Drop Size of Aerosols in Flame Spectrophotometry JOHN A. DEAN and WILLIAM J. CARNES Department of Chemistry, University of Tennessee, Knoxville, lenn.
b The drop-size distributions in aerosols injected into a flame from an integral-aspirator burner were determined. For this study, water, chloroform, and 4-methyl pentan-2-one were selected. Measurement of drop sizes was done b y the microscopic method and was based on the impact impression from the aerosol spray which was left on a slide that had been coated with magnesium oxide. Histograms are given of number frequency vs. nominal size for the three aerosols. By means of the upper-limit function, a variant of the log-normal distribution function, the size distribution parameters were determined. Three mean diameters were calculated for the solvents: the volume (mass) diameter, the volume surface (Sauter) diameter, and the geometric diameter. The significance of the drop-size distributions is discussed in relation to the time available for evaporation of the solvent and excitation of metal salts in the flame.
M
of introducing samples into the flame have been summarked b y hhvrodineanu and Boiteux (4). Of these, only gas stream, or pneumatic, atomization is generally employed in flame spectrophotometry because an aerosol, by its gaseous nature, can be intermingled with the fuel components and uniformly distributed throughout the body of the flame. However, the atomization process produces a range of drop sizes in the aerosol. Moreover, Smit, Alkemade, and Verschure (11) have demonstrated that the substitution of an organic solvent for water will increase the amount of small diameter drops in a n aerosol spray. Consequently, it seemed desirable to ascertain the dropsize distributions in some of the aerosols which are commonly injected into a flame when using a n integral aspirator burner. For this study, water, chloroform, and 4-methyl pentan-2-one were selected.
4-METHYLPENTAN-2-ONE
EXPERIMENTAL
T h e drop diameters were measured with a Bausch & Lomb Type M chemical microscope and accessories. T h e filar micrometer was calibrated against a standard ANALYTICAL CHEMISTRY
CHLOROFORM
60 50 c 4
,”
40
y.
0
5
30
V w
5
20
e 10 0 D I A M E T E R OF DROPS, m i c r o n s
Figure 1.
Representation of drop-size distribution A Beckman integral-aspirator was used
stage micrometer. T h e atomizer was a Beckman Model 4030 integralaspirator burner. Reagents. Chloroform, U.S.P. grade. Phlethyl pentan-2-one, practical grade. Demineralized water was prepared by passing distilled water through Amberlite MB-3 resin.
ETHODS
Apparatus.
192
WATER
Drop Size Measurement. The measurement of drop size in a n aerosol spray involves t h e statistical distribution of numerous size classes. Therefore, i t is necessary t o obtain a true representation of all size classifications and t o tabulate accurately the frequency of occurrence of a size group. Pilcher (9) has given an escellent review of the handicaps and meLhods of measuring drop sizes. Over 40 different methods can be classified under six main classes: microscopic methods, frozen droplet methods, photographic methods, optical methods, electronic methods, and cascade impactors. The microscopic method is the most general and requires the minimum of equipment. It seemed adequate for our purpose. The impact of a droplet upon a glass slide which has been coated with magnesium oxide from a ribbon of burning magnesium leaves a well defined hole which corresponds to the diameter of the droplet and n-hich can be observed through a microscope under strong transmitted light (6). For a large range of sizes and for a wide range of liquids and impact velocities, the ratio of true drop size to
impression size is constant and equal to 0.86 (6). Although a criticism of the method arises from the fact that smaller droplets may tend to follow the air (or oxygen) flow around the slide and not be collected, M a y (6) noted that droplets as small as 5 microns in diameter could leave an impression at sufficiently high impact velocities. I n this study droplet diameters less than 10 microns were observed. Droplet diameters were grouped together in size groups about a nominal size, 2: (h5 microns), and tabulated at intervals of 10 microns over the range of sizes from 0 to 70 microns. The lack of a better counting method precluded a narrower range of nominal size classifications. Histograms of number frequency us. nominal size for the three aerosols are shown in Figure 1. A Gaussian distribution is not precisely indicated; indeed i t is rare for a nominal size distribution to distribute equally about the Gaussian curve ( 1 ) . The drop-size distribution is distinctly different for each aerosol; both organic aerosols exhibit a larger number of the smaller drop sizes as compared to a water aerosol. The volume of drops in each size group was calculated assuming spherical geometry nhich is generally valid for fully developed sprays (Table I). Also tabulated are the cumulative volume and cumulative volume fraction for each size group. The uncertainty in measuring the droplet diameters was about i15%; consequently, the impression diameters were considered to be the true drop diameters essentially.
