Please explain how detergents clean dirty clothes?

How do detergents clean dirty clothes

Consider a wire frame (see the adjacent figure) equipped with a sliding wire AB. It is dipped in a soapy water. A film of liquid is formed on it. A force F has to be applied to hold the wire in place. Since the soap film has two surfaces attached to the wire, the total length of the film in contact with the wire is 2L.

T (surface tension) = .F/2L

Surface tension of a liquid is measured by the normal force acting per unit length. On either side of an imaginary line drawn on the free surface of a liquid, the direction of this force is perpendicular to the line and tangential to the free surface of liquid.

            T = F/L.