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It was named after Wilder Dwight Bancroft, an American physical chemist.
In all of the typical emulsions, there are tiny particles (discrete phase) suspended in a liquid (continuous phase). In an oil-in-water emulsion, oil is the discrete phase, while water is the continuous phase.
What the Bancroft rule states is that contrary to common sense, what makes an emulsion oil-in-water or water-in-oil is not the relative percentages of oil or water, but which phase the emulsifier is more soluble in. So even though there may be a formula that's 60% oil and 40% water, if the emulsifier chosen is more soluble in water, it will create an oil-in-water system.
There are some exceptions to Bancroft's rule, but it's a very useful rule of thumb for most systems.
- In Oil in Water emulsions – use emulsifying agents that are more soluble in water than in oil (High HLB surfactants).
- In Water in Oil emulsions – use emulsifying agents that are more soluble in oil than in water (Low HLB surfactants).
Bancroft's rule suggests that the type of emulsion is dictated by the emulsifier and that the emulsifier should be soluble in the continuous phase. This empirical observation can be rationalised by considering the interfacial tension at the oil-surfactant and water-surfactant interfaces.