2596 BURGESS AND WHEELER: THE PROPAGATION OF FLAME TNCCXLII.--The Pgdopayation of Flame in “Limit”Mixtures of Methane, Oxygen and Nitrogen.By MAURICE JOHN BURGESS and RICHAR~D VERNON WHEELER.IN a previous communication (T., 1911, 99, 2013) we argued that a“ lower-limit, ” mixture (and, similarly, a “ higher-limit ” mixture)is “one such that a given volume must, under the conditions of itscombustion, evolve just sufficient heat t o raise an equal volume t oits igriition-temperature.”According to this view, during the propagation of flame in any“limit ” mixture a balance is struck between heat generated bycombustion and heat employed in starting combustion, togetherwith heat “ lost ” by conduction and radiation.Theoretically, provided that the amount of energy imparted t othe system by the initial source of ignition-an electric spark, forexample-is small, so that no appreciable impetus t o the propaga-tion of flame occurs near the source of ignition, flame should travelthroughout a true limit mixture a t a uniform speed.Experiments,to be described a t a later date, establish the correctness of thissupposit ion.Further, it seems probable that the speed of travel of flame willbe the same in all limit mixtures that comprise the same constitu-ent gases. Experiments show this to be the case so far as horizontalpropagation in mixtures of methane, oxygen, and nitrogen isconcerned.Limit mixtures thus offer several advantages for the study of themanner of propagation of flame in gaseous mixtures.This paper contains the results of a series of determinations ofthe amounts of methane required to form higher- and lower-limitmixtures with various “ atmospheres ” ranging between air (20.9per cent.of oxygen) and a mixture of air and nitrogen containing13.45 per cent. of oxygen.** The results of preliminary experiments, obtained during the early months of1913, were communicated to the institution of Mining Engineers (Trans. Inst. Min‘‘ LIMI‘L’ ” MIXTURES OF METHANE, OXYGEN .lSD NLTROGEN. 2597The lower-limit mixtures contained a minimum of 5.6 per cent.of methane (when air was used) and a maximum of 6.45 per cent.(when the 13-45 per cent. oxygen “atmosphere” was employed).The minimum value for the higlier-limit mixtures was 6.7 per cent.of methane (with the 13.45 per cent.of oxygen “atmosphere ”) andthe maximum value 14.8 per cent. (with air).The compositions were thus determined of a number of limitmixtures containing widely different proportions of the same threegases-methane, oxygen, and nitrogen-from which calculationsof the heat bdances cauld be made with a reasonable expectationFIG. 1.12 13 14 15 16 17 18 190 1 ~ ‘ y p ~ in limit iuixtwes-per ccnt.that, although errors in calculating the specific heats of the gasesa t the ignition-temperatures of the mixtures might render theresults not strictly accurate, the relative values would be correct.The results obtained showing the percentages of methane thatform limit mixtures with the different ‘‘ atmospheres” can con-veniently bo given in the form of a diagram (Fig.1).I n this diagram percentages of methane are plotted againstEng., 1918, 46,1i, 125) by Mr. W. C. Blackett, a member of the Explosions inMiues Committee of the Home Office, a t whose request the work was cariied out.Since then accounts have appeared of similar researches by the United StatesBureau of Mines (Technical Paper, NO. 43, 1914) a i d by F. Le Prince Ringuet(Compt. rend., 1914, 158, 1999). Some deterniinations of the lower limits have alsobeen published by A. Parker (this vol., p. 1002).VOL. cv. 8 2598 BURGESS AND WHEELER: THE PROPAGATION OF FLAME INpercentages of oxygen in the limit mixtures. The different “atmo-spheres,” with the percentages of methane required iii each case toform higher- and lower-limit mixtures, are as follows:Atmosphere.Oxygen.I o g e n .20.90 79.10 (air)19-22 80.7818.30 81-7017-00 83.0015.82 84- 1814.86 85.1413.90 86-1013.45 86-5513.25 86.75Methane, per cent.L o w e r m l i m i t .5.60 14.82- 12.93- 11.916-80 10-555-83 8.966.15 8.366.35 7.266.50 6.70No mixture capable of propagating flameIt will be seen that as the oxygen-content of the atmosphereis reduced the higher- and lower-limits come closer together, untilwith 13.45 per cent. of oxygen only mixturw containing between6-50 and 6-70 per cent. of methane are capable of propagatingflame. A mixture of methane with an atmosphere containing13.25 per cent. of oxygen is incapable of propagating flame.Presumably the true ‘‘ extinctive ’’ atmosphere for methane-the atmosphere in which a jet of methane, however perfectlyaerated, would be just unable to burn-contains between 13.45 and13-25 per cent.of oxygen.