|MadSci Network: Physics|
While there is some physics involved in the agitation of the clothes and cleaning agent solution, I will focus on the chemistry of the cleaning process.
All soaps and detergents (so-called surfactants) have chemical structures which contain polar and nonpolar parts. The nonpolar parts interact with hydrophobic ("water-fearing")materials such as most of the dirt (oil, grease etc.)that we encounter. These materials get stuck in the fabric and they shed plain water that they would encounter.
The polar parts of the structure interact very well with water; they are hydrophilic ("water-loving"). When the surfactant molecules dissolve in water, they form micelles, spherical aggregates of the surfactant molecules or ions. These aggregates are large enough that the solution exhibits the Tyndal Effect, the path of a beam of light can be seen through the solution.
In the micelles, the nonpolar (hydrophobic) parts of the surfactant ions or molecules are near the center of the micelle, and the polar (hydrophilic) parts are on the outside providing a coating that is "friendly" to water. When these micelles encounter through mixing(agitation)some of the hydrophobic dirt, they can open up and capture within the interior some of the dirt.
This "captured" dirt (hydrophobic) is "happy" in the hydrophobic interior and stays there suspended in the water until it is rinsed away.
I like to think of surfactants as having a "split personality".
If some of this is not clear, let me know (firstname.lastname@example.org) and I will try to explain further.
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