Emulsifiers are molecules with a polar end (therefore attracted to polar molecules like water) and a nonpolar end (attracted to hydrocarbons or molecules largely made of hydrocarbons, like fats). Add an emulsifier to a fat-water mixture and the non-polar end - a long hydrocarbon chain - dissolves in the fat. The polar ends are attracted to the water, so the fat droplets which have absorbed the emulsifier then easily disperse in the water.
Examples of emulsifiers are sodium and potassium salts of long-chain carboxylic acids such as C15H31CO2Na. These are SOAPS. Others include long-chain alkyl sulfates such as C16H33OSO3Na, found in many detergents.
Electrophoresis is the separation of molecules in an electric field by their degree of charge and their mobility (dependent on size, to some extent). Look it up on the Net. Often used to separate large biomolecules like proteins or DNA.