Substances mix with like substances is the rule of thumb for solutions. Water is composed of polar molecules, meaning they have a non-uniform electron distribution, and oil is made of non-polar molecules, or the electrons are distributed uniformly between different atoms. Non-polar substances are (generally) hydrophobic, meaning they do not dissolve in water naturally. If you add a surfactant, like a detergent, however, the oil will blend with the detergent-water mixture.
You will never truly mix oil and water but you can get them to break up into smaller sections of oil in water by emulsifying them. I work with a colleague who routinely makes oil in water emulsions for her research and for this purpose we have a homogenizer which will mix the two liquids together and the resulting liquid will look as if it is one phase. If it is left long enough, however, the water will separate from the oil.
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