1446 PAYMAN THE PROPAGATION OF FLAME IN CXXXV1.-The Propagution of Flame in Complex Gaseous Mixtures. Payt 41. The Unifomi Moceinent of Flame in Mixtures of Air with the Paq-afin Hydrocarbons. By WILLIAM PAYMAN. IN the preceding paper it was shown that all mixtures of limit mixtures are themselves limit mixtures. With each of the paraffin hydrocarbons the speed of the uniform movement of flame at the limits tends to a constant value under standard conditions of experiment. The same speed was found with all limit mixtures of methane oxygen and nitrogen and with an equimolecular mixture of methane and pentane a t its limits with air. There is no reason to doubt that the same speed would be obtained with all mixtures of the paraffin hydrocarbons a t the limits. The generalisation' advanced in the previous paper was thus shown t o apply to all such mixtures.The question immediately arises whether what is true of the speeds of flames a t the limits holds also for other speeds. Whether for example given two or more mixtures of air with different individual gases in each of which the speed of flame was the same all combinations of the mixtures would propagate flame at the same speed. Should this be so a simple method would be available for the calculation of the speed of propagation of flame in complex gaseous mixtures from the known values for the simple constituent? gases. Such a calculation could naturally only apply over the whole range of mixtures when the maximum speed of flame in mixtures of the several individual gases with air was the same; otherwise calculation would be restricted to such mixtures as possessed a speed of flame not greater than the lowest of the individual maximum speeds.It is clear, also that$ the mixtures taken for the purpose of calculation must be all of the same nature; that is t o say must all contain excess of combustible gas or must all contain excess of oxygen. The mixtures of the paraffin hydrocarbons with air seemed most, suitable t o determine whether the generalisation that applies to speeds of flames at the limits is capable of extension to the speeds of the uniform movement over the whole range of inflammable mixtures. Measurements were therefore made of the speed of the uniform movement hmixtures of air with each one of the hydrocarbons of the paraffin series up to and including pentane.The determin-ations were carried out as described in the previous paper in COMPLEX QASEOUS MIXTURES. PART 11. 1447 horizontal glass tube 2.5 cm. in diameter and 3 metres long. The results are recorded in table I. The majority of the values in column 1 for methane were obtained by Mason and Wheeler (T., 1917 111 1052). With the exception of methane the maximum speeds are approximately the same namely about 82 cm. per second. The value for methane is rather lower than this being 67 cm. per second. Owing to the few data available for the thermal constants of the paraffin hydro-carbons it is not easy to explain this difference. In each instance, the mixture having the maximum speed of flame contains more combustible gas than is required for complete combustion, The results are shown diagrammatically in Fig.1. FIG. 1. 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 11 12 13 1 Combustible gas per cent. For testing the application of the generalisation * t o speeds other than the limiting speeds the gases methane and pentane were first chosen since they were both readily obtainable in ample quantity, 'Two air mixtures were prepared one containing 7-35 per cent. of methane and the other 1.98 per cent. of pentane. In these two mixtures the speed of the uniform movement is the same about 40 cm. per second (twice the speed a t the limits) and they both contain excess of oxygen. The mixtures were then combined in varying proportions and the speeds of the uniform movement deter-mined in the usual manner.The results are recorded in table 11. * This may be termed the " speed generalisation. TABLE I. Speed of Uniform iWovement of Flame in Mixtures of Air with Horizontal Glass Tube 2.5 cm. in Diameter. Methane. Ethane. Propane, 7- F - - Per cent. of Speed cm. Per cent. of Speed cm. Per cent. of Speed cm. Per combustible. per sec. combustible. per see. combustible. per see. combustible. h 5.7 1 5.80 6.06 6-28 6.95 7-10 7.47 7-82 8-58 9.12 9.52 9.96 10.32 10.64 11.10 11.63 12-25 12.55 13.09 13.35 13.42 Ball of flame to 15 em. from spark. 23.3 26.2 28.0 35.0 37.0 42.0 47.4 58-0 64-4 66.6 66.2 65.5 63.5 57.0 47.4 35-0 30-5 22.0 19.1 Flame to 5 cm.from spark. 3-16 3.30 3.58 4.47 4.90 5.57 6.08 6-53 7.07 7.38 7.70 8.23 9.00 9.50 10.09 10-60 10.71 Flare of flame only. 18.1 26.G 52.7 65.0 80.5 82.5 85.6 81.3 75.7 60.4 45.8 27.7 23- 1 20.8 19.7 Flame to 4 cm. from spark. 2.30 2.37 2-58 2.80 3.50 4.28 4.39 4.7 1 4.84 5.14 5.90 6.58 7.10 7.30 7.35 Flame to 6 cm. from spark. 