1044 MASON AND WHEELER THE " UNIFORM MOVBMENT " XCII.-The " Uniform Movement '? during the P~opayation of Flame?. By WALTER MASON and RICHARD VERNON WHEELER. THE initial slow propagation of flame that takes place when an inflammable mixture a t rest is ignited at a point is usually re-garded as controlled by the transference by conduction of the heat developed by the combustion of the mixture immediately surround-ing the point of ignition whereby successive contiguous portions of the mixture are raised in temperature until chemical action becomes rapid. The initial speed of propagation of flame in a given mixture away from the point of ignition should mainly depend according to this view (1) on the conductivity for heat of the unburnt mis-ture and (2) on the velocity with which a moderately heated layer begins to react chemically and so to rise gradually in temperature, or in other words on the rate of change of reaction velocity with temperature.Under certain conditions with all inflainniable mixtures of gases and air a t atmospheric temperature and pressure the initial slow propagation of flame can be maintained at a uniform speed over a considerable distance of travel from the point of ignition. The con-ditions most favourable o r necessary to obtain and maintain this '' uniform movement " of flame are that the inflammable mixture should be contained in a long straight and horizontal tube open a t one end and closed a t thehother; and that ignition should be effected a t the open end of the tube by a source of heat not greatly exceeding in temperature the ignition-temperature of the mixture, and not productive of mechanical disturbance of the mixture.The speed oaf the uniform movement then depends on the compositjon of the mixture (presumed to be a t atmospheric temperature and pressure) and on the diameter of the tube in which it is contained (see p. 1051); above a certain (sinall) diameter the material of which the tube is made does not appreciably affect the speed of the flame. With a tube of given diameter the speed of the uniform movement of flame in a mixture can be regarded as a definite physi-cal constant for that mixture. Following Vicaire (Ann. Chhn. Phys. 1870 [iv] 19 118) Mal-lard and Le Cliatelier (tlnn. des Mines 1883 [viii] 4 274) Put forward theoretical considerations respecting the transference of heat during the burning of gaseous mixtures from which i t should be possible to deduce the speed of the flame during the uniform movement as follows DURING THE PROPAGATION OF BLAME.1045 Suppose the flame to be propagated in a tube of uniform cross-section filled with the combustible mixture a t an initial tempera-ture 8. At a given moment during the propagation the “layer,” A (Fig. l) becomes inflamed. The mass of burnt gases which fills the tube behind ,4 is a t a temperature T the “ combustion-tempera-ture,” which can be calculated. The layer of gas immediately in contact with A and in front of i t is a t the ignition-temperature t , of the mixture or rather a t a temperature infinitely close t o t. The successive layers in front are a t temperatures gradually decreas-ing froin t to 6.The layer A itself must be a t a temperature T;, higher than T f o r a t the moineiit when i t was inflamed it had already been raised t o t . If we neglect t.he variation in the specific FIG. 1. T’ heats of the gases between T I‘i=T+ t . +--and TI and assume 8=0 then A t the moment of inflammation of the layer A of thickness ds, the distribution of temperatures in the tube can be represented as in Fig. 1 in which beyond d a gradual levelling of temperature froin Y’I t o T is shown. At the end of an infinitely short time d7, the layer A’ of thickness ds next to the layer A becomes inflamed in its turn and the whole diagram advances through a distance ds. For this to take place the front part of the tube must gain a quan-tity of heat represented by the infinitely small area tt‘88‘ which is equal to the rectangle AA’tt’.This quantity of heat is t h a t neces-sary to raise the temperature of the layer of thickness ds from 8 t 1046 MASON AND WHEELEE THE “ UNIFORM MOVEMENT ’’ t ; it is therefore equal t o cl(t-O)ds c’ being the specific heat of the burning or just burnt gases. The quantity of heat lost by the hinder part of the tube must balance that gained by the front part. Now the layer A that gives up its heat in front is a t a temperature TI. and is between a layer a t a temperature t and one a t T. Tlie quantity of heat given u p by A in unit time will therefore be a function of T and t and can be stated thus: d ( t - d)d.s=drF(T,t), whence we obtain for the speed of propagation of flame: v=~’S/ds=F(T,t)/cl(t-d) .. . . (1). The exact form of the function F ( T t ) cannot readily be deter-mined. However one can presume that it is proportional to the conductibility L of the unburnt gas; and one can state that it beconies zero when T = t and for that value of T only. It would seem that when the temperature of combustion T exceeds the temperature of inflammation t the heat necessary for the inflam-mation of a layer can be transmitted integrally. We can therefore put the expression for ‘I! in the forin: . (2) and i t may be that F ( T t ) is a constant. The only point open t o criticism in this otherwise lucid reasoning is t h a t which attributes t o the “layer” of gas that is actually burning a higher temperature (TI) than i t would attain if it biirned without previous heating to its ignition-temperature ( t ) .Mallard and Le Chatelier found confirmation of this view in the observation by Gouy (,4nn. Chim. Pl~ys. 1879 [v] 18 1) t.hat as judged from photometric measurements the surface of the bright green inner cone of a Bunsen flame is the hottest part of the flame; f o r the surface of this inner cone is the ‘‘ burning layer ” of a stationary explosion the rate of propagation of flame downwards in the mix-ture being equal to the rate of flow or^ the unburnt gases upwards. Gouy showed t h a t there is a simple relation between the area of surface of the inner cone the rate of flow of the mixture and th9 s p e d of propagation of flame therein; and llichelson (Ann,.Phys. Chem. 1889 [iii] 37 l ) who adopted in toto Mallard and Ide Chatelier’s theoretical considerations and a t a later date Mache ( A n n . Physik. 1907 [iv] 24 527) used this relation t o determine the “normal” speed of propagation of flame in a number of gaseous mixtures. Haber and Richardt (Zeitsch. mtorg. Chem. 1904 38 5) how-ever showed by actual thermo-electrical measurements that th DURING THE PROPAGATION OF FLAME. 1047 surface of the inner cone of a Bunsen flame is not the hottest part of the flame and concluded that its brightness is a phenomenon of luminescence. Further they denied tlie possibility of the burniiiq layer during the uniform movement in the propagation of flame along a tube attaining a higher temperature than i t would if i t were heated merely by its own heat of radiation f o r the reason that while i t is burning i t must lose to successive layers as much heat as it gained from earlier burnt layers.Haber and Richardt’:, argument is siirnmarised in the following quotation from their paper (p. 55) : ‘‘ Die Vorwarmung eines esplosibleii Gasgemenges erhiil t die Verbrennungstemperatur wenn sie auf Kosten dar Warnle des rerbrannten Gases erfolgt (Regenerativsystenl ()fen der Gasan-stalten u.s.w.) aber sie erholt sie nicht wenii sie auf Kosteri der Warme des verbrennenden Gases erfolgte (Flamme Explosion) tleiin da das Gebilde welches die Vorwarmung bewirkt soviel Wiirme abgibt als das vorgewarmte aufnimmt so kanii Temperatur-steigeruiig durch Vorwarmung nur eintreten wenn die Tf’arme-abgabe dem Temperaturansteig zeitlich nachfolgt und nicht..wen?^ sio ihn begleitet.” We consider Haber and Richardt’s view to be the correct one. Mallard and Le Chstelier’s equation (2) is however affected only as regards the magnitude of the function P(T,t) which is in any event indeterminate. The important deduction from the equ a -tion is that in mixtures t h a t have the same conductibility for heat, the speed of the fleme during the uniform movement should Iw directly proportional t o T - 2 and inversely proportional to f - H . The effect of variation in the conductibility of the mixture 011 the speed of the uniform movement of flame is well shown with mixtures of hydrogen and air (Haward and Otagawa T. 1916, 109 85).The fastest speeds are obtained with mixtures contain-ing from 38 t o 45 per cent. of hydrogen instead of with the mixture that contains hydrogen and oxygen in combining proportions anti has the highest temperature of combustion. The thermal conduc-tivity of hydrogen is 31.9 x 10-5 compared with that of air, 5-22 x 10-5 and as zlready stated the mixtures in which the speeds of the flames are fastest contain between one-third and one-half their volume of hydrogen. When the combustible gas has a thermal conductivity more nearly approaching that of the air with which i t is mixed and when it forms but a small proportion of t h e mixture as with methane the influence of thermal conductivity on tho speed of propagation of flame can be neglected o r regarded a s constant.If c’ also be regarded as constant over the range of temperature 1048 MASON AND WHEELER THE (' UNIFORM MOVEMENT " concerned the speed of