DISCUSSION
Drop-Size Distribution. T h e mechanism of atomization is y e t b u t little understood. As a result there is no theoretically sound method of predicting t h e distribution of drop sizes. Various statistical treatments have been developed for particular types of sprays; these have been critically reviewed b y Mugele and Evans ( 7 ) . I n general, representation of the drop-size distribution involves a distribution function with trvo evaluable parameters, the mean diameter and a n index of precision. The selection of a particular distribution function is governed largely b y the mathematical simplicity and ease of computation. The upper-limit function proved satisfactory for the representation of the observed droplet diameters. I n the upper-limit function, a variant of thp log-normal distribution function, Mugele and Evans ( 7 ) introduced a third constant, z,, a mayimum drop diameter. To them such an upper limit was more realistic than the concept of a n infinitely large drop of infinitely small probability of occurrence. Following their treatment of the data, the logarithm of the distribution function, z/(zm-z), is plotted us. the cwmulative volume fraction on a probability scale. The best value of 2 , was obtained b y a trial-and-error method of curve fitting. The size distribution parameter, 6, was determined from the slope of the curve. The parameter can be associated with the index of precision of the distribution. Large values of 6 imply that the distribution decreases very rapidly from its maximum value, R hile the inverse is true for small values of 6 (Table 11). Three mean diameters mere calculated for the solvents and are shown in Table 11. The volume (mass) diameter, 331, predicts a n order of decreasing diameter: water > chloroform > 4-methyl pentan-2-one. The volume surface (Sauter) mean diameter, 2a2, and the geometric mean diameter, fsa or 50th percentile, place the order as water > 4-methyl pentan-2-one > chloroform. The Sauter mean diameter, which is commonly employed to represent droplet size, can be visualized as the diameter obtained b y dividing the volume of a particle b y its surface area. The volume (mass) diameter is the diameter of a sphere which has the same density and volume (or mass) as the particle. The mean diameters obtained in this study can be compared with those reported by Nukiyama and Tanasawa ( 8 ) for a series of aqueous-methanol aerosols. Although an entirely different type of atomizer was used, the following Sauter mean diameters were reported: water, 26.5 microns; water
Table 1.
Sominal Size Group, x, in Alicrons 5
15 25 35 45 55
65 5 15 25
35 45 55
65 5 15
25 35 45 55
Frequency 154 209 111 23
15 7
6
295 165 40 5
8 3
3
189 220 81
17 11
3
Representation of Drop-Size Distribution
Volume of Drops, (Microns)3 Water i o x 103 370
910
Cumulative Volume, micron^)^
io x
103
380 1290
1810 2530 3140
520 720
610 4000 860 4-Methyl pentan-2-one 19 x 103 19 x 103 292 311 328 639 112
382 262 430 Chloroforni 11 x 103 390 660 380 525 260
plus 10% methanol, 24.9 microns; and water plus 50y0methanol, 15.9 microns. It would appear that comparable drop sizes can be obtained with aqueousorganic solvent mixtures. However, the cooling effect of water upon the flame temperature of oxygen-fuel flames detracts from the usefulness of aqueous mixtures as compared with nonaqueous solvents. Evaporation Process. T h e determination of evaporation rates of suspended droplets in fast moving air streams still remains conjectural. T h e added variable of t h e solvent's combustibility further complicates t h e process of evaporation. Nevertheless the atomization a n d evaporation of the aerosol in t h e flame from a n integral-aspirator burner do suggest certain restrictions upon the conditions which lead to excitation in the flame. The spray is injected directly into the highly energetic reaction zone of the flame. For the distance of 3 to 4 mm. between the top of the solution capillary and the flame front, the aerosol has certainly a minimum amount of time in which to become a fully developed spray. It is possible that the full droplet size distribution is never attained before the effects of the high-temperature combustion atmosphere are felt. The time required for the complete evaporation of a droplet has been related to the square of the initial drop radius ( 2 ) . For all practical purposes the time allowed for evaporation which leads ultimately to useful excitation in the flame is the same for any solvent system. Consequently, the droplet