*It may be noted that Haldane and Atkinson, who were thefirst to work on this subjech (Trans. Znst. .$fin. Eng., 1895, 8, 549),found that natural fire-damp could form an inflammable mixturewith oxygen and nitrogen when the oxygen present had beenreduced t o between 12 and 13 per cent. The higher- and lower-limit mixtures of pure methane with the 13-45 per cent. oxygenatmosphere, according to our experimemnts, contain 12.55 and 12.57per cent. of oxygen respectively.The general equation representing the heat balance during thespread of flame in a limit mixture is as follows:where cf, c’f represent the specific heats of the mixture ( M ) , and ofthe products of combustion (P) respectively, each a t the ignition-temperature ( T ) , t being the initial temperature of the mixture;q represents heat dissipated (by conduction and radiation), andz& heat evolved by t’he combustion of x parts of the combustiblegas.When methane is the combustible gas the calculations are com-plicated by the fact that combustion is incomplete. Appreciable* The extinctive atmosphere for methane is usually regarded as c ~ .~ t a i n i n g about17 per cent. of oxygen ; and the “residual” atmosphere-that in which a methaneflame has burnt to extinction-as containing about 15 per cent. of oxygen.( c ’ M + c f f P ) ( T - t ) + q = z & .. . . . (1(‘ LIMIT ” MIXTURES OF METHANE, OXYGEN AND NITROGEN. 2599quantities of carbon monoxide occur in the products of combustionof all the lower-limit mixtures, whilst with some of the higher-limit mixtures combustion is mainly to carbon monoxide, hydrogen,and stearn, and tho “ water-gas reaction ” proceeds as the productscool.Consequently, in order to calculate the heat balance jt isnecessary t o analyse samples of the products of combustion as soonas they are formed-before secondary reactions, which can playno part. in the propulsion of flame through the mixture, have takenplace.This was clone so far as practicable by withdrawing and coolingrapidly small samples of the “flame gases ” whilst the flames weretravelling through the mixtures (which were contained in largeglass globes), in the manner described in the experimental part ofthis paper.The analyses of these gases show a regular relationship betweenthe ratios O,,CH, in the original mixtures and the proportions ofmethane that burn completely to form carbon dioxide and steam.In the higher-limit mixtures the ratio 0,/CH4 varied from aminimum of 1-20 (in the mixture with air) to a maximum of 1.87(in the mixture with the 13.45 per cent. oxygen “atmosphere”).The proportion of the methane burned in the former mixture t ocarbon dioxide and steam was 32.2 per cent.; in the latter mixtureit was 83 per cent.The results have been summarised as follows:Oxygen-contentatmosphere.20.90 (air)19-2218.3017.0015.8214.8613-9013.45of Ratio OJCH, inhigher-limit mixture.1.201.291-351.441.601-621.771-87Proportions of methaneburned to carbondioxide and steam.32.237.842.649-059.064.577.483.0As the proportion of oxygen t o methane is increased, more andmore of the latter is completely burned.With a ratio 02/CH4 = 1.50half the methane burns to carbon dioxide and half ta carbonmonoxide; whilst when the oxygen present is less than one anda-half times the methane present the main reaction is representedby the equation:CH4 + 0 2 = CO + H, + HZO.For comparison with these results those obtained by Bone andDrugman with mixtures of methane and oxygen in equal propor-tions may be quoted (T., 1906, 89, 676).The percentage composi-tion of the gaseous products of combustion (no carbon was8 ~ 2600 BURGESS AND WHEELER: THE PROPAGATION OF F1,AME INdeposited) averaged: W2, 6 . 3 ; CO, 41*9; H,, 50.8; CH,, 1.0.Commenting OD these results, Bone and Drugman say: “It hasbeen shown that, below the ignition-point, methane burns, forminga t an early stage steam and formaldehyde. The process mayprobably be best expressed as follows:CH4 --+ CH,*OH -+ CH,(OH), + CH20 + H,O, etc.