the field of combustion) and the kinetics of the growth of carbon particles for example is not sufficiently well understood to allow fully predictive calculations. It is much simpler to measure the mobility of particles withdrawn from flames by electric fields experimentally measure their size and deduce their charge.The values used in the next section were so obtained. PRACTICAL EFFECTS AND THEIR LIMITATIONS The largest mobilities occur for droplets (or particles) charged during their dispersion. Fig. 6 shows velocities of charged kerosene droplets (corresponding to those shown in fig. 5) in applied fields. These velocities were measured by photo- graphing tracks by interrupted illumination for the lower range and by laser Doppler C 22 43 6Q 80 103 120 140 field intensity/kV m-I FIG.6.-Electrically sprayed droplets ; velocity against applied field. Circles and crosses show results obtained by photographing particles by interrupted illumination and by laser Doppler velocimetry respectively.Curve from theory see text. velocimetry for the higher range the solid curve being based on the mobility theory discussed above. Velocities of many m/s are attainable at quite modest fields. The lowest mobilities occur when large fields are applied to flames producing smokes. The large fields may be useful for controlling the trajectories of charged particles but where they are simultaneously used for particle charging they decrease ion concentra- tion and tend to remove particles from the zone of charge acquisition as soon as the first charge has been acquired. This has been shown for carbon and silica to result in mobilities of the order of m2 s-I kV-' as compared to lo-' ni2 s-I kV-I for electrically sprayed droplet^.^ The latter is an appreciable fraction of the mobility of unattached flame It.J. WEINBERG ions owing to the many millions of electronic charges carried by sprays produced in this manner. In order to assess thepracticability of various applications we need to know not only mobilities but also field inteasities attainable in practice. Now the maximum field to which these charge-carriers can be subjected is limited for unipolar space charges between the ion source and each elebtrode by the onset of breakdown at the electrode at which the field intensity reaches a maximum. This limits the maximum current density which can be drawn in a uni-dimensionat system.to j = EEkjgnX (17) where Eb is the breakdown field at the electrode and X is the distance between the electrode and the ion source.’ This applies for an unlimited source of charge; for weak sourcesthere is the obvious limitation where j represents th3,saturation current density for which charges are removed as fast as they are generated there being no time for recombination.For flames of hydrocarbons burning in air however the former restriction (eqn (17)) is generally limiting. This is because jsis relatively large at least for near stoichiometric mixtures and because the strength of an ion source can always be made greater the simplest method being by increasing the area of flame surface per unit area of electrode. Using these theoretical concepts l4 the absolute maximum effects obtainable by fields have been predicted. Thus for a system of minimum separation between cold electrodes (taken as I cm) in which only flame ions (taken as mostly H30+and negative ions of about the same mobility produced by attachment of electrons in the cold electrode space) drift along the maximum current density is 2.5 A rnU2providing at the absolute maximum one charge for each of 1.6 x 10l9 particles.The corres- ponding expenditure of power is W = kEi/6n (19) which predicts 920 W m-2 (the S1 system of units tends to disguise the fact that this is a negligible quantity ; the value is for hot gas and should be compared with the power generated per square metre of flame!) In the presence of particles or droplets two cases arise; that in which particles drift in the presence of ions and acquire charge from them and that in which the par-ticulate phase is the sole charge carrier (e.g.the electrically dispersed fuel droplets discussed above). In the former case the current density is almost entirely due to the ions alone and the space charge and consequent field distribution may be treated on this basis.I8 In the latter case taking electrical dispersion of droplets as an example the relevant mobility is that of the droplets which as mentioned above is exceedingly high. Although it is at the bottom of the droplet size range (fig. 5) that mobilities of the same order as that of ions arise it is the large droplets that transport most mass. Thus it follows from eqn (17) that the volume of liquid that can be conveyed in this manner per unit area per unit time is V = (E,2kjgnXNe)(4nr3/3).