751
1130 1390
Cumulative Volume Fraction 0,0025 0.095 0.32 0.45
0.63 0.78 1.oo
0.011 0.17 0.35 0.41
0.62 0.76
1820
1.oo
11 x 103 401 1060 1440 19TO 2230
0 005
0.18 0.48 0.63 0.88 1 .oo
Table II. Drop-Size Mean Diameters and Size Distribution Parameter
(Mean diameters are expressed in microns) -4erosol 231 fJ2 ?iQa 6 Water 19 6 27 5 37 0.81) 4-Methyl pentan-2-one 16.7 23 4 33 0.98 Chloroform 17.6 2 1 . 1 27 0.78
diameter will be a determining factor in the over-all flame excitation. That a particular solvent happens to be conibustible will not hasten materially the evaporation process except, perhaps, to provide a n additional source of heat to the evaporating droplets. I n fact, theories of droplet combust,ion recognize the fact that evaporation rates have a controlling influence upon combustion rates of fuel droplets ( 3 ) . Probert (10) has concluded that high initial rates of evaporation are favored by small mean diameters and a large size dist,ribution parameter. Since the reaction zone of a flame is rather thin and the time available for evaporation and excitation is short, it is reasonable to assume that only bhe smaller droplets m-ill be evaporated alld the salt content of the droplet excited in the time available. hlthough intermediate sized drops may be evaporated completely in the interconal region of a flame, which is located immediately above the reaction zone, the conditions for excitation are less favorable. The largest droplets may be swept t'hrough and out of the flame before evaporation is completed. This phenomenon has VOL. 34, NO. 2, FEBRUARY 1962
193
been observed with water droplets on numerous occasions. Wolfhard and Parker (1.2) showed that small organic droplets (diameters less than 20 microns) evaporated with sufficient rapidity so that the fine mist or vapor which resulted possessed essentially the combustion characteristics of a completely vaporized fuel. For the three solvents, droplets with a diameter less than 20 microns constituted these nuniber percentages: 4-methyl pentan-2-one, 89%; chloroform, 78%; and water, 69%. Since the amount of atomic and molecular excitation in the flame is dependent upon the number of droplets reaching the reaction zone and completely vaporizing before entering that energetic region, i t would be expected that an aerosol which contained a greater number of small diameter
droplets will provide a higher number of excitable species in the flame. This has been borne out in practice and has given rise to the widespread use of organic solvents, particularly 4-methyl pentan-a-one, in flame spectrophotometry. LITERATURE CITED
(1) Green, H. L., Lane, IT. R., “Partic-
ulate Clouds: Dusts, Smokes and Mists,” Van Nostrand, London, 1957. (2) Gudkov-Belyakov, V. K., Dizelestroenie 7, 10 (1940); C.A. 37, 4548 (1943). (3) Lewis, B., Pease, R . S . , Taylor, H. S., “Combustion Processes,” F’ol. 11, Princeton UniverFity Preps, Princeton, N. J., 1956. (4) Mavrodinennu, R . , Boiteux, H., “L’Analyse Spectrale Quantitative par la Flamme,” Masson et Cie, Paris, 1954.
(5) May, K. R., J. ,Sa. Instr. 2 2 , 187 (1945). (6) lbid., 27, 128 (1950). (7) Mugele, R. A., Evans, H. D., Ind. Eng.Chem.43,1317(1951). (8) Nukiyama, S., Tanasawa, Y., T r a n s . SOC. Mech. Engrs. ( J a p a n ) 5 , (18) 68 (1939). (9) Pilcher, J. &I., U. S. Air Force WADC TR 56-344,Chap. 4, Section I, (March 1957). (10) Probert, R. P., Phil. M u g . 37, 94 ( 1946). (11) Smit, J. A., Alkemade, C. Th. J., Verschure, J. C. M., Biochim. et Biaphys. Acta 6, 508 (1951). (12) Wolfhard, H. G., Parker, W. G., J.Inst. Petrol. 35, 118 (1949). RECEIVEDfor review March 20, 1961. Accepted Piovember 30, 1961. Taken from a portion of a dissertation submitted by William J. Carnes t o the Graduate School of The University of Tennessee in partial fullfilment of the requirements for the degree of Doctor of Philosophy, December 1961. Eastern Analytical Symposium, Xew York, November 1960.
