When a surfactant is used as a solute all the surfactant molecules do not acquire the interface. There is always equilibrium between diffusion and thermodynamics. At the same time, it is also interesting to note that a small amount of surfactant is sufficient for the desired result because the effect does not depend on their bulk concentration but on the concentration at the interface.
Beyond a critical concentration known as critical micelle concentration (CMC), aggregate formation of the surfactants in the bulk phase called micelle formation starts because the interface becomes saturated.

Fig 6.2: Micelle formation

The modified interfacial tension is expressed as a function of interfacial concentration of the surfactant.

where is the interfacial concentration of surfactant molecule.

= (number of moles on interface)/ Area

Interfacial concentration of component is defined as the number of moles of i on the interface per unit area. There is a problem in defining like this as in reality there is no zero thickness interface. Instead there exists an interfacial zone, so we choose any arbitrary interface in the interfacial zone using which we define . Volume of this surface is assumed to be zero. Model of such an interfacial zone is shown below.