(20) Substituting the Stokes mobility for this case (eqn 5) gives V = Ezr2/36nXq. (21) This is of the order of hundreds of litres m-2 s-I for electrode separations of the order of centimet res. Keeping electrode separations sinall is indeed the main problem in introducing s7-s SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS large field intensities into flames. Here it is important to note that the zone of ion generation (the exceedingly thin chemi-ionization region which accounts for well over 99 % of the free charges) generally does not coincide with the region in which particu- lates are formed. Even though the pyrolysis zone in carbon formation or the region in which metal oxide smokes condense may be quite a small distance from the chemi- ionization zone even a fraction of a millimetre makes an important difference to the field intensity as shown later.As regards the zone of ion generation the field intensity in this region of virtually infinitesimal thickness does not become appreciable until the applied potential exceeds that at which a saturation current is drawn. The field distribution is given by E2= Ei +8njx/k (22) where E, the field in the ion source remains small so long as the ion source can respond to increased potential by yielding more charge. Once saturation is reached further increases in potential result in a rapid rise of E,. However for strong ion sources and large electrode separations the breakdown condition (eqn (17)) is likely to be exceeded first. Fig.7 shows the maximum distance between cold electrodes 0.5-E 4 a 0 Y a I I I I 0.7 0.8 0.9 I.o fuel air ratio/fraction of stoichiometric FIG.7.-Maximum electrode separation for attainment of supersaturation field intensities in ion source as a function of fuellair ratio. 1 methane ; 2 propane ; 3 ethylene. (assumed symmetrical about the flame surface) for achieving appreciable fields in the chemi-ionization zone itself as a function of fuel/air ratio. However even when the field in the ion source is insignificant-perhaps because the electrode spacing has to be considerably larger than the values of fig. 7 so that the saturation condition is unattainable-the field intensity in a closely adjacent zone in F. J. WEINBERG which particulates axe formed can be appreciable.This is illustrated in fig. 8 which shows the growth of field intensity with distance from an unsaturated ion source. For example for an electrode spacing of 20 cm under conditions just below break- down at a cold electrode (3 x lo3 kV m-l) the field is 300 kV m-l at a distance of 1 mm from the ion source and still almost 100 kV m-1 at 1/10 mm. These correspond to velocities of metres per second even for the lowest mobilities mentioned above. 300-4 I f 200-$ x Y ..4 U 8 .--a 100--43 distance/fraction of electrode spacing FIG.8.-Field intensity as a function of (small) distance from ion source for conditions of incipient breakdown without attainment of saturation. We may conclude that this is a subject in which practical applications do not always follow directly from a scaling-up of laboratory experiments-no matter how spectac- ularly successful the latter are-and should not be attempted without a thorough understanding of the theory.Unsuccessful transposition to large-scale apparatus without taking theory into account have sometimes led to the equally erroneous conclu- sion that the methods are generally not useful. Thus there is obviously no prospect of removing all the soot generated in a jet engine flame tube by applying a field right across the duct-the ion source is much too strong in relation to the distance across which the potential is applied-this being a situation in which closely spaced plates are ruled out by the consequent pressure drop.Yet even under such conditions no great difficulty would be expected in attempting to prevent carbon deposition on some particular cold surface which is part of the device. Again as regards diminishing carbon formation by removal of the growing particles from the pyrolysis zone a local field intensity of 100V/cm will suffice to induce the least mobile of the particles mentioned above to cross a growth zone of 1 mm width in 0.1 s. For precipitation of particulate clouds the geometry of closely spaced plates as used in "electrostatic " precipitators is ideal the difference being that here no power is dissipated in producing a corona discharge. Under conditions when flame ions cannot be made to survive long enough (because distances are too large to apply a field) a small auxiliary flame or even ion emission from hot plates can provide the necessary charge.Lastly as regards droplets or particles deliberately charged during their dispersion very few of the above limitations apply. Owing to their high specific charges appreciable mass fluxes can be induced by quite modest fields linear velocities being 1-2 orders of magnitude greater than normal burning velocities. SMOKES DROPLETS FLAMES AND ELECTRIC FIELDS I am indebted to Mr. R.J Bowsex for checking the manuscript. K. G. Payne and F. J. Weinberg Proc. Roy. Soc. A 1959,250,316. E. R. Place and F. J. Weinberg Proc. Roy. Soc. A 1965 289 192. F J. Weinberg Proc. Roy Soc. A 1968,307 195. P. J. Mayo and F. J. Weinberg Proc.Roy. SOC.A 1970,319 351. K. C. Thong and F.J. Weinberg Proc. Roy. Soc. A 1971,324 201. D. R. Hardesty and F. J. Weinberg 14th Int. Symp. Combustion (The Combustion lnstitnte Pittsburgh 1972). J. Lawton and F. J. Weinberg Proc. Roy. SOC. A 1964 277,468. * T. P. Pandya and F. J. Weinberg Proc. Roy. SOC. A 1964,279 544. H. A. Wilson Phil. Trans. 1897 189 265. lo H. A. Wilson Phil. Trans. A 1899 192,403. l1 H. A. Wilson Phil. Trans. A 1899 193,289. l2 A. P. Chattock Phil. Mag. 1899,48,401. l3 J. Lawton P. J. Mayo and F. J. Weinberg Proc. Roy. SOC.A 1968 303 275. l4 J. Lawton and F. J. Weinberg Electrical Aspects of Cornbustion (Clarendon Press Oxford 1969) P. J. Mayo L. A. Watermeier and F. J. Weinberg Proc. Roy. SOC.A 1965 284 488. l6 L.B. Loeb Basic Processes of Gaseous Electronics (University of California Press Berkeley 1961.). l7 P. Langevin Ann. Chim. Phys. 1905 5 245. K. Gugan J. Lawton and F. J. Weinberg 10th Znt. Symp. Combustion (The Combustion Institute 1965) p. 709. l9 K. C. Thong and A. R.Jones J. Phys. D Appl. Phys. 1971,4 1159. 2o F. T. Smith J. Chem. Phys. 1958 28,746.