‘ I A t high temperatures the formaldehyde would certainly decom-pose into carbonic oxide and hydrogen, so that in explosivecombustion we should obtain :CH,O+7 CH, + 0, = CO + H2 + H20.“The 6 par cent. of carbon dioxide formed in our experimentswould obviously arise by the secondary interaction of steam andcarbonic oxide in the flame.”A s a general conclusion from our results, we hold the opinionthat the essential reaction in the propagation of flame in theselimit mixtures is that responsible for the formation of carbonmonoxide, hydrogen, and steam in equal volumes.The heat cvolved by this reaction is probably almost equallydivided between the products of combustion of one “layer” ofmixture and the adjoining unburnt “ layer ” ; it is, however, insuffi-cient to raise the unburnt layer to its ignition-temperature.Follow-ing rapidly upon this reaction, some of the carbon monoxide andhydrogen is burned, the proportion depending upon the oxygen-concentration. Tho additional heat added t o the system in thislatter manner enables the nearest unburnt layer to attain itsignition-temperature.Finally, as the burnt gases cool, the water-gas reaction comesinto play, as is shown by comparison of the analyses of the “flamegases ” and “ final gases” for the same mixture (compare also(‘ The Water--Gas Equilibrium in Hydrocarbon Flames,” by G.W.Andrew, this vol., p. 444).Assuming this to be the correct interpretation of the sequence ofevents, calculation of the heat balance of each mixture can bemade, using the data supplied by the analyses of the flame gases.Calculation having been made of the percentages by weightof the constituent gases of the mixture composed of equal volumesof burnt and unburnt gases, equation (1) can be put in the form:(co& 4- CCH~B 4- CN~C 4- Cc0,U f CcoE f CH%T+ Q20G)(T - 1 ) f Q =xQ + z’Q’,co2.CCH~, etc., being the specific heats of the respective gases a tthe tenperature T - t , and A , B, etc., the percentages by weight ofthose gases. Of the methane burned, x grams form carbon dioxid“ LIMIT ’’ MIXTURES OF METHANE, OXYGEN AND NITROGEN. 2601and steam, the heat evolved by the reaction being Q calories pergram; aild $1 grams form carbon monoxide, hydrogen, and steam,the heat evolved by the reaction being Qf calories per gram.*Some doubt attaches to the value which should be assigned ineach case to T, the ignitiontemperature of the mixture. Tablesof the “ignition-temperatures” of various gases do not, in themajority of cases, afford information as to the percentage composi-tion of the mixture formed by the combustible gas with air (oroxygen) when ignition occurs.Thus, the experiments of Dixon andCoward (T., 1909, 95, 514), in which a heated jet of the combust-ible gas was aIIowed to flow into a heated atmosphere of air oroxygen, only determined for each gas the ignition-temperature ofthe mixture having (presumably) the lowest ignition-temperature,without showing the composition of that mixture.I n a recent paper by Dixon and Crofts (this vol., p. 2036) therelative ignition-temperatures of different mixtures of hydrogenand oxygen, determined by the method of adiabatic conzpressionsuggested by Nernst, are given, and it appears that increasedoxygen-concentration is accompanied by decreased temperature ofignition.A similar conclusion for methane-air mixtures may bedrawn from the experiments of Taffanel and Le Floch (Compt.rend., 1913, 157, 469); so long as the ratio 02/CH4 was greateror not much less than 2.0, the ignition-temperatures of the mixtureswere the same ; a continued increase in the methane-concentration,however, was accompanied by a regular increase in the ignition-temperatures of the mixtures.Using this relationship between oxygen-concentration and igni-tion-temperature, established by Taffanel and Le Floch, we havecalculated the ignition-temperatures of our mixtures, taking Dixonand Coward’s lowest figure as being probably most nearly correctfor mixtures having ratios 0,/CH4=2-0 or m0re.t The tempera-tures range between 650° for such mixtures and 715O for the* The values employed in our calculations are: for the reaction CH,+20,=C0,+2H20, &=11,910 calories per gram ; for thc reactionQ= 3240 calories per gram.chosen the following determinations :CH,+O,=CO+H,+ H,O,For the specific hpatv (at constant volnme) we haveOxygen ....................................0.1548 0.000023tMethane ................................. 