the uniform movement of flame in mixtures such as those of methane with air should be proportional t o T - t / t - 8 if the uniform movement truly represents the transfer-ence of heat by conduction. I n order t o obtain data whereby t o k t this conclusion and t o elucidate the nature of the physical constant which we regard the uniform movement of flame t o be, we have determined the speeds (in a tube 5 cm. in diameter) in a number of mixtures of methane oxygen and nitrogen of which we have also determined the relative ignition-temperatures and of FIQ. 2. which the theoretical combustion-temperatures have been calcu-lated.The results are shown in Fig. 2 which apart from the problem with which we are now concerned is of interest in showing the effect of reducing the oxygen coiitent of the air on its ability t o support the combustion of methane. I n the topmost curve the speeds of the flames are plotted against percentages of methane in atmospheric air *; the curve below was obtained with an " atmo-* This curve which is reproduced also in Fig. 3 is constructed from the figures given by Wheeler (T. 1914. 105 2606) after applying a correctio DURING THE PROPAGATION OF FLAME. 1049 sphere” containing 20.60 per cent. of oxygen; then follow in suc-cession curves obtained with atmospheres containing 18.85 17.60, and 15-05 per cent. of oxygen respectively the percentages of methane in each instance being percentages in the particular ‘‘ atmosphere.’’ (For example the 7 per cent. methane mixture with the 15.05 per cent. oxygen “atmosphere” had the followixig composition methane 7.0 ; oxygen 14.0 ; nitrogen 79.0 per cent .) It will be seen t h a t the speeds of all the limit mixtures (in which a balance is struck between tlie heat generated on combustion and the heat required to start combustion) are the same. The calcu-lated ratios T - t / t - 8 for each limit mixture are however not the same being greater by about 50 per cent. for the higher limit mix-tures than for the lower. Calculation of the theoretical combustion-temperatures of the mixtures is comparatively simple so long as they contain sufficient oxygen to burn tlie methane completely.When the-oxygen is in defect it is necessary to take into account the mechanism of com-bustion of methane. This in accordance with Eone’s researches on the slow combustion of methane and as Burgess and Wheeler found in their experiments with ‘‘ limit ” mixtures of methane, oxygen and nitrogen (T. 1914 105 2596) involves as the reac-tion essential to the propagation of flame the formation of carbon monoxide hydrogen and steam in equal volumes according to the scheme : (CH,O) CH,+O = CO+H,+H,O. Following upon this reaction the carbon monoxide and hydrogen are burned practically completely to carbon dioxide and steam if the ratio O,/CH is 2.0 or greater; or if the ratio is less than 2.0, proportionally to the oxygen-concentration.Analyses of samples of the burnt gases taken during the propagation of flame before their cooling enabled the ‘‘ water-gas reaction ” to come into play, showed that with the mixture containing the lowest ratio O,/CH, (namely 1.20 for the higher limit mixture with air),. the propor-tion of the methane burned completely t o carbon dioxide and steam was nearly 33 per cent. ; whilst the proportion so burned increased regularly with the ratio O,/CH to just over 99 per cent. for mix-tures with a ratio 2.0. t,hat w~ls found to be necessary by reason of the fact that the “ standard ” $-seconds clock used for the determinations recorded 50 seconds per minute instead of 60. The speeds given in Wheeler’s paper although relatively correct (the paper dealt only with the relrct]ive speeds) are therefore too high by one-sixth 1050 MASON AND WHEELER THE “ UNIFORM MOVEMENT ” The1 relative ignition-temperatures of the mixtures were deter-mined in a manner which will be described in a subsequent paper.It warp found that over the range of mixtures covered by the experi-ments EOW described there was a nearly regular increase in the ignition-tempeKature as the’ ratio O,/ CH decreased. The relative ignition-temperatures can be regarded as ranging from 650° for a mixture containing 5.5 per cent. of methane in air to 700° for one containing 14.5 per cent. When the ratios T - t / t - 8 for all t,he mixtures comprised within the curves shown in Fig. 2 are calculated i t is found that Mallard arid Le Chatelier’s equation (2) holds very closely so long as the oxygen in the mixtures is in excess; that is t o say so long as it is possible for the comb us ti or^ of the methane to be carried rapidly t o completion When the combustion is incomplete however the ratio T - t l