Soap is whats called a surfactant, the issue with water is its only able to wash off whats water soluble (hydrophilic), there are things like oils that are not water soluble (hydrophobic). Surfactants are chemicals that have a side that is water soluble and another that isn’t, the side that isn’t water soluble is able to stick better to non water soluble chemicals like oils, and wraps them in usually small bubbles to which lets water carry them away. [Heres a diagram showing this.](https://media.beckman.com/-/media/stock-images/resource-center/images/micelles_liposomes-2021-11.jpg).
They also really like to kinda build themselves like legos on a microscopic scale, the hydrophilic heads are attracted to each other and attracted to water, the hydrophobic tails are attracted to each other as well to a lesser degree, so they arrange themselves sideways, can curve a little to make these small shells, bubbles in other words.
These bubbles on a smaller scale work also on a larger scale, which makes the foam we know. Bubbles are a mix of this and some water that gets attracted to the heads and also helps pull the different soap molecules together.
This isn’t always desirable though, for example dishwashers don’t particularly like foam cause it interferes with the spraying water that really washes the food, they mix some soap into the dishwasher soap but its a special non foaming one (we can make special surfactants that can make these bubbles on a smaller scale but can’t on a larger scale).
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