0.4501 0-000016tNitrogen ................................. 0.1677 0-000016tCarbon dioxide ........................ 0.1531 0.000059tCarbon monoxide ..................... 0.1730 0.00001 6tHydrogen ................................. 2.4020 0.000016tSteam .................................... 0.3300 0.000120tt Taffanel and Le Floch, in their determinations, did not adequately allow, a9 didDixon and Coward, for the influence of heated surfaces2602 BURGESS AND WHEELER: THE PROPAGATION OF FLAME INmixture having a ratdo O,/CH,= 1-20 (the higher-limit mixturewith air).The results of the calculations are shown in Fig.2, where Q, theheat evolve'd, is plotted f o r each limit mixture against q, the heatunaccounted for or "lost." It will be seen that the two are practi-cally proportional, the heat unaccounted for averaging f o r eachmixture 35 per cent. of the total evolved.This heat-loss, the magnitude of which is no doubt due to thefact that the accumulation of sufficient energy for the propagationof flame is a prolonged process-$he combustion of methane takingplace " by stages," * is necessarily made up of loss by (I) conduc-tion and convection, and (2) radiation.The number of calories t'ransmitted by the flame to any givendistant layer of unburnt gas by conduction and convection can beF I G .2."18 19 20 21 2's' 23 24Q= Lniye calories.regarded as approximately proportional to the difference in tem-perature between the two, and a curve representing such trans-mission of heat by flames of different temperatures would be, asiiearly asgossible, a straight line.As regards heat transmitted by flames as radiant energy-which,be it noted, has been found in the case of non-luminous coal gasflames, 30 mm. in diameter, may amount to as much as 15 or20 per cent. of the whole heat of combustion I--the effect of tem-perature is more difficult to estimate. Callendar suggests thatPlanck's equation for a single wave-length may be assumed, and,for a Bunson flame of mean wave-length 3 .5 ~ ~ gives the followingtable of approximate values for the variation in intensity with* The well-known " lag " in the ignitioii of methane is also explicable from thisI- Third Report, Gaseous Explosions Committee, British Associatioil, Appendix A.cause (compare T., 1911, 99, 2020)‘- .LIMIT ” MIXTLJIIEX OE’ METHANE, OXYGEN AND NITROGEN. 2603temperature, for comparison with the fourth-power law of Stefanfor the radiatdon of a black body:Absolute temperature ... 1000” 1500’ 2000’ 2500’ 3000’Radiation, Planck. ......... 0.016 0.059 0.142 0.233 0.331Radiation, Stefan.......... 0.009‘ 0-045 0.142 0.347 0.721Commenting on this table, Callendar says: “The rate of varia-tion, according to Planck’s formula for a single wave-length, ismuch slower than r,he fourth-power law, and tends in the limit tobe directly proportional to the absolute temperature a t high tem-peratures. The actual rate of variation should lie between theselimits, but nearer to Planck, unless carbon begins t o separate inrich mixtures at high temperatures.” *As already noted, q, the’ “loss” of heat from our mixtures (innone of which did carbon separate), is practically directly propor-tional t o &, the total heat evolved.EXPERIMENTAL.The different mixtures of oxygen and nitrogen were made inlarge glass gas-holders holding sufficient f o r a dozen or moreexperiments, and thO limit mixtures with methane prepared fromthem in smaller gas-holders over glycerol and water.The method of determining the limits, and the apparatusemployed, were similar to those described in our previous paper(Zoc.cit., pp. 2020-2024). The methane used was prepared fromaluminium carbide, and was purified from traces of acetylene bypassing through ammoniacal cuprous chloride, and from hydrogenby passing slowly over ‘( oxidised ” palladium precipitate heatedat 90°.Each mixture was analysed, the methane being determined byexplosion (with electrolytic gas or excess of air and oxygen addedas the case might require), and the oxygen by