t - 6 is in general higher than t,he speed of t h e i i n i -form movemelnt of flame in the niixture requires.It becomes as alrea,dy stated markedly high for the upper limit mixtures. The natural inference to be drawii from this result is that there is an enhanced radiation loss through the walls of the tube during the propagation of flame in mixtures containing excess of methane, presumably because the process of combustion of such of the methane as burns is more protracted than when excess of oxygen is present and the reacting molecules remain €or a longer time in a condition of vibration such a s to enable them to emit radiations.This presumed protraction of the process of combustion (of which a long luminous tail behind the flame-front in mixtures containing excess of methane is perhaps evidence) would prevent the atkain-ment of the calculated ‘‘ combustion-temperature.” It is in fact, evident from these experiments that little meaning attaches to the usual calculations of combustion- or flametemperatures if only for the reaqon that the effect of the 10% of energy by radiation and the variations in that loss dependent on the duration of chemicaI change during combustion are not taken into account. , The Infithence of the Diameter of the Tube o n the Speed of t h e Uniform Movement of Flame in Mixtures of Methane and Air.According to Mallard and Le Chatelier cooling of the hot gases by the walls of the tube does not appreciably affect the speed of the flame when the diameter is sufficiently great for the following reasons The quantity of heat withdrawn from the burning gases by the walls of the tube is proportional to the perimeter 2 r r of the tube; to the difference between the temperature of the gases and that of the tube T - 8 ; and to a coefficient of conductibility k DURING THE PROPAGATION OR' FLAME. 1051 The mass of the burnt gases is proportional to r2 and to the speed of propagation of the flame u; so that if Q be the heat of com-bustion and c the specific heat of the burnt gases, Qr%= c & I ( T - 8 ) + kr(T - O ) , whence T = 8 + & / ( c + k / r v ) .The temperature T will not be materi-ally affected when k / r v is negligible compared with c ; that is to say when T and u are sufficiently great. For their experiments with mixtures of methane and air Mallard and Le Chatelier used glass tubes 5 cm. in diameter which they considered to be sufficiently large to overcome the effects of cooling by the walls even with the most slowly moving flames. This we believe to be correct for there is not much difference in speed in tubes from 5 to 10 cm. in diameter whereas when the diameter of the tube is only 2.5 cm. the speed is reduced by about onethird. Cooling by the walls thus interferes with the measurement of the true speed of the uniform movement of flame in mixtures of methane and air unless the diameter of the tube exceeds about 5 cm.When however the diameter is increased above 10 cm. the speed of the flames is affected by the coming into play of another factor namely convection. The influence of convection currents is noticeable with the fastest moving flames in tubes 10 cm. in diameter the visible effect being a turbulence of the flame-front. So far as can be judged by eye, the turbulence is essentially a swirling motion in a direction nearly normal to the direction of translation of the flamefront which as in tubes of smaller diameter progresses a t a uniform speed for about 150 cm. before backward and forward vibrations (the " vibratory movement ") are set up. This swirling motion appears ab initio and is due to rapid movement of the hot gases from below upwards by convection.I n tubes of comparatively small diameter (5 t o 9 cm.) this rapid movement is suppressed although the shape of the flame-front shows that there is a definite movement of the hottest gases towards the upper part of the tube (see T., 1914 105 2609). We have determined the initial uniform speeds of the flames over the whole range of inflammable mixtures of methane and air in tubes 2.5 5 9 30.5 and 96.5 cm. in diameter. The results are shofn graphically in Fig. 3 in which the speeds of the flames are plotted against percentages of methane in air. If for any given mixture say 10 per cent. methane the speed of the flame is plotted against the diameter of the tube in which it travels a curve such as those shown in Fig.4 is obtained. From these curves it is clear that in tubes of less than 5 cm. diameter the speed of the flame is V O L 0x1. T 1052 MASON AND WHEELER THE “ UNIFORM MOVEMENT ” retarded by the cooling effect of the walls. I n tubes of large diameter however from 10 cm. upwards the speed of the flame is