188 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Another property that can be related to the close-packing of uniform spheres is the viscosity of an emulsion. At concentrations below seventy- four per cent the spheres are not in contact and the flow of the emulsion is not impeded by undue interference of the droplets with each other. As more concentrated emulsions are prepared, interference does appear and the resistance to flow becomes more marked. Finally the droplets may be packed so close to one another that flow is seriously impeded this is made manifest by a high viscosity, requiring a large shearing stress to overcome the structure built up by many spheres in contact. Manegold has published (7) a useful diagram, Fig. 1, that represents the dependence of some properties of emulsions on volume concen- tration. This is intended to represent a general summary, and it would be erroneous to rely on it for quantitative predictions of emulsion properties. It depicts a volume concentration (seventy-four per cent in Fig. 1) above which the property of the emulsion either becomes discontinuous (inversion) or continues to increase, with the production of deformed droplets in con- tact. The deformation of the drops from their original spherical shape is produced by packing them closer than seventy-four per cent. This type of emulsion is called "polyhedral-foam type" by Manegold, using an anal- I-- )- 180 o $60 ø :300 ø 0 [•3240 o Z -- r.)r,.) 60 ø '•...//V 0•0 20 40 60 80 I00 PERCENT. BENZENE Figure 2.--The viscosity of two types of emulsion as a function of composition. ogy with the structure of drained foam, and, like such a foam, has a huge structural viscosity. Ostwald called such emulsions "liquid-liquid foams." Emulsions of lower concentrations are called "spherical-foam type" by an analogy with a wet foam (for example, a milk shake before the milk drains down to the bottom of the glass is very fluid by comparison with the drained foam that is left on top after a short time). Measurements of the viscosity of emulsions illustrate this reasoning.

TOWARD EMULSION CONTROL 189 Figure 2 shows the data of Richardson (8) for both o/w and w/o types. The significant factor is the enormous increase in the viscosity of the o/w emulsion at concentrations above about seventy per cent. The other type of emulsion showed evidence of inversion at higher concentrations, with a consequent discontinuity in the observed property. It would be misleading, however, to leave the subject of the viscosity of emulsions with the implication that viscosity depends only on volume con- centration. The nature of the emulsifying agent also plays a large role it is possible to get emulsions of the same materials in the same volume con- centrations that differ hugely depending on the nature of the oil/water interface. The most stable or easily formed emulsions are generally the least viscous, and it may be interpreted as a danger sign about future sta- bility when an emulsifying agent produces an abnormally viscous emulsion. The size of the emulsion drops also has not been mentioned as having an effect on viscosity. At low volume concentrations, the size of the drop actually has little effect but as we appraoch the "polyhedral-foam" type of emulsion a wide distribution of drop sizes makes it possible to include larger volume concentrations before structural viscosity becomes marked. Homogenization of such an emulsion would then result in an increase of viscosity. Another and completely different physical property enables us to follow changes in emulsion composition. The electrical conductivity of an emul- sion is independent of particle size and is affected only slightly by nonionic emulsifying agents it varies chiefly, and in some cases solely, with the emulsion composition. Let us denote the specific electrical conductivity of an emulsion by L, that of the outer phase by L• and of the inner phase by L2. The specific electrical conductivity of the emulsion will depend only on the values of L•, L2, and F, the volume fraction of the inner phase, ac- cording to the following equation, developed originally by Clerk Maxwell (9): 2L• + L2 - 2(L• - L = L• ß 2L• 4- L2 q- (L• -- Le)F which is sometimes written in its equivalent form: L1 -- L L q- 2L• Since this equation specifies the inner phase and the outer phase, it yields two equations for any pair of liquids, one for the o/w type and another for the w/o type of emulsion that they can form between them. For example, if the liquids have values of L that are 2 X 10 -a and 2 X 10 -4 ohm -• cm -•, respectively, then the conductivity of the w/o type (low conductivity) emulsion is: 44-6t 2' Lw/o= 2X 10 -4-- 4-- 3V