PRODUCT STABILITY--PART II 315 studied the physical degradation of emulsions via molecular diffusion, i.e., not contact-caused coalescence but a no-contact process in which one droplet grows while another dissolves. The process which predominates could be determined by whether forces exist which hold the droplets apart (latter) or by whether there is a very low degree of solubility of internal phase in the external phase (former). Although no quantitative predictive technique was realized, Tober and Autian (21) pointed out that a straight-line relationship existed when time to reach 10% v/v sedimentation was plotted against the relative centrifugal force applied to an emulsion. This force is a function of the square of the revolutions per minute and the rotating radius. Stress of the formulation followed by such measurements might lead to predictive techniques. Singleton and co-workers (22) were interested in making emulsions which would be stable to the heat of the sterilizing autoclave. They did not plot their data kinetically but did describe two of the stresses they used. One was steam autoclaving for 20 minutes at 121 øC if the par- ticle size became greater than 7u, the formula was considered unstable. The other was a mechanical shock treatment in which 50 ml. of emulsion in a 100 ml. bottle was shaken horizontally 250 times per minute. Sim- ilarly, the emulsion was considered unstable if the particle sizes were greater than 7u in less than one hour of shaking. Harrison and James (23) in a study of O/W emulsions showed the existence of relationships between the electrical resistance and the con- centration of the dispersed phase. Although they did not use their data kinetically in a stability study, it is obvious that this might be done. King and Mukherjee (24, 25), in an attempt to create a quantitative criterion of emulsion stability, defined the stability coefficient of an emul- sion as the reciprocal of the rate of change of the interfacial area per unit area of existing emulsion interface. They also obtained curves of inter- est by plotting either the per cent of total number of droplets or the per cent of total oil volume against droplet diameter. They observed that, although the maximum number of droplets are of a certain size, the great- est volume of oil is in drops of a different diameter. These investigators also plotted specific interfacial area rs. time. The slopes, although they observed changes such that they used the early and steeper slopes, were equated to rates of decrease of area per unit area of interface. The latter quantity is known, and the rate of decrease could then be used to compare emulsions. Incidentally, one other parameter they suggested was a half-break time, or the time it takes to reach half of the initial

316 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS specific area. The change in slopes mentioned, due to two rates of coalescence, an early fast one and a later slower one, indicated the exist- ence of an exponential relationship. Levius and Drommond (26) also illustrated the heat stressing of emulsions after which the usual methods of size frequency analyses and calculations of interfacial areas were ap- plied. In our discussion of size and interfacial area relationships, it aids perspective and is interesting to note that Ross (27), in a discussion of emulsions, pointed out that 2-• droplets have a surface area of about 30,000 cm.2/cc. whereas 3-• droplets have an area of 20,000 cm.S/cc. Higuchi, Okada, and Lemberger (28) studied O/W emulsions in which the droplets were about 1• and the system relativdy monodis- persed. They use a Coulter counter to determine the distribution of the various sizes of droplet aggregates. Thus, they were able both to count and size the aggregates as a function of time. They developed a method which quantitatively studied aggregation directly so that the aggrega- tion would not have to be deduced from creaming or sedimentation rates. Hence, emulsions could be stored and the size distribution after various times be determined the distribution could indicate if larger aggregates are being formed. This would be a warning as larger aggre- gates would indicate an increased chance of coalescence in emulsions or caking in suspensions. Of interest is the early paper of Berkman (29) who studied emulsion stability by a size distribution method utilizing a projection microscope to measure globule size 1500 to 2000 measurements were made per curve. She found that changes in distribution were related to time and that the pattern of progression was followed and agreed with data taken on emulsions five years old. Lotzkar and Maclay (30) obtained interfacial areas by a size fre- quency analysis employing photomicrographs. They were able to plot the log of the specific surface area of the dispersed phase rs. time and obtained straight line plots. They noted that the degree of dispersion and the initial viscosity (although viscosity will hinder creaming) did not always increase stability. Mullins and Becker (31, 32) investigated factors influencing the stability of O/W emulsions using high pressure homogenization. They also studied the feasibility of adjusting the density of the phases by the addition of brominated oils and the possibility of making the internal phase thixotropic by adding wax. They used a size-frequency method of analysis and showed that specific interfacial area increases with increased