proportional t o the diameter of the tube. The “uniform movement” of flame as defined by Mallard and Le Chatelier (that is I ‘ le mode de propagation par conductibilit6 ”) is thus a strictly limited phenomenon obtainable onlv in tubes J FIG. 3. * 1 12 13 1 Methane. Per cent. in air. within a certain range of diameter large enough to prevent appreciable cooling by the walls but narrow enough to suppress the influence of convection currents.The initial speed of flame in mixtures of methane and air is uniform also in tubes of large diameter-the flames travelled a t a sensibly uniform speed over a distance of 10 metres in a tube 96.5 cm. in diameter and 44 metres long-but as we have shown this uniform movement does no DURING THE PROPAGATION OF FLAME. 1053 result from the normal transference of heat from layer t o layer of the mixture by conduction. When speaking of the uniform movement of flame in gaseous mixtures it is necessary therefore if Mallard and Le Chatelier’s definition be accepted t o specify the diameter of the tube in which the mixtures were contained. Alternatively the initial slow uniform movement can be regarded simply as a particular phase in the propagation of flame t h a t results tvlien ignition is effected (in a quiescent mixture) a t the open end of a straight horizontal tube of any diameter closed a t the other end; and not as resulting from a particular mode of heat transference.Fxa. 4. 0 Diameter of tube in cm. C3 E x P E R I M E N T A L. The method of recording the speed of the flames and the general mode of procedure for the experiments in glass tubes have been described by Wheeler (Zoc. c i t . p. 2610). The method was essenti-ally that of registering 011 a chronograph the times a t which fine screen-wirm of copper (0.025 mrn. in diameter) through which an electric current was passing were fused as the flame reached them. We may add to the description already given the detail that the electric current passing through the screen-wires was sufficient t o raise them nearly to red heat.This arrangement ensured the T T 1064 MASON AND WHEELER THE '' UNIFORM MOVEMENT " rapid melting of the wires as soon as the flame touched them and therefore gave very uniform results; wires made from metals or alloys of low melting point which could not be drawn so fine or of so uniform a diameter as copper were found to be unsatis-factory. For the experiments in the larger tubes (30.5 and 96.5 cm. iii diameter respectively) which were of mild steel the screen-wires were mounted on supports of brass wire reaching nearly to the horizontal axes of the tubes and fixed through screwed-in plugs of vulcanite 50 cm. apart along the length of each the first screen-wire being 50 cm.from the point of ignition. It' was filled with the required mixture which had previously been pre-pared in a gas-holder of 42.48 cubic metres capacity by displace-ment of air six times the volume of the tube being taken for dis-placement. Samples of the mixture for analysis were taken from the gas-holder and from near the open end of the tube just before ignition. The tube of 96.5 cm. diameter was 44.25 metres long and was provided with a by-pass tube 15-24 cm. in diameter running its whole length and fitted a t either end with valves which were closed during an experiment. A motor-driven fan was included in this by-pass connexion and served to circulate the contents of both tube and by-pass when making the mixture of methane and air required for an experiment.The mixtures were made by passing into the tube a measured quantity of methane from a storage holder displacing an equal quantity of air an3 circulating the contents as aforesaid during two hours the end of the tube a t which the mixture was t o be ignited being temporarily closed during this operation by a gas-tight cover of wood. Samples of the mixture for analysis were taken from both ends of the tube before each experiment ; no appreciable difference was found between the compositions of samples of the mixture at either elid of the tube. For all the experiments including those in the glass tubes the methane used was from a blower of firedamp in South Wales, whence it was obtained compressed in cylinders. It contained no appreciable impurity other than between 2 and 24 per cent.of nitrogen . The tube of 30.5 cm. diameter was 15-24 metres long. The analyses always closely agreed. In the opening paragraphs of this paper we indicated some of the conditions necessary t o ensure the obtaining of the uniform iiiovement of flame. One of the essential conditions is that igni-tion should be effected at or within 3 OT 4 on. of the open end o DURING THE PROPAGATION OF FLAME. 