Determination of Hydroxyl Number of Polyoxyalkylene Ethers by Acid -Cata Iyzed Acetylation R. S. STETZLER and C. F. SMULLIN Atlas Chemical Industries, Inc., Wilmington, Del. ,An acid-catalyzed acetylation method applicable to the determination of hydroxyl values of polyethers is described. p-Toluenesulfonic acid is used as the catalyst and acetic anhydride in ethyl acetate as the acetylating reagent. The method is rapid and requires no special apparatus. Precision and accuracy are better than obtained b y previous acetylation methods.
P
oxide adducts of sorbitol have recently gained widespread use in the manufacture of rigid urethane foams. The physical properties of these foams vary widely, depending upon the ratio of h ~ d r o u y lto isocyanate. I t is therefore important to have a rapid, simple, and reliable analytical method to determine the hydroxyl content of thew polyethers. The methods most commonly used for the determination of hydroxyl groups involve acetylation using acetic anhydride in pyridine, phthalation using phthalic anhydride in pyridine, and determination of actire hydrogen using Grignard reagent. An excellent review of the pertinent literature on these methods through 1952 is given by Mehlenbacher (4). Burns and Nuraca (1) used infrared spectroscopy to determine the hydroxyl concentration in polypropylene glycols. The use of perOLYPROPYLENE
194
ANALYTICAL CHEMISTRY
chloric acid to catalyze the acetylation of organic hydroxyl groups with acetic anhydride in ethyl acetate has been reported by Fritz and Schenk ( 3 ) . The same authors (3) mention briefly the possible use of p-toluenesulfonic acid, particularly for reactions carried out at elevated temperatures. Recently, Siggia, Hanna, and Culmo ( 5 ) employed pyromellitic dianhydride as the esterifying reagent, using tetrahydrofuran as the solvent. Base-catalyzed acetylation and phthalation reactions are slow, particularly when applied to secondary hydroxyl groups as found in polypropylene glycols and other propylene oxide adducts. Burns (1) found that an acetylation time of about 4 hours is required to acetylate polypropylene glycols quantitatively. The infrared method and the active hydrogen method both have the disadvantage that water interferes in the determination. Therefore, for precise results the sample must be anhydrous or the water content must be measured by a separate technique, usually the Karl Fischer procedure, and the final results corrected. Esterification methods employing perchloric acid as the catalyst are not applicable to polyethers, because of the attack of perchloric acid upon the ether groups ( 2 ) . This was confirmed in this laboratory.
With the present method, the hydroxyl content of polyethers is determined by acetylation in ethyl acetate solution, using p-toluenesulfonic acid to catalyze the reaction. Complete acetylation is obtained in 15 minutes a t 50’ C. The amount of hydroxyl is calculated from the difference between the blank and sample titrations with alcoholic potassium hydroxide. REAGENTS AND SOLUTIONS
2 M Acetic Anhydride in Ethyl Acetate. Add 14.4 grams of reagent grade p-toluenesulfonic acid (CH3C e H 4 S 0 3 H . H z 0 )to 360 ml. of ACS grade ethyl acetate in a clean, dry 500-ml. amber glass reagent bottle. Agitate the mixture with a magnetic stirrer until t h e acid is completely dissolved. Add, slowly, 120 ml. of ACS grade acetic anhydride, maintaining agitation during the addition. A slight yellow color will develop, but the anhydride content of the reagent will remain a t a satisfactory level for several days. 0.56N Potassium Hydroxide. Dissolve 334 grams of reagent grade potassium hydroxide in 2000 ml. of absolute methanol. Cool and filter t o remove precipitated carbonates. Dilute t h e filtrate t o 9000 ml. with absolute methanol. Standardize against primary standard potassium acid phthalate.