absorption bystrongly alkaline pyrogallol.A large num-ber of experiments with each atmosphere were madebefore the limits were fixed as closely as was desired.Correspond-ing mixtures were then carefully prepared and inflamed in aspecial form of explosion-vessel designed for securing a sample ofthe ‘( flame gases ” whilst the flame was travelling (Fig. 3, p. 2592).This explosion-vessel was a Zi-litre globe, with glasscoveredelectrodes reaching t o the centre. Through the side of this globewere fused, in the positions shown in the photograph, two finecapillary tubes, either of which could make connexion, through athree-way tap, with a small bulb filled with mercury t o within4.5 C.C. of its capacity. The space above the mercury in this small* Third Report, Gaseous Explosions Comniittee, British Association, Appendix A.It contained 99.7 per cent.of methanePer cent. by volume.Osygen- Lnalysis ofcontent Description limit mixture. Analysis of flame gases.of of limit 7- / \ /-20.90 (air) Higher 17.80 14.82 67.38 4.80 nil 10.10 10.50 0.85 73.75 4.9919.32 ,, 16.74 12.93 70.33 5.00 nil 8.19 8-19 0.72 77.91 5.3218.30 ,, 16.12 11.91 71.97 5.37 nil 7.23 7.26 0.82 79.32 5.5517-00 ?, 15-22 10.55 74.23 5-55 nil 5.78 5.75 0.38 82.54 5.6815.82 ,, 14.40 8.96 76.64 6.03 nil 4.19 2.93 0.25 86.62 6.4314.86 ’,, 13.59 8.36 78.05 6.27 nil 3.45 2.56 0.34 87.38 6.3913.90 ,, 12.88 7.26 79.86 6.41 nil 1.87 1.20 0.37 90.15 6-5213.45 ,, 12.55 6-70 80.75 6.62 nil 1.36 nil 0.55 91.32 6.9213-45 Lower 12.57 6.50 80.93 6.82 nil 1.31 0.35 0.35 91.17 6.9313.90 ,, 13.00 6.35 80.65 6.57 0.56 0.60 0.45 nil 91.82 7.2714.86 ,, 13-95 6-15 79.90 6.46 1.54 0.48 0.18 nil 91.34 7.0015.82 ,, 14.89 5.83 79.28 6.23 3.43 0.32 0.10 nil 89-92 6-6020.90 (air) ,, 19-73 5-60 74.67 6.25 9.65 0.07 nil nil 84.03 6.30atmosphere.mixture. 0,. CH,. N,. CO,. 0,. CO. H,. CH,. N?. CO,“ LIMIT’’ MIXTURES OF METHANE, OXYGEK AND NITROGEN. 2605bulb was thoroughly exhausted of air, and served, when the three-way tap was rapidly opened, to capture a sample of the gases a teither of the two points where the capillary tubes ended withinthe explosion-vessel. When the whole apparatus was inverted thissample could be withdrawn, by means of a mercury pump, throughthe tap shown a t the bottom of the photograph.I n all the limit’ mixtures the manner in which the flame travelledwas the same.So soon as the igniting spark had been passed aflame shot up to the top of the vessel, bent over, and, after thusfilling the whole of the to2 quarter of the globe, travelled down-wards t o the bottom as a uniform layer of light blue colour.+ Thislayer had an apparent thickness of between 13 and 2 inches, andtravelled sufficiently slowly to enable the tap leading t o thesamplingvessel to be manipulated a t the right moment.The moment chosen for all the samples of which analyses aregiven in this paper was when the layer of flame had passed half-way past the end of the upper capillary tube, as indicated inFig. 3 by the shading added to the photograph, which gives a veryfair idea of the appearance1 of the flame when observed throughthe side of the globe a t the moment of sampling.The gases were driven into the samplingvessel under pressure ofbetween 2 and 3 atmospheres, so that, although the space in thatvessel unoccupied by mercury was under 5 c.c., between 10 and15 C.C. of gases were obtained f o r analysis.Samples of the products of combustion remaining in the explo-sion-vessel were withdrawn for analysis after sufficient time hadbeen allowed for complete mixture.Results of 3zperiments.-The compositions of the limit mixtures,and the analyses of the “flame gases” and final gases” are givenon p. 2604.A correction has been introduced in the analyses of flame gasesfor the unburned mixture contained in the capillary-tube leadingto the sampling-vessel.The last two columns in the table record the calculated values ofQ and p plotted in Fig. 2.These results have already been discussed in the theoreticalportion of this paper. An additional point that should be notedis the preferential burning of hydrogen over carbon monoxide inall the mixtures that contain a ratio O,/CH, greater than 1.5.ESRMEALS,CUMBERLAED.* In some of the higher-limit mixtures the flame had a slightly reddish tinge