THERMODYNAMICS OF SPRAY FORMATION 213 ferred to the air entrained by the spray. Although this is not useful work as surface creation, it is useful in the final application of the spray, and might well mean the difference in a satisfactory product containing larger drops and an unsatisfactory one containing smaller drops. OTHER ATOMIZATION TECHNIQUES Another aspect of energy utilization is consideration of nozzles based on other mechanisms of atomization. The nozzle adopted widely for aerosol production is simple and inexpensive to manufacture, but it pro- duces larger drop sizes than other types. In applications requiring smaller drops without increasing the container pressure, or reduced pressures to obtain drops of the same or smaller sizes, two other techniques could be considered swirl-chamber nozzles and two-phase nozzles. Swirl-chamber nozzles would be similar in construction to the valves now in use, but the liquid should emerge tangentially into a cylindrical chamber containing the discharge orifice at the center of one circular face. The liquid emerges in the form of a hollow cone rather than as a cylin- drical jet. A much greater surface is available immediately, and the breakup distance would be shorter than for straight jets. Such a nozzle produces smaller drops for the same pressure difference across the orifice chamber. The spray pattern would be broad--from 45 to 90 degrees in- cluded angle--and the penetration less. The difference in performance is less for high viscosity liquids, but higher viscosities might be sprayed at a given container pressure. Two-phaze nozzles are modifications of gas-atomizing nozzles. The im- portance of high relative velocity between the liquid and the gas phase is unquestioned, and nozzles delivering all-liquid streams can achieve this high velocity only by increasing the pressure. If a gas can be expanded through an orifice onto the liquid, it can be given high velocities at low pres- sures. A container pressure of 15 psig. can deliver liquid through an orifice at velocities of less than 50 feet per second, but it can deliver gas at veloci- ties of 1000 feet per second. A nozzle design to utilize part of the pro- pellent in the gas phase would thus decrease particle size even more than a swirl-chamber nozzle. A design problem would be the vaporization of enough gas for more than short bursts of product. Vaporization in the con- tainer would require cooling of the entire container contents, and dis- agreeable cooling of the container itself in any continued operation. Vap- orization in the valve alone would cause frosting on the outside and per- haps freezing and malfunctioning of the valve. These difficulties are formidable, but might be surmounted for special applications requiring spray drops smaller than 10 microns, and residual particles correspond- ingly smaller.

214 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS SUMMARY The production of aerosol particulate matter from pressurized con- tainers has been analyzed and discussed according to the four major steps likely to occur: (1) primary atomization by "flash" vaporization and normal jet breakup, (2) secondary atomization by drag action of the air on drops formed in primary atomization, (3) evaporation during steps 1 and 2 and after to produce the residual pavtfid•_and (4) entrainment of surrounding air to develop the final aerosol. Available correlations from the literature have been presented where they might apply, affd'pr6B•t•5•e-5•errre'-•of--,.-•r-ariables predicted. Sec- ondary atomization was discarded as a significant factor. The energy relationships have been discussed, and the possible application of different atomizing techniques outlined. D L = R = 2aU/• R'= DU/•' = $c = n'/D• = U = If = U•/2oa/a a t = ! X0 P, P = (1) (2) (3) (4) (4a) (5) (6) (7) (8) (9) (10) (11) NOMENCLATURE Maximum drop diameter Diffusion coefficient of vapor into air Break up length Reynolds number of jet through orifice Reynolds number of drop with respect to air Schmidt number for vapor into air Jet velocity or drop velocity Weber number Radius of nozzle orifice Time Mass fraction of liquid evaporating by "flashing" from jet Dynamic viscosity of liquid, of air Evaporation rate in still air Density of liquid, of air Surface tension REFERENCES Baron, T., "Atomization of Liquid Jets and Droplets," Univ. Ill. Tech. Report 4 (Feb- ruary 15, 1949). Fr6ssling, N., "Uber die Verdunstung fallender Tropfen," Gerlands Beitr. Geophy •., 52, 170 (1938). Geist, J. M., York, J. L., and Brown, G. G., "Electronic Spray Analyzer for Electrically Conducting Particles," Incl. Eng. Chem., 43, 1371 (1951). Holroyd, H. B., "On the Atomization of Liquid Jets," J. Franklin Inst., 215, 93 (1933). Littaye, Guy, "Sur une Theorie de la Pulverisation des Jets Liquides," Comptes Ren- dus, 217, 217 (1943). Miesse, C. C., "Correlation of Experimental Data on the Disintegration of Liquid Jets," Incl. Eng. Chem., 47, 1690 (1955). Perry, J. H., (Ed.) "Chemical Engineers' Handbook," 3rd edition, New York, McGraw- Hill Company (1950), p. 259. Probert, R. P., "Influence of Spray Particle Size and Distribution on the Combustion of Oil Droplets," Phil. Mag., 37, 94 (1936). Rayleigh, Lord, "On the Instability of Jets," Proc. London Math. Soc., 10, 4 (1878). Reed, F. T., "The Propellent in Aerosol Products," J. Soc. COSMETro CHEM., 7, 137 (1956). Root, M. J., "Formulating for Pressure," J. Soc. CosM•TXC CHUM., 7, 149 (1956). Weber, C., "Zum Zerfall eines Flfissigkeitsstrahles," Z. angew. Math. u. Mech., 11, 136 (1931).