1055 the tube. This is particularly necessary with narrow tubes other-wise if the point of ignition be some considerable distance within the tube flame travels in both directions from the point of ignition, and the disturbance caused by the flame travelling towards the open end affects the flame travelling towards the closed end. The result is that a vibratory motion is imparted at the outset to the flame and records of the speed of the flame travelling towards the closed end show in consequence wide variations from one experi-ment to another with the same mixture.F o r example the following records were made of the speed of flame in a mixt>ure of methane and air con€aining 10.00 per cent. of methane. A tube 5 cm. in diameter and 5.2 metres long was used. I n one series of experiments the point of ignition was 4 cm. from the open end of the tube and in another it was 17 cm. The speeds were measured between t.wo screen-wires 50 cni. apart the first screen being 40 cm. from the point of ignition. Ignition was by a secondary discharge across a 3 mm. spark-gap using a “4-inch” induction coil with a current of 2.5 amperes through the primary circuit, Speed of ‘‘ Uniform Movement.” Cm.per second. Point of ignition 4 cm. from open end. 1 .................. 93.3 2 .................. 91.7 *> .................. 93.3 4 .................. 94. I 5 .................. 94. I 6 .................. 93.3 7 .................. 91-7 8 .................. 91.0 9 .................. 94.1 Mean ............ 92.9 Variation ...... -t 1.2 - 1.9 0 Point of ignition 17 cm. from open end. 88.0 91.3 88.8 87-2 80.9 00.3 94.5 83.3 86.2 87.8 + 6.7 - 6.9 Similarly with a glass tube 2.5 cm. in diameter when ignition of a mixture of methane and air containing 10.25 per cent. of niehhaiie was effected a t a point. 15 cm. from the open end vibra-tions were set up immediately in the flame travelling towards the closed end and wide variations were obtained in the records of speeds as follows 1056 MASON AND WHEELER ‘‘ UNIFORM MOVEMENT,” ETC.Speed of ‘( Uniform Movenient.” Cm. per second. Point of Point of ignition 4 cm. from open end. 1 65.5 59.1 2 6.5.5 50.0 3 66.2 52.5 4 65.5 57.0 ignition 15 cm. from open end. .................. .................. .................. .................. Mean ............ 65.7 Variation ...... -t 0.5 - 0.2 54.6 f 4 . 5 - 4.6 Apart from the wide variations in the recorded speeds when the point of ignition is too far within the tube it will be seen that the mean of the results shows a slower speed than when the point of ignition is properly placed.The reason for this is that the flame that travels towards the open end acts as a drag on the flame travelling towards the closed end. I n general unless care be taken t o avoid causing disturbance of the mixture a t the moment of ignition the records of speeds of flames obtained are of doubtful value. Another matter that requires attention is the possibility of any additional impetus given to the flame by the source of heat used to cause ignition affecting the recorded speed. This can be avoided by allowing the flame to travel a distance of 30 or 40 cm. before reaching the first screen-wire (see T. 1914 ,105 2610). When this precaution is taken the intensity and size of the source of heat used to ignite the mixtures can be varied considerably without affecting the measuremenk of the speeds of the flames as the following experiments illustrate.A glass tube 2.5 em. in diameter and 5 metres long was used, and the speed of the uniform movement of flame determined in a series of mixtures of methane and air. The mixtures were ignited by (i) secondary discharge sparks from an ‘(8-inch” X-ray coil with a current of 5 amperes through the primary circuit; (ii) secondary discharge sparks from a ‘( 4-inch ’) coil with a current of 2.5 amperes through the primary circuit; and (iii) the flame of a taper. The point of ignition was 4 cm. from the open end of the tube when sparks were used; a t the open end when the taper-flame was employcd. Tlie first screen-wire was 40 cni. from the open end of the tube THE HYDROLYSIS OF SODIUM CYANIDE. 1057 Speed of Met ham. Per cent. 7.10 7.80 23-05 8.60 9.10 9.50 9.95 10.25 10.55 11.60 12-25 Uniform Movement.” Cm. per second. Ignition by “ 8-inch ” coil. 37.0 47.0 51.0 57.3 64.6 66.6 66-2 65.5 61.0 46.7 35.0 Ignition by Ignition by &inch ” coil. taper. 37.3 36-6 47.7 47.5 52-5 52.1 58.0 58.7 64.0 64.4 68.3 66.6 67.8 65.5 65.5 66.2 61.8 61.5 47-5 47.9 35.1 35.0 It will be seen that for any of the mixtures the recorded speeds did not show any abnormal variations traceable to the means of of ignition employed. [Received October lDth 1917.