20.8 26.0 31.4 48.2 72.8 79.1 82-1 80.2 66.0 41.2 30.2 23.0 20.3 Flame to 16 em. from spark COMPLEX QASEOUS MIXTURES. PART 11. 1449 TABLE 11. Speeds of Uniform Movement of Flame in a Glass Tube 2.5 em. in Diameter with Mixtures containing 7.35 per cent. of Methane and 1-98 per cent. of Pentane respectively Mixed Together.Methane mixture. Pentane mixture. Per cent. Per cent. 75-0 25.0 50.0 50.0 25-0 75.0 21.2 78-8 - 100.0 - 100.0 Speed, cm. per sec. 39.3 39.2 39.6 39.9 39.2” 40-1 * Methane and pentane in equimolecular proportions. It will be seen that the speeds are identical within the limits of experimental error. Two mixtures containing excess of combustible gas with speeds further removed from that a t the limits were then examined in the same manner. These mixtures contained 11.00 per cent. of methane and 3-54 per cent. of pentane respectively and the speed of the uniform movement of flame in them was about 60 cm. per second three times the value a t the limits. The results are given in table 111. TABLE 111. Speeds of Uniform Movement of Flame in a Glass Tube 2.5 em.in Diameter with Mixtures containing 11-00 per cent. of Methane and 3-54 per cent. of Pentane respectively Mixed Together. Methane mixture. Pentane mixture. Per cent. Per cent. 100.0 -75.0 25-0 50.0 50-0 25.0 75-0 24-4 76-6 - 100.0 Speed, em. per sec. 59.1 59-1 60.3 59-1 59*1* 59-6 * Methane and pentane in equimolecular proportions. Once more the generalisation is found to hold with great accuracy and there is no doubt that it is true for all mixtures of the paraffins having the same speeds of flame provided that the maximum speed in mixtures of any individual paraffin with air is not too nearly approached. For if the generalisation could be supposed to apply to the ‘ I maximum-speed ” mixtures no mixture of air containing both methane and pentane should propagate th 1450 PAYMAN THE PROPAGATION OF FLAME IN uniform movement of flame a t a speed higher than the maximum speed in mixtures of methane and air.Similarly the generalisa-tion cannot apply to speeds a t the limits in mixtures of methane with atmospheres containing a high proportion of nitrogen for with such atmospheres both upper and lower limits of inflamma-bility lie a t the maximum flattened portion of the speed-per-centage curve. Bearing these limitations in mind it should be possible to calcu-late the values for the speed-percentage curve for any combination of the paraffins in air. An equimolecular mixture of methane and FIG. 2. CALCULATED VALUES:-3CsH,=+ 2Hz. . _ . ..___.... ._ ..& C5 H,2 + CH+ . . . . . .,. .... . ., . ... 3 4 5 G 7 8 9 Combustible gas per cent. pentane (which corresponds with propane) was chosen t o test the accuracy of such calculations. The results are recorded in table IV and are compared with the calculated values in Fig. 2. I n no instance was the difference between observed and calculated speeds greater than 1 cm. per second. The highest speed for which calculation was made was 60 cm. per second. It must be admitted that the gases chosen for these experiments are particularly f avourable towards the calculation since the maxi-mum speed of the uniform movement is nearly the same with each gas. As a more stringent test a mixture of pentane and hydrogen was prepared (3C,H1 + 2H2 carrespading with propam) end COMPLEX GASEOUS MIXTURES.PART 11. 1451 (a) CR4 + C6HW 7-Combustible gas. Speed, Per cent. cm. per sec. 2.55 6 cm. travel only 2.65 22.3 3.12 39.2 3.54 53.7 4-04 70.7 4-52 78-3 5.05 73.6 5.36 59.1 6-23 37-5 7-03 25.4 7-70 20.7 7.79 3 cm. travel only series of speed determinations and calculations made as before. I n this instance the maximum speeds of uniform movement in mix-tures of the individual gases with air differ widely being 82 cm. per second for pentane and 485 cm. per second for hydrogen. The results are recorded in table IV and in Fig. 2 are compared with those calculated. ( b ) 3C,H12 + 2%. /- -7 Combustible gas. Speed, Per cent. cm. per sec. 2-35 Cap only 2.47 19.7 3.02 43.3 3.56 67.7 4-03 82-7 4.48 89.5 4.91 83.7 5.77 54.0 6.25 43.6 7.10 27.9 7-80 23.1 8-60 21-5 8-72 15 cm.travel TABLE IV. The results are not in as good agreement with calculation as those obtained with the combination of methane and pentane but, even so the agreement is remarkably close considering the wide difference between the individual maximum speeds of flames. The greatest difference between observed and calculated results is only 4 cm. per second. The highest speed for which calculation was made was 60 cm. per second which is rather close to the maximum speed for pentane. It will no doubt be apparent that a limit is a t present set to the scope of the generalisation because only the speeds of flames in mixtures with air are available for purposes of calculation.When i t is remembered that the gas with the slower maximum speed