An emulsion disperses tiny droplets of one liquid through another liquid that would normally separate from it. In the kitchen, that usually means fat suspended in water: mayonnaise, hollandaise, vinaigrette and butter sauces all use the same underlying problem.
Droplet size matters
Whisking, blending or shaking divides one phase into droplets. Smaller droplets separate more slowly and feel smoother on the tongue. Adding oil gradually to mayonnaise is not ceremony: it keeps the amount of newly dispersed fat within what the mixture can hold.
Emulsifiers stabilise the boundary
Egg yolk, mustard and some food proteins contain molecules that can interact with both water and fat. They help coat droplets and keep them apart. A temporary vinaigrette may rely mostly on agitation; a stable mayonnaise needs an emulsifier and the right proportions.
Why an emulsion breaks
Too much fat added too quickly, insufficient water, extreme heat or a large temperature difference can cause droplets to join into a separate layer. The exact repair depends on the sauce, but often begins with a fresh spoonful of its water-based phase and slow incorporation of the broken mixture.
Not every separation is failure
A simple oil-and-vinegar dressing is expected to separate and can be shaken again. Stability is a design choice: the recipe should tell you whether the emulsion must last for seconds, through dinner or on a shop shelf.