THERMODYNAMICS OF SPRAY FORMATION 209 SECONDARY ATOMIZATION The second stage in the sequence outlined for producing an aerosol is the breakup of drops formed during primary atomization into smaller drops. This stage is the least understood of all, and is the most difficult to investigate. Breakup of a mass torn from the original jet depends upon the drag forces acting upon it, which in turn depends upon the size and shape of the mass, oscillations resulting from the way it was separated from the main jet, and the drag forces, the physical properties and the relative velocity of the mass and surrounding air. As indicated above, Baron's general relation is able to correlate sec- ondary atomization as it affects breakup length, but no correlation for maxi- mum drop size has included secondary atomization. By examining the factors which tend to cause secondary atomization some predictions of the direction of change have been made. Increasing the nozzle diameter, the jet velocity and the liquid density, and decreasing the surface tension all increase the tendency toward secondary atomization. All of these except increasing the nozzle diameter also tend to decrease the maximum drop diameter, thus they tend to reduce the final drop size. The effect of increasing the viscosity is still debatable, with conflicting opinions and insufficient data. The effect of high evaporation rates upon the drag forces and therefore upon the secondary atomization is not yet clear. Conflicting evidence indicates that evaporation may raise the drag force several fold or reduce it several fold. It is established that the drag force on decelerating drops of irregular shape is significantly higher than for spheres in steady motion. The best that can be brought out at this date is a criterion as to whether secondary atomization will occur or not. The most successful of these appears to be Littaye's (4a): (O•/:O) '•/V = constant Miesse (5) was able to apply this successfully to his sprays of water and liquid nitrogen through different types of orifices, determining the value of (pl/2)l/2k// to be about 6.3. Above this, secondary atomization is important below it, primary atomization predominates. The effect of "flashing" is unknown, but it probably lowers the constant somewhat. In any case, aerosol dispensers probably do not operate in the range of secondary atomization. Coalescence is frequently mentioned in the literature as altering the drop size distribution after primary atomization, but the latest evidence indicates that it rarely occurs without powerful external influences. At lower relative velocities drops simply bounce off each other with elastic rebound. This may be caused by a persistent air layer between the liquid surfaces, or by concentration of solutes at the surfaces. At high relative

210 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS velocities the contact appears to enhance shattering rather than com- bining. A narrow velocity range may exist in which some coalescence occurs, but it is statistically a small factor in affecting the size distribution. The imposition of strong oscillatory forces, such as sonic or ultrasonic standing waves or pressure oscillations in a combustion chamber, will segregate the drops into alternating zones of low and high population and varying residence times. Under these conditions coalescence is noted as a significant factor. EVAPORATION The last step in transformation of the liquid into the final particles is the evaporation of the propellent and other liquids present to the solid or liquid suspension desired. Obviously evaporation has been occurring throughout the atomization stage, and has had its effect upon them. Some cosmetic products may lose most of the propellent before atomiza- tion ceases, counting the 15 to 20 per cent "flashing" and the amount vaporizing during atomization. A large amount of experimental evidence on many different liquids indicates that large drops exposed to a constant relative velocity of air shrink at a rate corresponding to a linear relation of the surface area and time. Many different investigators have confirmed Fr6ssling's (2) cor- relation for pure liquids: d(D •.) - X0 (1 -- 0.276 (Sc)1/3 (Rt)•/,) dt The Schmidt number includes the diffusion coefficient of the vapor, which is difficult to evaluate and which is probably influenced by the relative velocity and the proximity of other drops. Probert (7) indicates that drops smaller than 50 microns probably evaporate at such a rate that the diameter shrinks linearly with time. It is not illogical to expect this shift as the drops decrease in size, but valid data are not available to confirm or deny it. Most of the aerosol products are not pure liquids, and many contain suspended solids, raising the question of applicability of relations for evaporation of pure liquids. Much qualitative information is available on evaporation of sprays of solutions, suspensions and drops changing in phase. The bulk of this is in the field of spray drying, to which this stage of the aerosol process is similar, if not identical. The influence of solid crystallization, for example, is frequently encountered in spray drying. Basically, the evaporating drop changes in temperature to the equilibrium temperature, remains there until evaporation is complete and then ap- proaches the ambient temperature. For most aerosols, this means cooling to the equilibrium temperature for the propellent, remaining there until the