of uniform movement of flame may have that maximum greatly enhanced if an atmosphere richer in oxygen than air is used it is clear that the generalisation should be capable of further extension, given the necessary experimental data. The consideration of this subject is reserved for a later paper. It now remains to deduce a method for calculating the maximum speed of the uniform movement of flame in a mixture of air with a mixture of inflammable gases and also for calculating the co 1452 PAYMAN THE PROPAGATION OF FLAME IN position of the mixture which will have this maximum speed of flame. The latter may be calculated by the method suggested in a previous communication (Payman and Wheeler this vol.p. 36), in which it was shown that if “maximum-speed” mixtures were mixed together the result would be the ‘‘ maximum-speed ” mixture for the mixed inflammable gases. For example the value for the maximum speed of uniform movement of flame for hydrogen is 38-5 per cent. for pentane 2.9 per cent. and for methane 9.9 per cent.* ‘The calculated value for the equimolecular methane-pentane mixture is 4.48 per cent. and for the pentane-hydrogen mixture (3C,HI2 + 2H,) 4.60 per cent. The value found is the same for both mixtures namely 4.55 per cent. It is interesting to note that the same value is found for propane with which these mixed inflammable gases correspond. ‘It was also suggested from a consideration of the results obtained with mixtures of air with an equimolecular mixture of methane and hydrogen that the gas for which the maximum speed of flame was the lower had the predominating effect in determining what would be the maximum speed with mixed inflammable gases.This is true for mixtures of methane and hydrogen but in general it is the gas requiring most air to attain the maximum speed of flame which is the deciding factor. This is indeed what one would expect from a consideration of the generalisation concerning the speeds in mixed gases. The larger the volume of air a combustible gas requires to produce its “ maximum-speed mixture,” the smaller is the percentage of that combustible gas in the f astest-speed mixture of air with a mixture of gases that contain it. A method for calculating approximately the maximum speed of the uniform movement of flame in mixtures of air with a mixed inflammable gas from the known values for its simple constituents, may be given from a consideration of this fact.The assumption is made that when “ maximum-speed ” mixtures are mixed together, the resulting speed is proportional to the amount of each mixture present and to the respective maximum speeds of their flames. This relationship which holds roughly for mixtures with air may be expressed as follows : aS,+bSb+cS,+ . . . . a+b+c . . . . S = 1 where S is the speed required; a b c . . . are the amounts present of each maximum-speed mixture with air; S, Sb S, . . . are the speeds of flame in those mixtures respectively. The use of the formula will be best explained by an actual * In each instance the figure given is the mean percentage over a range of mixtures having nearly the same speed COMPLEX UASEOUS MIXTURES.PART II. 1453 calculation of the maximum speed of flame for the equimolecular mixture of methane and pentane in admixture with air. The calculated value for the mixture to have the maximum speed of flame is 4.5 per cent. and this mixture will contain 2.25 per cent. each of methane and pentane. I n the maximum-speed mix-ture of pentane and air 100 parts of the mixture contain 2.9 parts of pentane and therefore 2.25 parts of pentane correspond with 2?? x 100 = 77 parts of pentane-air mixture. 2.9 Similarly 2-25 parts of methane correspond with 23 parts of methane-air mixture since the maximum-speed mixture of methane and air contains 9.9 per cent. of methane. Substituting these values in the above formula, (77 x 82) + (23 x 67) 100 s = = 78-5 cm. per second. The value found was 79 cm. per second showing an extremely close agreement. The agreement is not so good with the pentane-hydrogen mix-ture (3C,Rl2 + 2H2) the calculated value being 100 cm. per second and the speed found 90 cm. per second. The discrepancy does not appear so great however when it is remembered that there is a difference of 400 cm. per second between the maximum speeds of the flames in mixtures of pentane and air and hydrogen and air. The maximum speed of flame with mixed gases and air may also be found by a graphical method. If on a speed-percentage graph the maxima for any two gases tztken singly is joined by a straight line all the maxima for mixtures of these two gases lie approxim-ately on this line. The composition of the “maximum-speed” mixture is calculated by the method given by Payman and Wheeler (loc. cit.) and the speed then read off from the graph. ESKMEALS, CUWRERLAND. [Received October 1 Otk 19 19.