Microemulsions, Macroemulsions, and the Bancroft Rule

In most cases, in both micro- and macroemulsions, the phase in which the surfactant is most soluble constitutes the continuous phase. There are, however, violations to this Bancroft rule, and the goal of the paper is to delineate the conditions of validity of the rule. For microemulsions two ratios are significant from this point of view. One of them, R1, compares the interactions in the bulk between surfactant and oil to those between surfactant and water; the other, R2, compares the interactions between the hydrocarbon chains of the surfactant in the interfacial layer and oil to those between the head groups of the surfactant molecules in the interfacial layer and water. Ratio R1 indicates the preferred phase, while ratio R2 indicates the preferred curvature. When both ratios are smaller or larger than unity, the Bancroft rule is obeyed. When one of them is smaller and the other larger than unity, the Bancroft rule is violated. The violations observed by Binks regarding the phase behavior of the ternary mixture C12E5 (a nonionic surfactant of the polyoxyethylene glycol ether type)/water/heptane can be thus explained. For macroemulsions, three regimes are identified. At low surfactant concentrations, the type of emulsion is controlled by the mixing process, at sufficiently high concentrations by the mass transfer (case in which the Bancroft rule is obeyed), and at even higher concentrations by hole nucleation in black films. The violations of the Bancroft rule noted by Binks are in the mixing controlled regime.