PARAMETERS OF EMULSION STABILITY 235 Coalescence or Breaking Coalescence, by which is meant irreversible formation of larger oil drops or of a separated bulk oil phase, represents the ultimate destruction of the emulsion. When a colloid chemist speaks of emulsion stability it is resist- ance to this process which he has (or should have) in mind. The rate- determining step in this process might be the rate at which water can drain from between the fiocculated oil drops, the rupture of the adsorbed film of stabilizer surrounding the drops, the rate at which desorbed emulsifier can diffuse away from the interface where coalescence is occurring, or the effect of electrostatic attractions and repulsions on the rate at which drops come into actual contact. Much of the current theoretical research on emul- sions is directed toward trying to differentiate among these alternative pos- sibilities. The hydrodynamic problems involved in the rate of approach of drops toward a plane interface or toward each other have been studied exten- sively by Mason (9, 10) and are also involved in the studies of the rate of thinning of soap films by Mysels and Overbeek (11, 12). The equations derived suggest that, as the radius of the drops becomes smaller, the rate of approach under a given driving force should become greater, i.e., the water between the drops should be squeezed out more rapidly, thus causing them to come in contact sooner. Alternatively, the slow step in the process may be the rate at which the adsorbed stabilizer surrounding the drops is displaced, enabling coalescence to occur. This will depend primarily on the mechanical properties--sur- face viscosity and surface yield value--of the interfacial film. Since rup- ture of the film involves an initial increase in area, it may be that a higher interfacial tension may be desirable for stability even though this might make initial emulsification difficult. The role of zeta potential, with its effect on electrostatic interactions, is still somewhat controversial with respect to the coalescence process. While it is necessarily important in a consideration of fiocculation, it may well be that it has only a minor effect on the rate of coalescence. Interpretation of these mechanisms in terms of molecular explanations is of both great theoretical interest and distinct practical importance with re- spect to suggesting possible ways of increasing or decreasing the stability of a given system. Orientation of molecules in adsorbed films, closeness of molecular packing, the cohesive forces between the molecules in the film, and electrostatic repulsions between the charged head groups of the ad- sorbed molecules will have an effect not only on surface viscosity and sur- face yield value but also on the electrical interactions. The magnitude of the repulsive force, calculable from, the theory of the electrical double layer, will be greatly affected by the addition of indifferent electrolytes, or even by

236 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS increasing the concentration of an ionizable stabilizing agent. Since most emulsifying agents are association colloids, it becomes important to deter- mine whether it is the monomer or the micelle that is effective in stabiliza- tion and to recognize in the case of colloidal electrolytes that the critical micelle concentration (cmc) sets an upper limit to the attainable concen- tration of monomer ion. Moreover, this limiting value is greatly decreased by addition of simple salts which lower the cmc. Changes in the volume ratio of oil to water may well modify the relative importance of the preceding variables. METHODS FOR THE MEASUREMENT OF STABILITY' What is most needed for further progress in the field of emulsion tech- nology is development of a sufficiently detailed theory of stability which could give a mathematical prediction of a rate or an equilibrium quantity, together with an experimental method which truly measures the quantity which is predicted. None of the currently available methods is genuinely satisfactory (5). Change of total interfacial area with time is generally in- sufficiently sensitive. Determination of the change of drop-size distribu- tion with time is a very tedious experiment, although the recent introduc- tion of the Coulter counter greatly increases its feasibility. Moreover, different systems appear to behave differently, since in some the size distri- bution changes reproducibly (13) while in other cases (5) there is little or no change with time. In any event, the ultimate criterion of instability is the appearance of free oil, and there is no clear proof that this is greatly de- pendent on the drop size distribution within the emulsion. Centrifugal methods for direct measurement of the rate of separation of free oil are generally too slow with all except relatively mobile liquids, and with the latter are frequently beset with difficulties, due to deformation of the liquid-liquid boundary on stopping the centrifuge. Rheological methods may be of considerable empirical value but are of limited use in understand- ing the nature of the processes occurring, because of the dependence of the theological properties on a large number of other factors in addition to the stability of the emulsion. Use of the ultracentrifuge for evaluation of stability has the advantage that the rate of appearance of demulsified oil is measured directly rather than some other property which it is hoped will be proportional to it. It results in a qum'•titative characterization of a stability attribute of the emulsion within a precision of 3 to 5%. Finally, it offers the advantage of speed, since it is possible to complete the preparation, measurements and calculations within two days. There are, however, some serious disadvantages as well. It is not cer- tain that it can be used effectively with very viscous systems or very stable emulsions. The equipment involved is relatively expensive and the tech-