What is an interface?

An interface is the surface of contact between any two condensed phases. It is not sharp in the sense that it cannot be clearly defined where a particular phase ends and the next begins. And unlike a mathematical surface, it is a diffused entity (Fig 1.3). Higher the miscibility of the two phases, higher the diffusion between the two surfaces. In the interfacial zone, there is a  gradual change in density. An interface is in a sense a colloid because here we have a system in the range of or smaller.

Figure 1.3 Water-oil interface